Patent Publication Number: US-10311243-B2

Title: Method and apparatus for secure communication

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit under 35 U.S.C. § 119(e) of provisional application Ser. No. 61/783,708, entitled “LISTS THAT ARE SMALLER THAN THEIR PARTS: A NEW APPROACH TO SECRECY,” filed Mar. 14, 2013 and also to provisional application Ser. No. 61/783,747, entitled “METHOD AND APPARATUS FOR PROVIDING A SECURE SYSTEM,” filed Mar. 14, 2013, both applications are hereby incorporated herein by reference in their entireties. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under Contract No. FA8721-05-C-0002 awarded by the U.S. Air Force. The government has certain rights in the invention. 
    
    
     FIELD 
     The subject matter described herein relates generally to communication systems and, more particularly, to systems and related techniques for enabling secure communications in communication networks. 
     BACKGROUND 
     As is known in the art, computationally secure cryptosystems, which are largely based upon unproven hardness assumptions, have led to cryptographic schemes that are widely adopted and thrive from both a theoretical and a practical perspective in communication systems. Such cryptographic schemes are used millions of times per day in applications ranging from online banking transactions to digital rights management. Increasing demands for large-scale high-speed data communications, for example, have made it important for communication systems to achieve efficient, reliable, and secure data transmissions. 
     As is also known, information-theoretic approaches to secure cryptosystems, particularly secrecy, are traditionally concerned with unconditionally secure systems, i.e. systems with schemes that manage to hide all bits of a message from an eavesdropper with unlimited computational resources available to intercept or decode a given message. It is well known, however, that in a noiseless setting unconditional secrecy (i.e., perfect secrecy) can only be attained when both a transmitting party and a receiving party share a random key with entropy at least as large as the message itself (see, e.g., “Communication Theory of Secrecy Systems,” by C. E. Shannon,  Bell Systems Technical Journal , vol. 28, no. 4, pp. 656-715, 1949). It is also well known that, in other cases, unconditional secrecy can be achieved by exploiting particular characteristics of a given scheme, such as when a transmitting party has a less noisy channel (e.g., wiretap channel) than an eavesdropper. (see, e.g., “Information Theoretic Security,” by Liang et al.,  Found. Trends Commun. Inf. Theory , vol. 5, pp. 355-580, April 2009). 
     Traditional secrecy schemes, including secure network coding schemes and wiretap models, assume that an eavesdropper has incomplete access to information needed to intercept or decode a given data file. Wiretap channel II, for example, which was introduced by L. Ozarow and A. Wyner, is a wiretap model that assumes an eavesdropper observes a set k out of n transmitted symbols (see, e.g., “Wiretap Channel II,” by Ozarow et al,  Advances in Cryptography,  1985, pp. 33-50). Such wiretap model was shown to achieve perfect secrecy, but practical considerations limited its success. An improved version of Wiretap channel II was later developed by N. Cai and R. Yeung, which addressed a related problem of designing an information-theoretically secure linear network code when an eavesdropper can observe a certain number of edges in the network (see, e.g., “Secure Network Coding,” by Cai et al.,  IEEE International Symposium on Information Theory,  2002). 
     A similar and more practical approach was later described in “Random Linear Network Coding: A Free Cipher?” by Lima at al. in  IEEE International Symposium on Information Theory , June 2007, pp. 546-550. However, with an ever increasing amount of data being streamed over the internet and in both near and far-field communications, for example, there remains a need for new and more efficient methods and systems for use in providing secure communication in communications systems and networks. Additionally, there remains a need for characterizing and optimizing such secrecy schemes through improved information-theoretic metrics. 
     SUMMARY 
     The present disclosure provides secrecy scheme systems and associated methods for enabling secure communications in communications networks. Additionally, the present disclosure provides improved information-theoretic metrics for characterizing and optimizing said secrecy scheme systems and associated methods. 
     In accordance with one aspect of the present disclosure, a transmitting system for secure communication includes a receiver module operable to receive a data file at a first location; an encoder module coupled to the receiver module and operable to encode the data file using a list source code to generate an encoded data file; an encryption module coupled to one or more of the receiver module and encoder module and operable to encrypt a select portion of the data file using a key to generate an encrypted data file; and a transmitter module coupled to one or more of the encoder module and encryption module and operable to transmit the encoded data file and the encrypted data file to an end user at a destination location, wherein the encoded data file cannot be decoded at the destination location until the encrypted data file has been received and decrypted by the end user, wherein the end user possesses the key. 
     In accordance with another aspect of the present disclosure, the encoded data file of the transmitting system for secure communication is a unencrypted data file. In another aspect, the encrypted data file is an encoded encrypted data file. 
