Abstract:
Data files with digital envelops may be used for many new applications for cloud computing. The new applications include games and entertainments such as digital fortune cookies, and treasure hunting, unique techniques for digital right management, or even additional privacy and survivability on data storage and transport on cloud computing. Wavefront multiplexing/demultiplexing process (WF muxing/demuxing) embodying an architecture that utilizes multi-dimensional waveforms has found applications in data storage and transport on cloud. Multiple data sets are preprocessed by WF muxing before stored/transported. WF muxed data is aggregated data from multiple data sets that have been “customized processed” and disassembled into any scalable number of sets of processed data, with each set being stored on a storage site. The original data is reassembled via WF demuxing after retrieving a lesser but scalable number of WF muxed data sets. A customized set of WF muxing on multiple digital files as inputs including at least a data message file and a selected digital envelop file, is configured to guarantee at least one of the multiple outputs comprising a weighted sum of all inputs with an appearance to human natural sensors substantially identical to the appearance of the selected digital envelop in a same image, video or audio format. Enveloping processing is a subset of WF muxing processing. The output file is the file with enveloped or embedded messages. The embedded message may be reconstituted by a corresponding WF demuxing processor at destination with the known a priori information of the original digital envelope. In short, digital enveloping/de-enveloping can be implemented via WF muxing and demuxing formulations. WF muxed data featured enhanced privacy and redundancy in data transport and storage on cloud. On the other hand, data enveloping is an application in an opposite direction for conventional WF muxing applications as far as redundancy is concerned. Enveloped data are intended only for limited receivers who has access to associated digital envelope data files with enhanced privacy for no or minimized redundancy.

Description:
RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. provisional application Ser. No. 62/038,767, entitled “Enveloping and De-enveloping for Cloud Computing via WF Muxing,” filed Aug. 18, 2014. This application is also related to a non-provisional application Ser. No. 12/848,953, filed on Aug. 2, 2012, a non-provisional application Ser. No. 13/938,268, filed on Jul. 10, 2013, and a non-provisional application Ser. No. 13/953,715, filed on Jul. 29, 2013, all of which are incorporated herein by reference in their entireties. 
     
    
     BACKGROUND OF THE DISCLOSURE 
     Field of the Disclosure 
       [0002]    The disclosure relates to methods and architectures of packing or enveloping data for cloud storage and transport using Wavefront multiplexing (WF muxing). It is focused to appearance of data package/envelop and reliability of enclosed data. 
         [0003]    According mailonline (http://www.dailymail.co.uk) on Aug. 31, 2014, naked images of high-profile actors, models, singers and presenters have been leaked online in an apparent hacking leak linked to the Apple iCloud service. The photos appeared after a user on 4chan, an image sharing forum, posted private pictures of 101 celebrities including Jennifer Lawrence, Ariana Grande, Victoria Justice and Kate Upton. The images, which were posted on Sunday night, were reportedly accessed due to au iCloud leak_that enabled celebrities&#39; phones to be hacked. Apple has declined to comment. Privacy of the celebrities were terribly violated. 
         [0004]    There are needs for better privacy protection on cloud. Enveloping techniques will enhance privacy protection on cloud. 
         [0005]    WF muxing techniques have been presented extensively in the above mentioned US patent application Ser. Nos. 12/848,953, 13/938,268, 13/953,715. The WF muxing techniques will use less memory space to achieve better redundancy, reliability, and survivability as compared to conventional techniques. In addition, these techniques enable capabilities of monitoring integrity of stored data sets without scrutinizing the stored data sets themselves. The same techniques can be extended to data streaming via cloud. 
         [0006]    There are two more concerns. Many operators offer secured and encrypted storage services. However, secured files are only encrypted on the server side and therefore a client has to rely on honesty of the server operator. The second is concerns about the right of stored data; which are under debate. 
         [0007]    This invention application addresses enhanced privacy, and reliability of data transports and stored data on cloud. Many of the data may even be image or audio related. Since multiple data sets to be transported or stored will be preprocessed on client sides, each of the transported or stored data on cloud is a multiplexed (muxed) data set individually which is unintelligible by itself. Therefore, the proposed approaches shall remove the concerns on professional integrity confidence of operators, and those on the right of stored data. Known images, audio tracks, or multimedia streams may all be used as digital “envelopes” for cloud data storage and transport. Most applications are aiming for games and entertainments in cloud communications. It may be applied as tools for various digital right management on copy right, protecting IP holders. Authentications with known “chokes or stamps” via these techniques for multilayer enveloping will be one highlight of this patent application. 
         [0008]    Digital images will be used to exemplify the digital enveloping/de-enveloping techniques in this patent application. Other types of digital streams may be easily incorporated for the proposed enveloping techniques. 
         [0009]    Embodiments of “writing” and “reading” processes will be summarized and presented concisely. “Writing” features a process on multiple original images concurrently via WF muxing transformations, generating WF muxed data to be stored on cloud. A “reading” process corresponds to a WF demuxing transformation on WF muxed data stored on cloud, reconstituting original data sets. The enveloping is a subset of “writing” procedures under constraints that enveloped messages, or products of the writing procedures, shall preserve some desired features in digital appearance, and the de-enveloping is a subset of reading procedures to reconstitute embedded mails from the enveloped messages. 
         [0010]    Enveloping processing is a subset of WF muxing processing. A customized set of WF muxing on multiple digital files as inputs including at least a data message file and a selected digital envelop file, is configured to guarantee at least one of the multiple outputs comprising a weighted sum of all inputs with an appearance substantially identical to the appearance of the selected digital envelop in a same image, video or audio format, as far as to human natural sensors are concerned. The output file is the file with enveloped or embedded messages. The embedded message may be reconstituted by a corresponding WF demuxing processor at destination with the known a priori information of the original digital envelope. 
         [0011]    In short, digital enveloping/de-enveloping can be implemented via WF muxing and demuxing formulations. WF muxed data featured enhanced privacy and redundancy in data transport and storage on cloud. On the other hand, data enveloping is an application in an opposite direction for most of the WF muxing applications as far as redundancy is concerned. Enveloped data are intended only for limited receivers who has access to associated digital envelope data files with enhanced privacy for no or minimized redundancy. 
       SUMMARY OF THE DISCLOSURE 
       [0012]    Wavefront multiplexing/demultiplexing (WF muxing/demuxing) process features an algorithm invented by Spatial Digital Systems (SDS) for satellite communications where transmissions demand a high degree of power combining, security, reliability, and optimization. WF muxing/demuxing, embodying an architecture that utilizes multi-dimensional transmissions, has found applications in fields beyond the satellite communication domain. One such application is data transport/storage on cloud where privacy, data integrity, and redundancy are important. Enveloping and de-enveloping on digital data may be used for both data transport and data storage. They may be used for gifts and games such as digital fortune cookies. We will use data transport, such as delivering mails, to exemplify the concept of enveloping and de-enveloping digital data. 
         [0013]    This invention is about to send not all but a portion of WF muxed data strings through cloud to destinations. An enveloped data streams are WF muxed with a known data files as an envelope which may be a sender&#39;s personal picture indicating who is sending the enveloped (embedded) data string. Different envelops may feature various pictures of sender&#39;s indicating sender&#39;s mood while sending the enveloped data. The digital envelopes may be an old digital video clip for delivering new digital data streams for communications among family members only. All family members shall have access to the original old video clip. 
         [0014]    WF muxing/demuxing for enveloping are configured to use additional known digital data streams for probing, authentications and identifications. A method for enveloping and then storing data in IP cloud comprises: transforming multiple first data sets into multiple enveloped second data sets at a transmitting side, wherein one of said enveloped second data sets comprises a weighted sum of said first data sets; storing said enveloped second data sets in an IP cloud via an internet; and storing multiple links linking to said enveloped second data sets at said transmitting side. 
         [0015]    A data processing method comprises: transforming multiple first data sets and a known data set into multiple enveloped second data sets at a transmitting side, wherein one of said enveloped second data sets comprises a weighted sum of said first data sets; and recovering a third data sets from some of said enveloped second data sets and said known data set at a receiving side, wherein one of said third data sets comprises a weighted sum of said some of said enveloped second data sets. 
         [0016]    A method for storing data in IP cloud, comprises: transforming multiple first data sets into multiple enveloped second data sets at a transmitting side, wherein one of said enveloped second data sets comprises a weighted sum of said first data sets and carries an image with intensities mainly controlled by one of said first data sets. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]    The drawings disclose illustrative embodiments of the present disclosure. They do not set forth all embodiments. Other embodiments may be used in addition or instead. Details that may be apparent or unnecessary may be omitted to save space or for more effective illustration. Conversely, some embodiments may be practiced without all of the details that are disclosed. When the same reference number or reference indicator appears in different drawings, it may refer to the same or like components or steps. 
           [0018]    Aspects of the disclosure may be more fully understood from the following description when read together with the accompanying drawings, which are to be regarded as illustrative in nature, and not as limiting. The drawings are not necessarily to scale, emphasis instead being placed on the principles of the disclosure. 
           [0019]      FIG. 1  depicts a block diagram on “sealing” a digital envelope for an embedded digital file via a 2-to-2 WF muxing processor by a sender at a source, sending only one of the two outputs as the digitally enveloped data to a destination via cloud, and opening the digital envelop and recovering the embedded data in accordance to some embodiments of this invention. The digital envelope is chosen by the sender from one of the known candidate digital envelopes to both the sender at the source and the receiver at the destination. The sealing and opening process for an envelope are also referred as enveloping and de-enveloping, respectively. 
           [0020]      FIG. 1A  depicts a set of 6 candidate digital envelopes according to embodiments of this invention. 
           [0021]      FIG. 1B  depicts another set of 5 candidate digital envelopes according to embodiments of this invention. 
           [0022]      FIG. 2  depicts a replicates of the  FIG. 5D  in U.S. patent application Ser. No. 13/953,715; published with a PA publication No. US 2014-0081989 A1; demonstrating computer simulated results of Camouflaging. The four images are inputs to a 4-to-4 WF muxing processor. The running horse was chosen as the digital camouflaging image. Effectively, the four images on the second rows are enveloped data sets, according to some embodiments of this invention. 
           [0023]      FIG. 3  depicts a block diagram on enveloping/de-enveloping via a 2-to-2 Wavefront muxing techniques when a receiver in a destination does not have access to original digital envelope according to some embodiments of this invention. It is similar to the one in  FIG. 1 . The senders send both outputs to a receiver for recovering the original digital envelop and embedded information data via a WF demuxing processor as a post processor. 
           [0024]      FIG. 4  illustrates a block diagram of double enveloping in accordance to some embodiments of this invention. 
           [0025]      FIG. 5  illustrates block diagram of double de-enveloping in accordance to some embodiments of this invention. 
           [0026]      FIG. 6  illustrates a block diagram of enveloping via higher order WF muxing for one enveloped digital stream carrying embedded information data in accordance to some embodiments of this invention. 
           [0027]      FIG. 7  illustrates a block diagram of de-enveloping via higher order WF de-muxing from one enveloped digital stream carrying embedded information data in accordance to some embodiments of this invention. 
           [0028]      FIG. 8  illustrates a block diagram of enveloping via higher order WF muxing for two enveloped streams carrying embedded information data in accordance to some embodiments of this invention. 
           [0029]      FIG. 9  illustrates a block diagram of de-enveloping via higher order WF de-muxing from two enveloped digital streams in accordance to some embodiments of this invention. 
           [0030]      FIG. 10  illustrates a block diagram of enveloping via a 4-to-4 WF muxing for sending three of the 4 available enveloped streams carrying embedded information data via cloud in accordance to some embodiments of this invention. 
           [0031]      FIG. 11  illustrates a block diagram of de-enveloping via a 4-to-4 WF de-muxing from any two of three enveloped digital streams on cloud in accordance to some embodiments of this invention. 
           [0032]      FIG. 12  illustrates another block diagram of de-enveloping via a 4-to-4 WF de-muxing from any two of three enveloped digital streams on cloud in accordance to some embodiments of this invention. 
           [0033]      FIG. 13  illustrates a block diagram of de-enveloping via a 4-to-4 WF de-muxing from all three enveloped digital streams on cloud in accordance to some embodiments of this invention. 
           [0034]      FIG. 14  illustrates another block diagram of de-enveloping via a 4-to-4 WF de-muxing from all three enveloped digital streams on cloud in accordance to some embodiments of this invention. 
           [0035]      FIG. 15  illustrates a block diagram of double enveloping via a 4-to-4 WF muxing and a 2-to-2 WF muxing to form one enveloped digital streams on cloud in accordance to some embodiments of this invention. 
           [0036]      FIG. 16  illustrates a block diagram of double de-enveloping via a 2-to-2 WF de-muxing and a 4-to-4 WF demuxing from one enveloped digital streams on cloud in accordance to some embodiments of this invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0037]    The present invention relates to distributed transport paths or storage with built-in redundancy via an M-to-M wavefront multiplexing (WF muxing) techniques; where M≧2 and must be an integer. The M inputs to the WF muxing comprising N streams of information data with additional M-N known data files; where N≧1 and is an integer. The M independent input data streams are transformed and concurrently converted into WF muxed domain with M output wavefront components (wfcs). Only M′ of the M outputs will be used for data transport and/or data storage on cloud, where M-N≦M′≦M; where M′ is an integer. 
         [0038]    Furthermore, any one of the known data files may be chosen to serve as a digital transporting envelop and will be processed accordingly in an enveloping process as a part of the M-to-M WF muxing. 
         [0039]    Multiple inputs to an M-to-M WF muxing processor are properly “emphasized” or “weighted” so that at least one of the M outputs will be selected to be a “carrier” for transporting embedded message. A selected “carrier”, an enveloped data file, shall appear substantially identical to the appearance of the selected digital envelop to human sensors. The identical appearance comprises unique and easily distinguishable features from other digital data files. These features may be visual pictures, videos, audio music, word files, or multimedia files 
         [0040]    At least one of the enveloped data streams will be sent to a destination via cloud. An enveloped data stream may appear as a digital picture, a video clip, a music clip, an audio recording, or a digital cartoon while being transported or stored on cloud. Just as functions of regular envelops, these digital envelops may convey context and authors of the embedded mail, a preview of intentions and moods of the author, and or information of where the embedded mail coming from. 
         [0041]    The digital envelop and the enveloped digital data stream shall have substantially identical features which are identifiable and distinguishable by human sensors; hearing, visually or both. 
         [0042]    At destination, a desired receiver shall reconstitute the embedded information data by a post processing such as wavefront demultiplexing (WF demuxing) with the help of accessing the known file of the original digital envelop. 
         [0043]    The present invention discloses operation concepts, methods and implementations of enveloping/de-enveloping via wavefront multiplexing for cloud transport as depicted in  FIG. 1 . Similar techniques can be applied to video streaming, secured data storage services, secured file transfers, and other applications via Internet Clouds. The embodiments of present inventions comprise three important segments including (1) the pre-processing for enclosing a mail in a selected envelope, i.e. the above WF muxing, at a user end; (2) transporting embedded mails via enveloped digital streams on cloud, and (3) a post-processing of retrieval or de-enveloping, i.e. the above WF demuxing, at the user end. We will use a single user for both pre-processing and a post-processing as an example for illustrating the operation concepts. 
         [0044]    In principle, the pre-processing and the post-processing are all performed in user segments and performed in equipment at the user end. For cloud storage, these enveloping/de-enveloping may also be performed in storage facilities of an operator. The operator will aggregate the data storage sets in cloud distributed over remote networks. 
       Embodiment 1 
       [0045]      FIG. 1  depicts an operation concept of communications between a sender at a source and a receiver at a destination. The sender takes advantages of a 2-to-2 WF muxing processor  130  for sealing or enveloping a set of input data S(t) by a selected digital envelope E5(t). The input data is an English phrase “Open Sesame” and its Chinese translation in a word format written in 4 Chinese characters and associated pronunciation symbols. The chosen digital envelope is a digital picture of a famous painting of “a running horse” by a Chinese painter, Xu Beihong, in early 1900&#39;s. There are 11 digital envelopes  180  commonly known to a user community which both the sender and the receiver belong to. There are two outputs from the WF muxer  130 ; one is for the enveloped mail Es(t), and the other is grounded. The Es(t) is a result of pixel-by-pixel processing from the two inputs data files; S(t) and E5(t). The WF muxing features a 2*2 Hadamard transform. S(t) and E5(t) will be “scaled” properly to enable Es(t) appearance substantially identical to that in E5(t); as discussed extensively in the US patent application publication no. 2014/0081989A1. In this case, the running horse in Es(t) appears to be a flipped image of the same house in E5(t). 
         [0046]    After the WF muxing, Es(t) is an enveloped data stream, and is the only file to be sent to a destination via IP networks 010. Es(t) features with a visual appearance nearly identical to the picture of the famous running horse in E5(t). At the destination, a receive can reconstitute the embedded message of “Open Sesame” written in Chinese via a 2*2 WF demuxer  140  or an equivalent post processor; only when the digital picture of the original envelop is available to the receiver. There are three segments including (1) a pre-processing  130 , (2) IP propagation Channel 010, and (3) post processing  140  at downstream of the cloud. 
         [0047]    Pre-Storage Processing  130 : 
         [0048]    In the pre-processing for mail enveloping, an 2-to-2 WF muxer  130  is used to convert 1 set of input mail data S(t) and a selected digital envelop string E5(t) to two output data strings, i.e. Es(t), and Ed(t), where: 
         [0000]        Es ( t )= S ( t )+ am*E 5( t )  (1-1)
 