     In accordance with one aspect of the present disclosure, a receiving system for secure communication includes a receiver module operable to receive, at a destination location, one or more of an encoded data file, an encrypted data file, or a key from a first location; a decryption module coupled to the receiver module and operable to decrypt the encrypted data file using a key to generate a decrypted data file; and a decoder module coupled to one or more of the decryption module and the receiver module and operable to decode one or more of the encoded data file and the decrypted data file to generate an output data file. 
     In accordance with another aspect of the present disclosure, the encoded data file of the receiving system for secure communication is a unencrypted data file. In another aspect, the encrypted data file is an encoded encrypted data file. In another aspect, the output data file comprises a list of potential data files. In another aspect, the decoder module is further operable to determine a data file from the list of potential data files, wherein the data file is representative of the encoded data file in combination with the encrypted data file. 
     In accordance with one aspect of the present disclosure, a method of secure communication includes receiving a data file at a first location, encoding the data file using a list source code to generate an encoded file, encrypting a select portion of the data file using a key to generate an encrypted file, and transmitting the encoded file and the encrypted file to an end user at a destination location, wherein the encoded file cannot be decoded at the destination location until the encrypted file has been received and decrypted by the end user, wherein the end user possesses the key. In another aspect, a large portion of the encoded file is transmitted before the encrypted file and the key are transmitted to the end user. 
     In accordance with another aspect of the present disclosure, a method of secure communication also includes encrypting a select portion of the data file before, during, or after transmission of the encoded file. In another aspect, the method additionally includes transmitting the key to the destination location either before, during or after transmission of the encoded file to the destination location. In another aspect, the method further includes only needing to abort transmission of the encrypted file if the key is compromised during the transmission of the encoded file. In yet another aspect, security of the method is not compromised if the transmission of the encoded file is not aborted. 
     In accordance with yet another aspect of the present disclosure, the method is applied as an additional layer of security to an underlying encryption scheme. In another aspect, the method is tunable to a desired level of secrecy, wherein size of the key is dependent upon the desired level of secrecy, wherein said size can be used to tune the method to the desired level of secrecy. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing features of the concepts, systems, circuits, and techniques described herein may be more fully understood from the following description of the drawings in which: 
         FIG. 1  is a block diagram of an example encoding and decoding system; 
         FIGS. 2A and 2B  are block diagrams of an example system comprising a modulator system and demodulator system, respectively; 
         FIG. 3  is a diagram illustrating an example data file (X n ) and an associated list source code; 
         FIG. 4  is a plot of an example rate list region for a given normalized list and code rate; 
         FIG. 5  is a flow diagram which illustrates an exemplary process for secure encoding and encryption according to an embodiment of the disclosure; 
         FIG. 6  is a flow diagram which illustrates an exemplary process for secure decoding and decryption according to an embodiment of the disclosure; and 
         FIG. 7  is a block diagram of an example node architecture that may be used to implement features of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The features and other details of the disclosure will now be more particularly described. It will be understood that the specific embodiments described herein are shown by way of illustration and not as limitations of the broad concepts sought to be protected herein. The principal features of this disclosure can be employed in various embodiments without departing from the scope of the disclosure. The preferred embodiments of the present disclosure and its advantages are best understood by referring to  FIGS. 1-7  of the drawings, like numerals being used for like and corresponding parts of the various drawings. 
     Definitions 
     For convenience, certain terms used in the specification and examples are collected here. 
     “Code” is defined herein to include a rule or set of rules for converting a piece of data (e.g., a letter, word, phrase, or other information) into another form or representation which may or may not necessarily be of the same type as the piece of data. 
     “Data file” is defined herein to include text or graphics material containing a representation of a collection of facts, concepts, instructions, or information to which meaning has been assigned, wherein the representation may be analog, digital, or any symbolic form suitable for storage, communication, interpretation, or processing by human or automatic means. 
     “Encoding” is defined herein to include a process of applying a particular set of coding rules to readable data (e.g., a plain-text data file) for converting the readable data into another format (e.g., adding redundancy to the readable data or transforming the readable data into indecipherable data). The process of encoding may be performed by an “encoder.” An encoder converts data from one format or code to another, for the purposes of reliability, error correction, standardization, speed, secrecy, security, and/or saving space. An encoder may be implemented as a device, circuit, process, processor, processing system or other system. “Decoding” is a reciprocal process of “encoding,” with a “decoder” performing a reciprocal process of an “encoder.” A decoder may be implemented as a device, circuit process, processor, processing system or other system. 
     “Encryption” is defined herein to include a process of converting readable data (e.g., a plain-text data file) into indecipherable data (e.g., cipher-text), wherein the conversion is based upon an encoding key. Encryption can encompass both enciphering and encoding. “Decryption” is a reciprocal process of “encryption,” involving restoring the indecipherable data into readable data. The process requires not only knowledge of a corresponding decryption algorithm but also knowledge of a decoding key, which is based upon or substantially the same as the encoding key. 
     “Independent and Identically Distributed (i.i.d.) source” is defined herein to include a source comprising random variables X 1 , . . . , X n  where P X1, . . . , Xn (X1, . . . , Xn) =P x(X1)  P x(X2)  . . . P x(Xn)  for a discrete source and ƒ X1, . . . , Xn(X1, . . . , Xn) =ƒ x(X1) ƒ x(X2)  . . . ƒ x(Xn)  for a continuous source. 
     “Linear code” is defined herein to include a code for which any linear combination of codewords is also a codeword. 
     “List source code” is defined herein to include codes that compress a source sequence below its entropy rate and are decoded to a list of possible source sequences instead of a unique source sequence. 
     “Modulation” is defined herein to include a process of converting a discrete data signal (e.g., readable data, indecipherable data) into a continuous time analog signal for transmission through a physical channel (e.g., communication channel). “Demodulation” is a reciprocal process of “modulation,” converting a modulated signal back into its original discrete form. “Modulation and coding scheme (MCS)” is defined herein to include the determining of coding method, modulation type, number of spatial streams, and other physical attributes for transmission from a transmitter to a receiver. 
     Referring now to  FIG. 1 , an exemplary system  100  includes an encoding system  101  and a decoding system  102 . System  100  may be used with the embodiments disclosed herein, e.g., to encode and decode data. The encoding system  101  comprises an encoder circuit  110  configured to receive a data file (X n )  105  at an input thereof and configured to encode the data file (X n )  105  and generate one or more encoded data files  114 , 116  at an output thereof. Encoded data files  114 , 116  may, for example, comprise a smaller encoded file and a larger encoded file, wherein the smaller encoded file is to be later encrypted. Conversely, the decoding system  102  comprises a decoder circuit  150  configured to receive an encoded unencrypted data file  144  and an encoded decrypted data file  146  at an input thereof and configured to decode data file ( )  155  at an output thereof from the encoded unencrypted data file  144  and the encoded decrypted data file  146 . 
     It is to be appreciated that the encoder circuit  110  and/or the decoder circuit  150  may be embodied as hardware, software, firmware, or any combination thereof. For instance, one or more memories and processors may be configured to store and execute, respectively, various software programs or modules to perform the various functions encoding and/or decoding techniques described herein. For example, in certain embodiments, the coding system may be implemented in a field-programmable gate array (FPGA), and may be capable of achieving successful communication for high data rates. Alternatively, coding system may be implemented via an application specific integrated circuit (ASIC) or a digital signal processor (DSP) circuit or via another type of processor or processing device or system. 
     Referring now to  FIGS. 2A and 2B , an exemplary modulator and demodulator system, collectively system  200  (e.g., an expansion of system  100  above) comprises a modulator system  201 , shown in  FIG. 2A , and a demodulator system  202 , shown in  FIG. 2B . 
     Referring now to  FIG. 2A , the modulator system  201  comprises an encoder circuit  210 , an encryption circuit  220 , and a transmitter  230 , wherein the encoder circuit  210  may be the same as or similar to encoder circuit  110  of  FIG. 1 . Referring briefly to  FIG. 2B , the demodulator system  202  comprises a decoder circuit  270 , a decryption circuit  260 , and a receiver  240 , wherein the decoder circuit  270  may be the same as or similar to decoder circuit  150  of  FIG. 1 . Transmitter  230  and receiver  240  can be coupled to antennas  235  and  242 , or some other type of transducers, to provide a transition to free space or other transmission medium. In some embodiments, the antennas  235 ,  242  may each include a plurality of antennas, such as those used in multiple-input multiple-output (MIMO) systems. Such an approach may, for example, improve capacity of system  200 , i.e., maximize bits/second/hertz as compared to single antenna implementations. The receiver  240  can be an end user at a destination location, with the destination location being a remote location according to some embodiments and the same as a first location of the transmitter  230  according to other embodiments. 