         [0000]        Ed ( t )=− S ( t )+ am*E 5( t ),  (1-2)
       Where am&gt;&gt;1 is a magnification factor, and image dependent, usually set between 5 and 30.       
 
         [0050]    A 2-to-2 Hadamard matrix (HM), in which all elements are “1” or “−1” only, is chosen for the 8-to-8 WF muxing. Equations (1-1) to (1-2) can be written in a matrix form as 
         [0000]    
       
         
           
             
               
                 
                   O 
                   = 
                   
                     HM 
                     * 
                     I 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     Where 
                      
                     
                       : 
                     
                      
                     
                         
                     
                      
                     O 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             1 
                           
                           , 
                           
                             O 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ] 
                       
                       T 
                     
                     = 
                     
                       
                         [ 
                         
                           
                             Es 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           , 
                           
                             Ed 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                         ] 
                       
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   HM 
                   = 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           1 
                         
                       
                       
                         
                           
                             - 
                             1 
                           
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   I 
                   = 
                   
                     
                       
                         [ 
                         
                           
                             I 
                              
                             
                                 
                             
                              
                             1 
                           
                           , 
                           
                             I 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ] 
                       
                       T 
                     
                     = 
                     
                       
                         [ 
                         
                           
                             S 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           , 
                           
                             am 
                             * 
                             E 
                              
                             
                                 
                             
                              
                             5 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                         ] 
                       
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
         [0051]    The input ports of a WF muxer are referred to as slices, and its output ports are wavefront components (wfc&#39;s). The two input data sets S1 and am*E5, are connected to the input ports, i.e. slice 1, and slice 2 of the WF muxer respectively. The 2 output data sets i.e. O1-O2, are connected to the output ports, i.e. wfc1-wfc2, of the WF muxer  130  respectively. 
         [0052]    In general a 2-to-2 WF muxing processor features 2 orthogonal wavefront vectors or WFV&#39;s. Let us define a coefficient wjk of a WF transformation to be the coefficient at the j th  row and k th  column of the WF muxer  130 . A WF vector of the WF muxer  130  featuring a distribution among the 2 outputs, i.e. O1-O2 at the 2 WF component ports wfc1-wfc2, is defined as a 2-dimensional vector. They are mutually orthogonal. The two WFVs of the WF muxer  101  are: 
         [0000]        WFV 1 =[w 11 ,w 21] T =[1,−1] T   (3.1)
 
         [0000]        WFV 2 =[w 12 ,w 22] T =[1,1] T   (3.2)
 
         [0053]    S(t), and E5(t) are “attached” to the 2 WF vectors by respectively connected to the two input ports of the WF muxing device  130 . All components of the 2 orthogonal WFVs are related to input and output port numbers or (spatial) sequences, but are independent from the input and output data sets. 
         [0054]    The arithmetic operations of “linear combinations” may operate on blocks of data after all inputs are aligned as digital streams sample-after-sample for various inputs. A “byte” of data may be “selected” as a sample and a block of X samples, i.e. 7 samples or 7 bytes, of a digital data stream will be treated as a numerical number for calculations in WF muxing transformations. Two streams of 7 samples or bytes may be the respective inputs of the 2-to-2 WF muxer. A block size of X+1 samples, i.e. 8 samples or 8 bytes in this case, will be reserved for the results of arithmetic operations on a number of the digital streams to avoid issues of overflows and underflows at the two outputs of the WF muxing transformations. There shall be 12.5% in data size overhead of the 7 byte arithmetic operations, with respect to the results in 8 byte forms in the outputs. In different embodiments, we may choose blocks with a block length of 99 bytes for arithmetic operation, i.e. X=99, reducing the operation overhead to 1%. 
         [0055]    There are other choices in selecting data blocks for arithmetic operations of linear combinations or weighted sums in the WF muxing transformations. For imaging processing, a pixel by pixel as operation blocks may be more important preserving unique features for some applications, or a row or a column of pixels as a data block for efficient usage of storages. 
         [0056]    In this example, only one of the two outputs will be delivered to a destination. The intended receiver must have “additional information” in order to reconstitute the embedded message or mail; “Open Sesame” and its Chinese translation in a word format written in 4 Chinese Characters. The additional information is the original file of the selected digital envelop. If both outputs were delivered to the receiver, both the embedded mail and the selected original digital envelop could all be reconstituted independently at the destination without any additional a priori known information. 
         [0057]    In general at least one of WF muxed output streams from higher order muxing or multilayer enveloping will be sent to the destination  140  via IP cloud 010. The embedded mail is in the enveloped digital data stream. The higher order muxing is usually referred to an N-to-N WF muxing with N in between 4 and 5000. The numbers of WF muxed streams to be sent to a destination shall be always smaller than a critical numbers of muxed data streams; Ncr. There are not enough information in the Ncr independent muxed data streams to reconstitute the embedded information without any additional information known a priori. 
         [0058]    Cloud 010: 
         [0059]    Only one WF muxed file is sent from a source to a destination via the cloud 010. The original digital envelope file is known a priori to both the sender at a source and receiver at the destination. Therefore the required channel bandwidth for Es(t) is about the same as that of the embedded message, S(t). The differentials in required bandwidths between that for Es(t) and that for S(t) are due to processing overhead. 
         [0060]    Post Processing  140 : 
         [0061]    The post processing  140  for data retrieval comprises a WF demuxing processor, converting the received WF muxed data into an output of embedded data file. The original digital envelope file, E5(t), is also used as one of the inputs to the WF demuxing in the post processing. The received WF muxed data is substantially equivalent to the corresponding output data set, Es(t), of the WF muxing device in the preprocessing  130 , if not contaminated, and is therefore represented by Es(t) or Es&#39;(t). Similarly, the recovered embedded data file is substantially equivalent to the input data sets, S(t), and is therefore referred to as S(t) or S′(t). 
         [0062]    According to equation (1-1); the recovered embedded data can be derived from the received WF muxed data Es(t) and the digital envelope E5(t); 
         [0000]        S ( t )= Es ( t )− am*E 5( t )  (4)
 
         [0000]    Where am can be experimentally optimized or through a priori knowledge set. Therefore, the missing second output of the WF muxing can also be re-constructed in the destination according to Equation (1-2) and Equation (4) 
         [0000]        Ed ( t )=− Es ( t )+2 *am*E 5( t ),  (5)
 
         [0063]    A 2-to-2 Hadamard matrix with scaling factor of ½ may be chosen as the 2-to-2 WF demuxer. The matrix elements of 2-to-2 Hadamard matrix feature “1” or “−1” only. The relationship may be written in a matrix form as 
         [0000]        SM=HM*D   (6)
 
         [0064]    Where: 
         [0000]        D=[D 1 ,D 2 ]=[Es ( t ), Ed ( t )] T   (6-1)
 
         [0000]        SM=[S ( t ), amE 5( t )] T   (6-2)
       HM is a 2-to-2 Hadamard matrix in equation (2-2).       
 
         [0066]    The input ports of a WF demuxer in the post processor  140  are referred to as wavefront components (wfcs), i.e. wfc1, and wfc2, and its output ports are slices, i.e. slice1, and slice2. In this example, the 2 input data sets, i.e. Es(t) and Ed(t), are connected to its input ports wfc1-wfc2 of the WF demuxer  140 , respectively. The retrieved data set, S1, is from its first output ports. Normally the second output of the demuxing device  140  will be “grounded” for this application. 
         [0067]    As an option, the respective second output from the WF demuxing device  140  may be used to reconstitute a copy of the original digital envelop which will be compared to the known digital envelope file for the integrity of received data. It is a good indication that the received embedded data has been compromised only if a set of comparison results showing the two digital envelopes are different digital files. 
         [0068]      FIG. 1A  and  FIG. 1B  depict candidates for 6 and 5 digital envelopes, respectively. E5(t) is chosen for the example in  FIG. 1 . Ell in  FIG. 1B  is a category of common known digital files between a sender and a receiver for private communications between them. 
         [0069]      FIG. 2  is a replica of  FIG. 5D  in the U.S. patent application Ser. No. 13/953,715 with a publication No. 20140081989. It illustrates an example of WF muxing/demuxing as pre-processing and post processing for a data storage application on cloud, presenting image storage/retrievals via 4-to-4 wavefront muxing on distributed cloud storages. The WF muxing/demuxing may be via orthogonal matrixes or non-orthogonal matrixes, as long as their inverse matrixes exist. It depicts the original inputs in the first row  521 , stored images or images to-be-transported in wavefront muxed formats in the second row  522 , and reconstituted and recovered images at a destination in the third row  523 . The four pictures on the top row  521  are four input images; 3 photos token recently at Bronx Zoo in city of New York, and the 4 th  one is an image of a classic painting, “a running horse”, by a famous Chinese painter Mr. Xu. Beihong in 1930&#39;s. The first, the second and the third photos depict, respectively, a picture of an “Eagle” indicated as A1.png, a picture of a “Tiger” indicated as A2.png, and a picture of a “white head animal” indicated as A3.png. The “horse” is depicted as A4.png. They are all in PNG formats. 
         [0070]    Let us assume a 4-to-4 Hadamard transform as WF muxing matrix. 
         [0071]    The 4 WF muxed files Ov, Ox, Oy and Oz are in the second row  522 . To create various camouflaged effects on the WE muxed data for storage; the original images have been “heavily weighted” for the “horse” painting. In order to assure that the A1 image of the Chinese horse painting to be more dominant features in the 4 multiplexed outputs as camouflaged, we have emphasized the pixel intensities of A1 via: 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               am 
                               * 
                               A 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               4 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0072]    Where am&gt;1. Usually am is set to be greater than 10. It is also assumed the dimensions of pixel lattices among the 4 input images have been fully equalized. Depending on the selection of a camouflaging image, the emphasizing factor, am, may applied to any of the input images in ∥A∥. Furthermore, equation (7) may also be written equivalently as: 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               + 
                               am 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               am 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               am 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               am 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               4 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     
                       - 
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
         [0073]    As a result, the image of “horse” painted by Xu Baihong becomes dominant among the 4 participating images and appears on all 4 WF muxed data, i.e. Ov, Ox, Oy and Oz, with appearances of various intensity settings. 
         [0074]    Additional processing is required before the WF muxing to “flip, rotate, zone-in or zone-out” images or appearances on the WF muxed files with respect to the appearance of the digital envelope. 
         [0075]    Each of the WF muxed data sets Ov, Ox, Oy and Oz features a size about 2 to 3 times larger than those of the original images A1-A4 or recovered images Sv, Sx, Sy and Sz to avoid overflow and underflow in the simulations. 
         [0076]    The images on the third row are restructured images via a reading process. A “reading” processing also features two steps. The first step involves retrieving all 4 WF muxed files individually from cloud. The second step involves via a wavefront demultiplexing transformation, converting the 4 WF muxed files, i.e. Ov, Ox, Oy and Oz, in ∥O∥ into four recovered or reconstituted equalized files Sv, Sx, Sy and Sz in ∥S∥ substantially equivalent to the four equalized pictures A1-A4 respectively if the WF muxed files, i.e. Ov, Ox, Oy and Oz, are not contaminated. The four recovered or reconstituted equalized image files may then be converted via a de-equalizing process into four recovered or reconstituted image files Sv, Sx, Sy and Sz substantially equivalent to the four original pictures A1-A4 respectively. 
         [0077]    Assuming all four files Ov, Ox, Oy and Oz are available, the WF demuxing transformation (WF demuxing) shall follow: 
         [0000]      ∥ S∥=∥WDmx∥∥O∥.   (8)
 
         [0000]      Where, ∥ WDmx∥∥WMux∥=∥I∥.   (8-1)
 
         [0078]    More explicitly, “intensities” of individual pixels, in the lattice of the same row and column, of the 4 reconstituted images in Sv, Sx, Sy and Sz in ∥S∥ are 4 respective linear combinations, each of which is a linear combination of intensities of individual pixels, in the lattice of the same row and column, of the four WF muxed files, i.e. Ov, Ox, Oy and Oz, in ∥O∥, multiplied by four respective weighting parameters in ∥WDmx∥. For example, “intensities” of individual pixels, in the lattice of the 41 th  row and 51 th  column, of the 4 reconstituted or recovered images in Sv, Sx, Sy and Sz in ∥S∥ are 4 respective linear combinations of intensities of each individual pixels, in the lattice of the 41 th  row and 51 th  column, of the four WF muxed files, i.e. Ov, Ox, Oy and Oz, in ∥O∥, multiplied by four respective weighting parameters in ∥WDmx∥. 
         [0079]    For applications of enveloping, only one of the 4 WF muxed files is sent to a destination from a sender at a source via cloud instead of sending all 4 WF muxed files to cloud. As an example. A1 is the information data to be delivered to a destination via cloud and A4 is a selected digital envelope file. A2, A3 and A4 are known a priori to both the sender and a desired receiver at the destination. 
         [0080]    Any one of the 4 files on the second row  522  can be used to convey the embedded message A1 via cloud. Let us select Ov as the enveloped data file to be transported to destinations. It is clear that the image on enveloped data file, Ov, is a running horse which is substantially identical to the running horse image on the enveloping file, A4. The enveloped file, Oy, comprising information of the embedded message, A1, is the one to be sent to destinations via cloud. 
         [0081]    We will not repeat all mathematical details on the Figure here. In short, we utilize the same mathematical manipulations for “enveloping” digital messages or embedding mails for cloud transport as those in “camouflaging” pictures in the above mentioned patent application. We want to show two important features of WF muxing/demuxing in the enveloping/de-enveloping applications. For an enveloping processing by a selected digital envelope (A4);
       1) selected message (A1) are embedded in a selected enveloped data set (Ov),   2) To human sensors, the original digital envelope (A4) and the enveloped data set (Ov) shall appear substantially identical, and distinguishable from other digital data sets (A2, A3 and A1) clearly.   3) A2 and A3 may serve for purpose of authentication or identifications       
 