     Returning now to  FIG. 2A , the modulator system  201  is coupled to receive a data file (X n )  205 , which can be the same as or similar to data file (X n )  105  of  FIG. 1 , at an input thereof. In particular, the data file (X n )  205  is received at an input of the encoder circuit  210 . The encoder circuit  210  is configured to encode the data file (X n )  205  in accordance with a particular encoding process using a list source code (e.g., with particular reference to  FIG. 5 ) to generate a plurality of encoded data files  215 ,  218  at an output thereof. A first encoded data file  215 , which comprises encoded unencrypted data, is provided to an input of transmitter  230  for transmission. A second encoded data file  218 , which according to a preferred embodiment is substantially smaller than the first encoded data file  215 , is provided to an input of the encryption circuit  220 . The encryption circuit  220  is configured to encrypt the second encoded data file  218  in accordance with a particular encryption process using a key (e.g., with particular reference to  FIG. 5 ) to generate an encoded encrypted data file  222  at an output thereof, wherein the key controls the encryption and decryption of the data file (X n )  205 . The transmitter  230  is configured to receive the first encoded data file  215  and the encoded encrypted data file  222  as inputs and transmit the data files  215 ,  222 , in addition to the key, to a receiver, which can be receiver  240  of demodulator system  202  of  FIG. 2B . 
     Referring now to  FIG. 2B , the receiver  240  is coupled to receive an encoded unencrypted data file  244 , an encoded encrypted data file  246 , and a key as inputs, wherein the inputs can be the same as or similar to the first encoded data file  215 , the encoded encrypted data file  222  and the key of the modulator system  201 . The receiver  240  is configured to deliver the encoded unencrypted data file  244 , encoded encrypted data file  246 , and key to the decoder circuit  270  and decryption circuit  260 , respectively. The decryption circuit  260  is configured to decrypt encoded encrypted data file  246  with the key and generate an encoded decrypted data file  262  at an output thereof. The decoder circuit  270  is coupled to receive the encoded decrypted data file  262 , with the decoder circuit  270  configured to decode the encoded decrypted data file  262  and the encoded unencrypted data file  244  into a data file ( )  275 , as will be further discussed in conjunction with  FIG. 6 . In some embodiments, the decoder circuit  270  is configured to decode the encoded decrypted data file  262  and the encoded unencrypted data file  244  into a list of potential list source codes and extract a data file ( )  275  from the list of potential list source codes. 
     In an alternative embodiment (not shown), the data file (X n )  205  can be received at inputs of an encoder circuit and an encryption circuit. The encoder circuit can be configured to encode the data file (X n )  205  in accordance with a particular encoding process using a list source code to generate an encoded file at an output thereof. The encryption circuit, on the other hand, can be configured to encrypt a select portion of the data file (X n )  205  in accordance with a particular encryption process using a key to generate an encrypted file at an output thereof, wherein the key controls the encryption and decryption of the data file (X n )  205 . A transmitter can be configured to receive the encoded file and the encrypted file as inputs and transmit the files in addition to the key, to a receiver, which can be receiver  240  of demodulator system  202  of  FIG. 2B . 
     Referring now to  FIG. 3 , a diagram illustrating an example data file (X n ) and an associated list source code is shown. The data file (X n ) comprises a plurality of data packets (with only two data packets Dp 1 , Dp 2 , (being illustrated in  FIG. 3 ) each of which comprises one or more data segments, denoted by Message  1  and Message  2 , for example. Select data segments (Message  1 , Message  2 ) are encrypted using a key (e.g., with particular reference to  FIG. 5 ) that is smaller than the list source code, as indicated by “Aux. info.” The list source code, in some embodiments, can be implemented using standard linear codes. A linear code C, for example, can be represented as a linear subspace of F 2   n , composed of elements {0,1} n . For every linear code C, there exists a parity check matrix H and a generator matrix G which satisfy C={x∈F 2   n : H x =0} and C={G y : y∈{0,1} m }. As illustrated, the key (denoted as “Aux. info.” In  FIG. 3 ) is representative of only a fraction of the list source code. List source codes are key-independent, which allows content to be distributed when a key distribution infrastructure is not yet established. 
     As explained above in the Definitions section, a list source code includes codes that compress a source sequence below its entropy rate and are decoded to a list of possible source sequences instead of a unique source sequence. More detailed definitions and embodiments of list source codes and their fundamental bounds are provided herein. 
     In particular, a (2 nR , |X| nL , n)-list source code for a discrete memory-less source X comprises an encoding function ƒ n : X n →{1, . . . , 2 nR } and a list-decoding function g n : {1, . . . , 2 nR }→P(X n )/∅, where P(X n ) is a power set (i.e., collection of all subsets) of X n  and |g(w)|=|X| nL  ∀w∈{1, . . . , 2 nR }, and where L is a parameter that determines the size of a decoded list, with 0≤L≤1. A value of L=0, for example, corresponds to a traditional lossless compression, i.e., each source sequence is decoded to a unique sequence. On the other hand, a value of L=1 represents the trivial case when a decoded list corresponds X n . 