         [0085]    In another scenario, where A1 is the data set to be sent to a destination via cloud, A2 and A3 for authentication, and A4 as a selected digital envelope, Ov and Oz are sent to cloud. At the destination, a first reader has all three digital data file A2, A3, and A4, and only needs to access 1 of the 2 enveloped data files on cloud; Ov or Oz to recover the embedded images, Sv. It is important to notice that there is redundancy in wavefront multiplexed images as far as the first reader is concerned. On the other hand, a second reader does not have the digital “horse” A4 but has original digital files for both A2 and A3 and he must download both of two enveloped data files Ov and Oz sent via cloud in order to recover a the embedded image, A1. It is also important to notice that the second reader has the capability to capture the file of the digital envelope A4 for later usage. 
         [0086]    For a third scenario, where A1, A2, and A3 are the data sets to be sent to a destination via cloud, and A4 as a selected digital envelope, Ov, Ox, and Oz are sent to cloud. At the destination, a first reader has only has a digital data file A4, and needs to access all 3 enveloped data files on cloud; Ov, Ox, and Oz to recover the embedded images, Sv. It is important to notice that there is no redundancy in wavefront multiplexed images as far as the first reader is concerned. On the other hand, a second reader does not have the digital “horse” A4 and he may download all two enveloped data files Ov, Ox and Oz sent via cloud, but he will not be able to reconstitute the embedded image, A1. 
         [0087]    For a fourth scenario, where A1, A2, and A3 are the data sets to be sent to a destination via cloud, and A4 as a selected digital envelope, Ov, Ox, Oy, and Oz are sent to cloud. At the destination, a first reader has only has a digital data file A4, and needs to access any 3 of the 4 enveloped data files on cloud; Ov, Ox, Oy, and Oz to recover the embedded images, Sv. It is important to notice that there is redundancy in wavefront multiplexed images as far as the first reader is concerned. On the other hand, a second reader does not have the digital “horse” A4 and he must download all four enveloped data files Ov, Ox Oy, and Oz sent via cloud, in order to reconstitute the embedded image, A1. There is no redundancy in wavefront multiplexed images as far as the second reader is concerned. 
       Embodiment 2 
       [0088]      FIG. 3  depicts an operation concept of using the above WF multiplexing techniques for 2 enveloped messages. There are three segments: (1) a pre-processing or enveloping  130 , (2) transported via cloud 010, and (3) post processing or de-enveloping  140 . It is nearly identical to the one shown in  FIG. 1 .  FIG. 3  features a technique to send a digital data set and an original envelope to a desired receiver. Both outputs of the pre-processor  130 , Es(t) and Ed(t) are sent to the receiver. 
         [0089]    A message are embedded in the 2 enveloped data file Es(t) and Ed(t) are sent from a sender at a source to a receiver at a destination. The receiver utilizes both enveloped data sets to recover the embedded message and the original digital envelop which may be used for subsequent transmissions between the sender and the receiver. Once the digital envelop data becomes known to both sides of a cloud based communication channel, only one of the two WF muxed files either ES(t) or Ed(t) will be sent to cloud. 
         [0090]      FIG. 3  features a technique to send a digital data set and an original digital envelope data set to a desired receiver. Both outputs of the pre-processor  130 , Es(t) and Ed(t) are sent to the receiver for reconstituting both the embedded data, and the original digital data of the digital envelope. 
       Embodiment 3 
       [0091]      FIG. 4  depicts a transmitting (Tx) operation concept of double enveloping using 2-to-2 WF multiplexing for enveloping a message data set via two envelopes sequentially. It depicts first two of the three segments in  FIG. 1 : (1) a pre-processing or enveloping  130 , (2) transported via cloud 010, and (3) post processing or de-enveloping  140 . 
         [0092]    There are two enveloping processing in series in  FIG. 4 . Each one is identical to the enveloping shown in  FIG. 1 . In the first pre-processing  130 - 1 , there are two inputs; S(t) and E1(t), and one output x(t). The second output is grounded. S(t) comprises of a phrase of “Open Sesame” and its Chinese translation, and is the message to be delivered to destinations via cloud. E1(t) is a selected inner envelope and is one of the candidate envelopes  180 . The first output x(t) features an appearance substantially identical to human sensors as that in E1(t). The second output is grounded. 
         [0093]    In the second preprocessing  130 - 2 , there are also two inputs, x(t) and E5(t), and only one output Es(t). E5(t) is a selected outer envelope and is also one of the candidate envelopes  180 . The first output Es(t) features an appearance substantially identical to human sensors as that in E5(t). 
         [0094]    There is no appearance of a phrase of “Open Sesame” and its Chinese translation in Es(t). The required bandwidth for transporting the Es(t) shall be near identical to that of sending S(t) via cloud when the enveloping files, E1(t) or E5(t) are properly chosen. 
         [0095]    In other embodiments, images in the enveloping files may have been processed for various purposes such as minimized dynamic range of individual pixels or simply for enhanced authentication and identifications before WF muxing. Many can be pre-stored in the envelop candidate files as optional candidates. Certainly, these additional processing can be included as a part of the pre-processing  130  in  FIG. 1 . It may also be implemented for double enveloping in either  130 - 1  or  130 - 2  blocks or both in  FIG. 4 . 
         [0096]      FIG. 5  depicts a receiving (Rx) operation concept of de-enveloping doubly enveloped messages using 2-to-2 WF demultiplexing techniques for de-enveloping a message data set via two envelopes sequentially. It depict the last two of the three segments in  FIG. 1 ; (1) a pre-processing or enveloping  140 , (2) transported via cloud 010, and (3) post processing or de-enveloping  140 . 
         [0097]    There are two de-enveloping processing in series. Each one is identical to the de-enveloping shown in  FIG. 1 . In the first post-processing  140 - 1  to open the outer envelope, there are two inputs; Es(t) and E5(t), and one output x(t). The second output is grounded. Es(t) is the received digital data file with embedded message for the receiver in the destination. E5(t) is a selected outer envelope and is one of the candidate envelopes in a candidate file  180  known priori to both the sender and the receiver. 
         [0098]    The first input Es(t) is a received data file in a desired receiver at a destination, and shall be substantially equivalent to the only output of the second pre-processing  130 - 2  in  FIG. 4 . In addition it shall feature an appearance substantially identical to human sensors as those in E5(t). Similarly, the first output x(t) of the first post processor  140 - 1  features an appearance substantially identical to human sensors as those in E1(t). The second output is grounded. In the second post-processing  140 - 2 , there are also two inputs, x(t) and E1(t), and only one output S(t). E1(t) is the selected inner envelope and is one of the candidate envelopes in the candidate file  180 . The first output is the recovered embedded message which shall read as “open sesame” and its Chinese translation in 4 Chinese characters. 
       Embodiment 4 
       [0099]      FIG. 6  depicts a transmitting (Tx) operation concept of enveloping using higher order WF multiplexing techniques for enveloping a message data set. A higher order WF muxing is referred to M-to-M WF muxing; where M is an integer and 4. We use a 4-to-4 WF muxing to exemplify operation concepts. The three grouped segments for enveloping and de-enveloping are identical to the ones shown in  FIG. 1 . It depicts first two of the following three segments: (1) a pre-processing or enveloping  630 , (2) transported via cloud 010, and (3) post processing or de-enveloping  640 . 
         [0100]    A 4-to-4 WF muxing is implemented in the pre-processing  630 . There are four inputs connected to S(t), E10(t), E1(t), and E5(t), and only one output used for Ex(t). The remaining three outputs of the WF muxing are grounded. S(t) comprises of a phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters, and is the message to be delivered to destinations via cloud. E5(t) is the selected envelope and is one of the candidate envelopes in the candidate file  180 . The first output Ex(t) features an appearance substantially identical to human sensors as those in E5(t). The second and the third inputs E10(t) and E1(t) are also in the file  180  for candidate envelopes known a priori to both the sender and the receiver. 
         [0101]    The mathematic derivations are identical to the ones for  FIG. 2  when we use a 4-to-4 Hadamard matrix for both the WF muxing and demuxing. The 4-to-4 WF muxing in the preprocessing  630  is formulated based on Equation (7) as; 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Ex 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               am 
                               * 
                               E 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               E 
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               E 
                                
                               
                                   
                               
                                
                               10 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               S 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     
                       - 
                     
                      
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0102]    The first output O1 is name ex(t), the other 3 outputs are grounded in  FIG. 6 . The scaling factor am is set to ˜10, so that the Ex(t) appears substantially identical to the appearance of E5(t) to human sensors. Ex(t) is to be delivered to destinations via cloud 010. 
         [0103]      FIG. 7  is a block diagram of de-enveloping in a destination; reverse processing of those in  FIG. 6 . It depicts a receiving (Rx) operation concept of de-enveloping using higher order WF de-multiplexing techniques for de-enveloping a message data set. A higher order WF demuxing is referred to M-to-M WF demuxing; where M is an integer and ≧4. The three segments for enveloping and de-enveloping are identical to the ones shown in  FIG. 1 ; (1) a pre-processing or enveloping  630 , (2) transported via cloud 010, and (3) post processing or de-enveloping  640 . It depicts last two of the three segments. 
         [0104]    Only one of the four WF muxed data set was sent to a destination via cloud 010. The required communication channel bandwidth may be nearly identical to that of S(t) signal itself, when the digital envelope, E5, is properly chosen and further optimized in pre-processing  630  accordingly. 
         [0105]    In the post-processing  640  a 4-to-4 WF demuxing is incorporated. There are four inputs; (1) Ex(t) the only received data set, (2) E10(t) a known digital data in the envelop candidate file, (3) E1(t) a second known digital data in the envelop candidate file, and (4) E5(t) a known digital data for the selected digital envelop. Based on Equation (7-2); 
         [0000]        Ex ( t )= am*E 5( t )+ E 1( t )+ E 10( t )+ S ( t )  (8)
 
         [0000]      And  S ( t )= Ex ( t )−( am*E 5( t )+ E 1( t )+ E 10( t ))  (8-1)
 
         [0106]    Only one received enveloped file Ex(t) is used in Equation (8-1). The second, the third, and the four inputs of the 4-to-4 WF demuxing are known data sets. The recovered S(t) from the WF demuxing shall be the embedded message delivered and shall comprise of the phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters. 
         [0107]    Furthermore according to Equation (7-2), O2, O3, and O4 can now be reconstructed based on the recovered Ex(t). The restructured O2, O3, and O4 may be used for enhanced identifications. 
       Embodiment 5 
       [0108]      FIG. 8  and  FIG. 9  depict the enveloping and de-enveloping using higher order WF muxing and demuxing. Two of the four outputs from a 4-to-4 WF muxing are used as enveloped data sets to be sent to destinations via cloud 010. 
         [0109]      FIG. 8  depicts a transmitting (Tx) operation concept of enveloping using higher order WF multiplexing techniques for enveloping a message data set. We use a 4-to-4 WF muxing to exemplify operation concepts. The three grouped segments for enveloping and de-enveloping are identical to the ones shown in  FIG. 1 . It depicts first two of the following three segments: (1) a pre-processing or enveloping  630 , (2) transported via cloud 010, and (3) post processing or de-enveloping  640 . 
         [0110]    A 4-to-4 WF muxing is implemented in the pre-processing  630 . There are four inputs connected to S(t), E10(t), E1(t), and E5(t), and only two outputs used for Ex(t) and Ey(t). The remaining two outputs of the WF muxing are grounded. S(t) comprises of a phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters, and is the message to be delivered to destinations via cloud. E5(t) is the selected envelope and is one of the candidate envelopes in the candidate file  180 . As to the first output Ex(t) and the third output Ey(t), each features an appearance substantially identical to human sensors as those in E5(t). The second and the third inputs E10(t) and E1(t) are also in the file  180  for candidate envelopes known a priori to both the sander and the receiver. 
         [0111]    The mathematic derivations are identical to the ones for  FIG. 2  when we use a 4-to-4 Hadamard matrix for both the WF muxing and demuxing. The 4-to-4 WF muxing in the preprocessing  630  is formulated based on Equation (7) as: 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Ex 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         
                           
                             Ey 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               am 
                               * 
                               E 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               E 
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               E 
                                
                               
                                   
                               
                                
                               10 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               S 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     
                       - 
                     
                      
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
         [0112]    The first and the third outputs, O1 and O3, are named Ex(t) and Ey(t) respectively. The other 2 outputs are grounded in  FIG. 8 . The scaling factor am is set to ˜10, so that both the Ex(t) and Ey(t) appear substantially identical to the appearance of E5(t) to human sensors. Ex(t) and Ey(t) are to be delivered to destinations via cloud 010. 
         [0113]      FIG. 9  is a block diagram of de-enveloping in a destination; reversed processing of those in  FIG. 8 . It depicts a receiving (Rx) operation concept of de-enveloping using higher order WF de-multiplexing techniques for de-enveloping a message data set. 
         [0114]    Only two of the four WF muxed data set are sent to a destination via cloud 010. The required communication channel bandwidth may be about twice as that of S(t) signal itself. Each of the two enveloped files may be as large as that of S(t) itself when the digital envelope, E5, is properly chosen and further optimized in pre-processing  630  accordingly. Additional bandwidth differentials are due to processing overhead. 
         [0115]    In the post-processing  640  a 4-to-4 WF demuxing is incorporated. There are four inputs; (1) Ex(t) a first received data set, (2) Ey(t) a second received data set, (3) E10(t) a known digital data in the envelop candidate file  180 , and (4) E5(t) a known digital data for the selected digital envelop. Based on Equation (7-3); 
         [0000]        Ex ( t )= am*E 5( t )+ E 1( t )+ E 10( t )+ S ( t )  (7-4)
 
         [0000]        Ey ( t )= am*E 5( t )+ E 1( t )− E 10( t )− S ( t )  (7-5)
 
         [0000]      And  S ( t )=[ Ex ( t )− Ey ( t )]/2 −E 10( t )  (9)
 
         [0116]    Two received enveloped files, Ex(t) and Ey(t), are used in Equation (9). The third input for the 4-to-4 WF demuxing is E10(t); a known data set. The fourth input for the 4-to-4 WF demuxing is E5(t); also a known data set. But the formulation in Equation 9 does not need E5(t) in restoring S(t). However, there are 6 different combinations in choosing 2 from 4 WF muxed files as the 2 enveloped carriers. Many of the 6 configurations requires more than one known data sets among E10, E1, and E5 in order to restore S(t). 
         [0117]    The recovered S(t) from the WF demuxing shall be the embedded message delivered and shall comprise of the phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters. 
         [0118]    Furthermore according to Equation (7-2), O2, and O4 can now be reconstructed based on the recovered S(t) at the destination. The restructured O2, and O4 may be used for enhanced identifications. 
       Embodiment 6 
       [0119]      FIG. 10  depicts a transmitting (Tx) operation concept of enveloping using higher order WF multiplexing techniques for enveloping a message data set. We use a 4-to-4 WF muxing to exemplify operation concepts. Three of the four outputs from a 4-to-4 WF muxing are used as enveloped data sets to be sent to destinations via cloud 010. 
         [0120]    A 4-to-4 WF muxing is implemented in the pre-processing  630 . The four inputs are connected to S(t), E10(t), E1(t), and E5(t), and only three outputs used for Ex(t), Ey(t) and Ez(t). The remaining one output of the WF muxing is grounded. There are 4 possible configurations to choose  3  out of four outputs. S(t) comprises of a phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters, and is the message to be delivered to destinations via cloud. E5(t) is the selected envelope and is one of the candidate envelopes in the candidate file  180 . As to the first output Ex(t), the second output Ey(t), and the third output Ez(t), each features an appearance substantially identical to human sensors as those in E5(t). The second and the third inputs E10(t) and E1(t) are also in the file  180  for candidate envelopes known a priori to both the sender and the receiver. 
         [0121]    The mathematic derivations are identical to the ones for  FIG. 2  when we use a 4-to-4 Hadamard matrix for both the WF muxing and demuxing. The 4-to-4 WF muxing in the preprocessing  630  is formulated based on Equation (7) as: 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Ex 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             Ey 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             Ez 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             O 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             
                               + 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               + 
                               1 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               am 
                               * 
                               E 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               E 
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               E 
                                