     An error results for a given list source code when a string generated by a source is not contained in a corresponding decoded list. The average probability of the error is given by:
 
 e   L (ƒ n   ,g   n )= Pr ( X   n   ∈/g   n (ƒ n ( X   n ))).
 
     Additionally, for a given discrete memory-less source X, a rate list size pair (R, L) is said to be achievable if for every δ&gt;0, 0&lt;ϵ&lt;1 and sufficiently large n there exists a sequence of (2 nRn , |X| nLn , n)-list source codes (ƒ n , g n ) such that R n &lt;R+δ, |L n −L|&lt;δ and e L     n   (ƒ n , g n )≤ϵ. A closure of all rate list pairs (R, L) is defined as a rate list region. 
     Referring now to  FIG. 4 , shown is a plot of an example rate list region for a given normalized list size L and a code rate R. A rate list function R(L) is representative of an infimum (i.e., greatest lower bound) of all rates R such that (R, L) is in a rate list region for a given normalized list size 0≤L≤1. For any discrete memory-less source X, the rate list function R(L) is bounded by R(L)≥H(X)−L log|X|. 
     For example, with δ&gt;0 and (ƒ n , g n ) a sequence of codes with a normalized list size L n  such that L n →L, 0&lt;ϵ&lt;1, and n is given by 0≤e L (ƒ n , g n )≤∈, then 
                 Pr   ⁡     [       X   n     ∈       ⋃     w   ∈     W   n         ⁢       g   n     ⁡     (   w   )           ]       ≥     Pr   ⁡     [       X   n     ∈       g   n     ⁡     (       f   n     ⁡     (     X   n     )       )         ]           ≥     1   -   ϵ             
where W n ={1, . . . , 2 nRn } and R n  is the rate of the code (ƒ n , g n ).
 
                       1   n     ⁢     log   ⁡     (       ∑     w   ∈     W   n         ⁢            g   n     ⁡     (   w   )              )         =       ⁢       1   n     ⁢     log   ⁡     (       2     nR   n       ⁢          X          nL   n         )                     =       ⁢         R   n     +       L   n     ⁢   log   ⁢        X            ≥                     ⁢         1   n     ⁢   log   ⁢            ⋃     w   ∈     W   n         ⁢       g   n     ⁡     (   w   )                ≥                     ⁢       H   ⁡     (   X   )       -   δ                 
if n≥n 0 (δ, ϵ, |X|). With the above holding any δ&gt;0, it follows that R(L)≥H(X)−L log|X| for all n given by 0≤e L (ƒ n , g n )≤ϵ.
 
     A rate list function R(L) bounded by R(L)≥H(X)−L log|X| can be achieved in accordance with multiple schemes. In a conventional scheme, for example, with a source X uniformly distributed in Fq, i.e., Pr(X=x)=1/q ∀x∈Fq, R(L)=(1−L)log q. The rate list function R(L) can be achieved with a data file X n =(X p , X s ), where X p  denotes a first p=n−[Ln] symbols of data file (X n ) and X s  denotes the last s=[Ln] symbols of data file (X n ), respectively. The data file (X n ) can be encoded, for example, by discarding X s  and mapping prefix of X p  to a binary codeword Y nr  of length nR=[n−[Ln] log q] bits. Additionally, the data file (X n ) can be decoded, for example, by mapping binary codeword Y nr  to X p . In doing so, a list of size q s , composed by X p , is computed with all possible combinations of suffixes of length s. It will be apparent that optimal list-source size is achieved with n sufficiently large and R˜=[n−[Ln] log q]. 
     The conventional scheme, although substantially capable of achieving a rate list function R(L) bounded by R(L)≥H(X)−L log|X|, is largely inadequate for highly secure applications. In particular, an eavesdropper that observes a binary codeword Y nR  can uniquely identify a first coset of source p symbols of an encoded source with uncertainty being concentrated over the last s sequential symbols. Ideally, assuming that all source symbols are of equal importance, uncertainty should be spread over all symbols of the encoded source. More specifically, for a given encoding function ƒ(X n ), an optimal security scheme would provide an uncertainty no greater than I(X i ; ƒ(X n ))≤ϵ&lt;&lt;log q for 1≤i≤n. An improved scheme, which is an asymptotically optimal scheme based upon linear codes that substantially achieves the uncertainty of the optimal security scheme, will be discussed in conjunction with process  500  of  FIG. 5 . 
     Referring now to  FIG. 5 , shown in an example encoding, encryption, and transmission process  500  according to the list source code techniques described above. A process  500  begins at processing block  510 , where a modulator system, which can be the same as or similar to modulator system  201  of  FIG. 2A , receives a data file (X n ). 