                               
                                   
                               
                                
                               10 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               S 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     
                       - 
                     
                      
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
         [0122]    The first, second and the third outputs, O1, O2, and O3, are named Ex(t), Ey(t), and Ez(t) respectively. The fourth output is grounded in  FIG. 10 . The scaling factor am is set to ˜10, so that both the Ex(t), Ey(t), and Ez(t) appear substantially identical to the appearance of E5(t) to human sensors. Ex(t), Ey(t), and Ez(t) are to be delivered to destinations via cloud 010. 
         [0123]    The required communication channel bandwidth may be about three times as that of S(t) signal itself. Each of the three enveloped files may be as large as that of S(t) itself when the digital envelope, E5, is properly chosen and further optimized in pre-processing  630  accordingly. Additional bandwidth differentials are due to processing overhead. 
         [0124]      FIG. 11  is a block diagram of de-enveloping in a destination; reversed processing of those in  FIG. 10 . It depicts a receiving (Rx) operation concept of de-enveloping a message data. Only two of the three WF muxed data sets sent via cloud 010 are received at a desired destination on time. It is assume that Ex(t) and Ey(t) are received at the destination. 
         [0125]    In the post-processing  640  a 4-to-4 WF demuxing is incorporated. There are four inputs; (1) Ex(t) a first received data set, (2) Ey(t) a second received data set, (3) E10(t) a known digital data in the envelop candidate file  180 , and (4) E5(t) a known digital data for the selected digital envelop. Based on Equation (7-6); 
         [0000]        Ex ( t )= am*E 5( t )+ E 1( t )+ E 10( t )+ S ( t )  (7-8)
 
         [0000]        Ey ( t )= am*E 5( t )− E 1( t )+ E 10( t )− S ( t )  (7-9)
 
         [0000]        Ez ( t )= am*E 5( t )+ E 1( t )− E 10( t )− S ( t )  (7-10)
 
         [0000]      And  S ( t )=[ Ex ( t )− Ey ( t )]/2 +E 1( t )  (10)
 
         [0126]    Two received enveloped files, Ex(t) and Ey(t), are used in Equation (10). The third input for the 4-to-4 WF demuxing is E1(t); a known data set. The fourth input for the 4-to-4 WF demuxing is E5(t); also a known data set. But the formulation in Equation (10) does not need E5(t) in restoring S(t). 
         [0127]    The recovered S(t) from the WF demuxing shall be the embedded message delivered and shall comprise of the phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters. 
         [0128]    Furthermore according to Equation (7-2), O3, and O4 can now be reconstructed based on the recovered S(t) at the destination. The restructured O3, and O4 may be used for enhanced identifications. 
         [0129]      FIG. 12  is a block diagram of de-enveloping in a destination; reversed processing of those in  FIG. 10 . It depicts a receiving (Rx) operation concept of de-enveloping a message data. Two of the three WF muxed data sets sent via cloud 010 are received at a desired destination on time. Ez(t) and Ey(t) are received at the destination. 
         [0130]    In the post-processing  640  a 4-to-4 WF demuxing is incorporated. There are four inputs; (1) Ex(t) a first received data set, (2) Ey(t) a second received data set, (3) E10(t) a known digital data in the envelop candidate file  180 , and (4) E5(t) a known digital data for the selected digital envelop. Based on Equation (7-6); 
         [0000]        Ey ( t )= am*E 5( t )− E 1( t )+ E 10( t )− S ( t )  (7-11)
 
         [0000]        Ez ( t )= am*E 5( t )+ E 1( t )− E 10( t )− S ( t )  (7-12)
 
         [0000]      And  S ( t )= am*E 5( t )−[ Ey ( t )+ Ez ( t )]/2  (11)
 
         [0131]    Two received enveloped files, Ey(t) and Ez(t), are used in Equation (11). The third input for the 4-to-4 WF demuxing is E1(t); a known data set. The fourth input for the 4-to-4 WF demuxing is E5(t); also a known data set. But the formulation in Equation (11) does not need E1(t) in restoring S(t). The recovered S(t) from the WF demuxing shall be the embedded message delivered and shall comprise of the phrase of “Open Sesame” and its Chinese translation by 4 Chinese characters. Furthermore O1 and O4 can now be reconstructed according to Equation (7-6) based on the recovered S(t) at the destination. The restructured O1 and O4 may be used for enhanced identifications. 
         [0132]      FIG. 13  is a block diagram of de-enveloping in a destination; reversed processing of those in  FIG. 10 . It depicts a receiving (Rx) operation concept of de-enveloping a message data, when all three WF muxed data sets sent via cloud 010 are received at a desired destination on time. Ex(t), Ey(t) and Ez(t) are received at the destination on time. 
         [0133]    In the post-processing  640  a 4-to-4 WF demuxing is incorporated. There are four inputs; (1) Ex(t) a first received data set, (2) Ey(t) a second received data set, (3) E1(t) a known digital data in the envelop candidate file  180 , and (4) Ez(t) a third received data set. 
         [0134]    Based on Equation (7-6); 
         [0000]        Ex ( t )= am*E 5( t )+ E 1( t )+ E 10( t )+ S ( t )  (7-13)
 
         [0000]        Ey ( t )= am*E 5( t )− E 1( t )+ E 10( t )− S ( t )  (7-14)
 
         [0000]        Ez ( t )= am*E 5( t )+ E 1( t )− E 10( t )− S ( t )  (7-15)
 
         [0000]      And  S ( t )= am*E 5( t )−[ Ey ( t )+ Ez ( t )]/2  (12-1)
 
         [0000]      Or  S ( t )=[ Ex ( t )− Ey ( t )]/2 −E 1( t )  (12-2)
 
         [0000]      Or  S ( t )=[ Ex ( t )− Ez ( t )]/2 −E 10( t )  (12-3)
 
         [0135]    Two of the three received enveloped files, Ex(t), Ey(t) and Ez(t), are used in Equation (12). There are three options to restore the embedded mail, S(t); as delineated in Equations (12-1), (12-2), and (12-3), respectively. They all need a third input for the 4-to-4 WF demuxing. The required 3 rd  file for a restoration processing according to Equation (12-1) is the digital file of the original digital envelope E5(t). Similarly the 3 rd  files for those according to Equation (12-2) and (12-3) are the digital file of E1(t) and that of E10(t), respectively. 
         [0136]    With the flexibility in all 3 techniques in Equations (12), a receiver may pick any first two of three possible arrivals, Ex(t), Ey (t) and Ez(t), in restoring the S(t). For delivering music or video clips, these techniques at a destination feature redundancies for better survivability, and enhanced streaming speed of S(t) using only first two arrivals and discarding the last (the third) arrival among the three WF muxed files sent by a source. 
         [0137]    In different embodiments for various applications, multiple restoration means described above may be used to differentiating service preferences in a multicasting, or broadcasting modes. For those without accessing to E1 and E10; their services can be completely denied by sending Ey and Ez only via cloud 010. Similarly, controlling delivery of Ex(t) to a slower rate via cloud 010 in streaming a video clip, there will only be ⅓ probability at a normal rate to restore S(t) by using first two arrivals out of three total arrivals in a receiver at destinations. The corresponding overall flow rate may be degraded by ⅔ in receivers to a flow rate at 33% of a normal flow, when Ex(t) delivery are delayed significantly. 
         [0138]      FIG. 14  is a block diagram of de-enveloping in a destination; reversed processing of those in  FIG. 10 . It is for a scenario that the 3 selected WF muxed data sets to be sent via cloud 010 are Ex(t), Ey(t), and Ew(t). It depicts a receiving (Rx) operation concept of de-enveloping a message data, when all three WF muxed data sets sent via cloud 010 are received at a desired destination on time. Ex(t), Ey(t) and Ew(t) are received at the destination on time. 
         [0139]    In the post-processing  640  a 4-to-4 WF demuxing is incorporated. There are four inputs; (1) Ex(t) a first received data set, (2) Ey(t) a second received data set, (3) E1(t) a known digital data in the envelop candidate file  180 , and (4) Ez(t) a third received data set. 
         [0140]    Based on Equation (7-6); 
         [0000]        Ex ( t )= am*E 5( t )+ E 1( t )+ E 10( t )+ S ( t )  (7-16)
 
         [0000]        Ey ( t )= am*E 5( t )− E 1( t )+ E 10( t )− S ( t )  (7-17)
 
         [0000]        Ew ( t )= am*E 5( t )− E 1( t )− E 10( t )+ S ( t )  (7-18)
 
         [0000]      And  S ( t )= E 10( t )+[ Ey ( t )− Ew ( t )]/2  (12-4)
 
         [0000]      Or  S ( t )=[ Ex ( t )− Ey ( t )]/2 −E 1( t )  (12-5)
 
         [0000]      Or  S ( t )=[ Ex ( t )+ Ew ( t )]/2 −am E 5( t )  (12-6)
 
         [0141]    Two of the three received enveloped files, Ex(t), Ey(t) and Ew(t), are used in Equation (12). There are three options to restore the embedded mail, S(t); as delineated in Equations (12-4), (12-5), and (12-6), respectively. They all need a third input for the 4-to-4 WF demuxing; similar to the block diagram in  FIG. 13 . The required 3 rd  file for a restoration processing according to Equation (12-4) is the digital file of the original digital file E10(t). Similarly the 3 rd  files for those according to Equation (12-5) and (12-6) are the digital file of E1(t) and that of E5(t), respectively. 
         [0142]    With the flexibility in all 3 techniques in Equations (12), a receiver may pick any first two of three possible arrivals, Ex(t), Ey(t) and Ew(t), in restoring the S(t). For delivering music or video clips, these techniques at a destination feature redundancies for better survivability, and enhanced streaming speed of S(t) using only first two arrivals and discarding the last (the third) arrival among the three WF muxed files sent by a source. 
       Embodiment 7 
       [0143]      FIG. 15  depict a Tx operation concept of double enveloping using WF multiplexing for enveloping a message data set via two envelopes sequentially. It depicts first two of the three segments in  FIG. 1 : (1) a pre-processing or enveloping  130 , (2) transported via cloud 010, and (3) post processing or de-enveloping  140 . 
         [0144]    There are two enveloping processing in series in  FIG. 15 . The inner enveloping and the outer enveloping are, respectively, identical to the enveloping shown in  FIG. 6  and that in  FIG. 1 . In the first pre-processing  630 , there are four inputs connected to 4 digital data files, S(t), E10(t), E1(t), and E4(t), and a first of the 4 outputs is assigned as output w(t). The other 3 outputs, x(t), y(t), and z(t), are grounded. S(t) comprises of a phrase of “Open Sesame” and its Chinese translation, and is the message to be delivered to destinations via cloud. E4(t) is a selected inner envelope and is one of the candidate envelopes in the candidate file  180 . The first output w(t) features an appearance substantially identical to human sensors as that in E4(t). 
         [0145]    In the second preprocessing  130 , there are two inputs, w(t) and E5(t), and a first output assigned as output Es(t). The second output is grounded. E5(t) is a selected outer envelope and is also one of the candidate envelopes in the candidate file  180 . The first output Es(t) features an appearance substantially identical to human sensors as that in E5(t). 
         [0146]    Only one WF muxed file, Es(t) is sent to destinations via cloud 010. There is no phrase of “Open Sesame” or its Chinese translation on the appearance of Es(t). The required bandwidth for transporting the Es(t) shall be near identical to that of sending S(t) via cloud when the enveloping files, E4(t) or E5(t) are properly chosen. 
         [0147]    In other embodiments, images in the enveloping files may have been processed for various purposes such as minimized dynamic range of individual pixels or simply for enhanced authentication and identifications before WF muxing. Many can be pre-stored in the envelop candidate files as optional candidates. Certainly, these additional processing can be included as a part of the first pre-processing  630  and/or the second  130 . 
         [0148]      FIG. 16  depicts a receiving (Rx) operation concept of de-enveloping doubly enveloped messages using WF demultiplexing techniques. There are two de-enveloping processing in series. A first post-processing  140  to open the outer envelope is identical to the de-enveloping shown in  FIG. 1 . There are two inputs connected to Es(t) and E5(t). Es(t) is the received digital data file with embedded message for a desired receiver in the destination, and shall be substantially equivalent to the only output of the second pre-processing  130  in  FIG. 15 . In addition it shall feature an appearance substantially identical to human sensors as those in E5(t). E5(t) is a selected outer envelope and is one of the candidate envelopes in a candidate file  180  known priori to both the sender and the receiver. 
         [0149]    Similarly, there are two outputs from the post processor  140 . The first output w(t) of the first post processor  140  features an appearance substantially identical to human sensors as those in E4(t). The second output is grounded. 
         [0150]    In the second post-processing  640 , there are four inputs, connected to w(t), E10(t), E1(t), and E4(t). E4(t) is the selected inner envelope and is one of the candidate envelopes in the candidate file  180 . E10(t) and E1(t) are digital files in the candidate file  180 . There are two outputs, and the first one is assigned as output S(t) and a second one is grounded. The first output is the recovered embedded message. 
         [0151]    It is conceivable to extend the double enveloping/de-enveloping depicted in  FIG. 15  and  FIG. 16  to multiple layers of enveloping and de-enveloping by cascading more M-to-M WF muxing processors in preprocessing in a source and more M-to-M WF demuxing processors in post processing in a receiver, where M≧2 and is an integer. 
         [0152]    Additional Comments 
         [0153]    With regards to the above applications via WF muxing, a WF muxer may alternatively perform a first non-orthogonal matrix on the inputs of the WF muxer. With regards to the above WF demuxing applications, a WF demuxer may alternatively perform a second non-orthogonal matrix, inverse to the first non-orthogonal matrix, on the inputs of the WF muxer. 
         [0154]    The components, steps, features, benefits and advantages that have been discussed are merely illustrative. None of them, nor the discussions relating to them, are intended to limit the scope of protection in any way. Numerous other embodiments are also contemplated. These include embodiments that have fewer, additional, and/or different components, steps, features, benefits and advantages. These also include embodiments in which the components and/or steps are arranged and/or ordered differently. 
         [0155]    Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain. Furthermore, unless stated otherwise, the numerical ranges provided are intended to be inclusive of the stated lower and upper values. Moreover, unless stated otherwise, all material selections and numerical values are representative of preferred embodiments and other ranges and/or materials may be used. 
         [0156]    The scope of protection is limited solely by the claims, and such scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows, and to encompass all structural and functional equivalents thereof.