     In processing block  520 , the modulator system encodes the data file (X n ) in an encoder, like encoder circuit  210  of  FIG. 2A , using a list source code. In some embodiments, encoding the data file (X n ) using the list source code includes encoding the data file (X n ) with a linear code. In other embodiments, the list source code is a code that compresses a source sequence below its entropy rate. 
     The improved scheme, referred to briefly above in  FIG. 4 , is herein discussed further. In particular, X is an independent and identically distributed (i.i.d.) source (i.e., elements in the source sequence are independent of the random variables that came before it) with X∈X with entropy H(X), and S n  is a source code with an encoder s n : X n →F q   m     n    and a decoder r n : F q   m     n   →X n , wherein X n  is the data file. Additionally, C is a (m n , k n , d) linear code over F q  with an (m n −k n )×m n  parity check matrix H n  (i.e. c∈C H n c=0). Furthermore, k n =nL n  log|X|/log q for 0≤L n ≤1, L n →L as n→∞, and k n  is an integer according to some embodiments. 
     The improved scheme comprises an encoding process, wherein data file X n  is a sequence generated by a source with syndrome S m     n   =H n s n (X n ). In particular, each syndrome S m     n   =H n s n (X n ) is mapped to a distinct sequence of nR=[(m n −k n )log q] bits, denoted by Y nR . The improved scheme also comprises a decoding process, which will be discussed further in conjunction with process  600  of  FIG. 6 . Using the encoding, the improved scheme has been shown to achieve an optimal list-source tradeoff point R(L) for an i.i.d. source, where R is an ideal rate list function when S n  is asymptotically optimal for a given source X, i.e., m n /n→H(X)/log q. 
     In particular, with (1) a size of each coset corresponding to a syndrome S m     n     −k     n   , where S m     n     −k     n    is exactly q n , (2) a normalized list size L n  given by L n =(k n  log q)/(n log|X|)→L, and (3) m n /n=H(X)/log q+δ n , where δ n →0, it follows that (4) R=[(m n −k n )log q]/n=[(H(X)+δ n  log q)n−L n n log|X|]/n. The aforementioned has been shown to achieve a rate list function R(L) that is bounded substantially close to R(L)≥H(X)−L log|X| for a sufficiently large n. It is notable that if source X is uniform and without loss, where L n =L and L n  is an integer, substantially any message in the coset of C determined by S (1−L)n  of the improved scheme is equally likely. As such, H(X n |S (1−L)n ) will be equal to q Ln . 
     Accordingly, the improved scheme provides a systematic way of hiding information, specifically taking advantage of properties of an underlying linear code to make precise assertions regarding “information leakage” of the scheme. 
     In an embodiment, a plurality of encoded data files is generated in processing block  520 . In this embodiment, as described above in  FIG. 2A , a first encoded data file (i.e., encoded unencrypted data) is provided to an input of a transmitter, while a second encoded data file is provided to an input of an encryption circuit for encryption (processing block  530 ). The second encoded data file is ideally substantially smaller than the first encoded data file. In an alternative embodiment, a single encoded data file is generated in processing block  520 . 
     In processing block  530 , the modulator system encrypts a select portion of the data file (X n ) using a key to generate encoded encrypted data. As discussed above in conjunction with  FIG. 3 , the select portion of the data file (X n ), specifically data segments (e.g., Message  1 , Message  2  of  FIG. 3 ) is, in a preferred embodiment, encrypted with a key that is smaller than the list source code. It is to be appreciated that the process of encrypting a select portion of the data file (X n ) can occur before, during, or after transmission of the encoded unencrypted data in a processing block  550 , as will become more apparent below. As noted in the discussions related to  FIG. 2A , the select portion of the data file (X n ) to be encrypted may be received from an encoder circuit (like encoder circuit  210 ) or directly (in the alternative embodiment). In one embodiment, the select portion of the data file (X n ) encrypted is smaller than the encoded unencrypted data generated in processing block  520 . 
     Various approaches may be used for selecting the portion of the file to be encrypted. In one approach, for example, a portion of the file that has been deemed private may be encrypted. In another approach, a combination of messages may be encrypted. In still another approach, the file may be encrypted as a whole. A further approach includes encrypting a function of the original file, rather than just a segment (e.g. the hash of the file, coded versions of the file, etc.). Other strategies for selecting the portion of the file to be encrypted may alternatively be used. 
     In processing block  540 , the modulator system determines a transmission path and order of the data (i.e., encoded unencrypted data, encoded encrypted data, and key) to be transmitted. 
     In processing block  550 , the modulator system transmits the encoded unencrypted data, the encoded encrypted data, and optionally the key to a receiver (e.g., end user) at a destination location, wherein the receiver may be the same as or similar to demodulator system  202  of  FIG. 2B . In one approach, a substantial portion of the encoded unencrypted data is transmitted before the encoded encrypted data and the key are transmitted to the receiver. In some embodiments, the encoded unencrypted data cannot be decoded at the destination location until the encoded encrypted data has been received and decrypted by the receiver, wherein the receiver possesses the key. In other embodiments, the key is transmitted to the receiver before, during, or after transmission of the encoded unencrypted data to the receiver. In some embodiments, if the key is compromised during transmission of the encoded unencrypted data, only the transmission of the encoded encrypted data needs to be aborted. In particular, security of process  500  is not compromised if the transmission of the encoded unencrypted data is not aborted. 
     In alternative embodiments, the encoding and transmission process  500  of  FIG. 5  is applied as an additional layer of security to an underlying encryption scheme. In yet other embodiments, process  500  may be implemented as a two-phase secure communication scheme which, in one embodiment, uses list source code constructions derived from linear codes. The two-phase secure communication scheme can, however, be extended to substantially any list source code by using corresponding encoding/decoding functions in lieu of multiplication by parity check matrices. 
     In one embodiment of the two-phase secure communication scheme, it is assumed that a transmitter, which can be the same of or similar to transmitter  230  of modulator system  201  of  FIG. 2A , and a receiver, which can be the same as or similar to receiver  240  of demodulator system  202  of  FIG. 2B , have access to an encryption/decryption scheme (Enc&#39;, Dec&#39;). The encryption/decryption scheme (Enc&#39;, Dec&#39;) is used in conjunction with a key, wherein the encryption/decryption scheme (Enc&#39;, Dec&#39;) and the key are sufficiently secure against an eavesdropper. This embodiment can be, for example, a one-time pad. 
     In a first (pre-caching) phase (hereinafter denoted “phase I”) of the two-phase secure communication scheme, which can occur in a modulation system, the transmitter receives one or more of the following as inputs: (1) a source encoded sequence X n ∈F q   n , (2) parity check matrix H of a linear code in F q   n , (3) a full-rank k×n matrix D such that rank ([H T  D T ])=n, and (4) encryption/decryption functions (Enc&#39;, Dec&#39;). From the inputs, the transmitter is configured to generate S n−k =HX n  of an output thereof and transmit the output to the receiver, while maintaining a level of secrecy determined by an underlying list source code. List source codes provide a secure mechanism for content pre-caching when a key infrastructure has not yet been established. In particular, a large fraction of a data file can be list source coded and securely transmitted before termination of a key distribution protocol. Such is particularly useful in large networks with hundreds of mobile nodes, where key management protocols can require a significant amount of time to complete. 
     In a second (encryption) phase (hereinafter denoted “phase II”) of the two-phase secure communication scheme, which can also occur in a modulator system, the transmitter is configured to generate E k =Enc&#39;(DX n , K) from the inputs of phase I at an output thereof and transmits the output to the receiver. 
     In a receiving phase, which can occur in a demodulation system, the receiver is configured to compute DX n =Dec&#39;(E k ) and recover data file (X n ) from S n−k  and DX n . Assuming that (Enc&#39;, Dec&#39;) is secure, the above two-phase secure communication scheme actually reduces security of an underlying list source code. In practice, however, the effectiveness of the encryption/decryption functions (Enc&#39;, Dec&#39;) may depend on the key, wherein the key provides sufficient security for a desired application. Additionally, assuming that a data file (X n ) is uniform and i.i.d. in F q   n , Maximum Distance Separable (MDS) codes (i.e., linear [n, k]q-ary (n,M,d)-codes where M≤q n−d+1 ; q k ≤q n−d+1 ; and d≤n−k+1) can be used to make strong security guarantees. In such case, an eavesdropper that observes S n−k  cannot infer any information concerning any sets of k symbols of the data file (X n ). 
     Even if the key were compromised before phase II of the two-phase secure communication scheme, the data file (X n ) is still as secure as the underlying list source code. Assuming a computationally unbounded eavesdropper has perfect knowledge of the key, the best the eavesdropper can do is to reduce a number of possible data file (X n ) inputs to an exponentially large list until the last part of the data file is transmitted. As such, the two-phase secure communication scheme provides an information-theoretic level of security to the data file (X n ) up to the point where the last fraction of the data file (X n ), particularly the encoded unencrypted data and the encoded encrypted data, is transmitted. Additionally, if the key is compromised before phase II of the two-phase secure communication scheme, the key can be redistributed without retransmitting the entire encoded unencrypted data and the encoded encrypted data. In one embodiment, as soon as a key is reestablished, the transmitter can simply encrypt a remaining portion of the data file (X n ) in phase II of the two-phase secure communication scheme with a new key. 
     In contrast, if an initial seed is leaked to an eavesdropper in a conventional scheme (e.g., stream cipher based on a pseudo-random number generator), all portions of the data file (X n ) transmitted up until when the eavesdropper is detected are vulnerable. 
     In other embodiments, process  500 , in conjunction with the two-phase secure communication scheme, may comprise a tunable level of secrecy wherein size of the key is dependent upon a desired level of secrecy, wherein the size can be used to tune process  500  to the desired level of secrecy. In particular, an amount of data sent in phase I and phase II can be appropriately selected to match properties of an available encryption scheme, the key size, and a desired level of secrecy. Additionally, list source codes can be used to reduce a total number of operations required by the two-phase secure communication scheme by allowing encryption of a smaller portion of the message in phase II, specifically when an encryption procedure has a higher computational cost than the list-source encoding/decoding operations. In one embodiment, list source codes are used to provide a tunable level of secrecy by appropriately selecting a size of a list (L) of an underlying code, with the selection being used to determine an amount of uncertainty an adversary can have regarding a data file (X n ). In the two-phase secure communication scheme, a larger value of L can lead to a smaller list source coded data file (X n ) in phase I and a larger encryption burden in phase II of the scheme. 
     In yet other embodiments, list source codes can be combined with stream ciphers in the two-phase secure communication scheme. A data file (X n ), for example, can be initially encrypted using a pseudorandom number generator initialized with a randomly selected seed and then list source coded. The initial randomly selected seed can also be part of the encoded encrypted data in a transmission phase of the two-phase secure communication scheme. The arrangement has an advantage of augmenting security of an underlying stream cipher in addition to providing randomization to the list source coded data file (X n ). 
     Referring now to  FIG. 6 , shown in an example receiving, decoding and decryption process  600  according to the list source code techniques described herein. A process  600  begins at processing block  610 , where a demodulator system, which can be the same as or similar to demodulator system  202  of  FIG. 2B , receives encoded unencrypted data  612 , encoded encrypted data  614 , and a key  616 , which can be the same as or similar to the encoded unencrypted data, the encoded encrypted data, and the key from encoding and encryption process  500  of  FIG. 5 , from a modulator system, which can be the same as or similar to modulator system  201  of  FIG. 2A . It is to be appreciated that the process of receiving the encoded unencrypted data  612 , encoded encrypted data  614 , and key need not occur in any particular order. However, as mentioned above in conjunction with process  500  of  FIG. 5 , in one embodiment a large portion of the encoded unencrypted data is transmitted before the encoded encrypted data and the key are transmitted to the receiver. 
     In processing block  620 , the demodulator system decrypts the encrypted data with a key. As discussed above in conjunction with  FIG. 5 , the demodulator system may receive the key before, during or after receiving the encrypted data and/or the encoded data. 
     In a processing block  630 , the demodulator system decodes a data file ( ) using the encoded unencrypted data and the encoded decrypted data. In one embodiment, the demodulator system decodes the encoded unencrypted data and encoded decrypted data into a list of potential list source codes. The decoding can, for example, be achieved by the improved scheme discussed above in conjunction with  FIG. 5 . In a decoding process of the scheme, a binary codeword Y nR  is mapped to a corresponding syndrome S m     n     −k     n    to produce an output r n (x m     n   ) for each x m     n    in a coset of H n  corresponding to S m     n     −k     n   . Using the decoding processes, the improved scheme has been shown to achieve a rate list function R(L) bounded by R(L)≥H(X)−L log|X| for an i.i.d. source, when S n  is asymptotically optimal for a given source X, i.e. m n /n→H(X)/log q. 
     In the embodiment discussed above, the demodulator system can extract a data file ( ) from the list of potential list source codes. However, it is to be appreciated that alternative methods apparent to those of skill in the art can also be used. In some embodiments, the data file (^X n ) is the same as, or substantially similar to, data file (X n ) of process  500 . In particular, the demodulation system can extract the ( ) using the improved scheme. 
     Specifically, with knowledge of a syndrome of a data file (X n ), the data file (X n ) can be extracted in several ways. In one embodiment, an approach is to find a k×n matrix D having a full rank such that the rows of D and H form a basis of F q   n . Such k×n matrix can be found, for example, using a Gram-Schmidt process (i.e. method for orthonormalising a set of vectors in an inner product space) with rows of H serving as a starting point. Element T Ln  of the Gram-Schmidt process equation shown below is computed where T Ln =DX n  and subsequently transmitted to a receiver, which can be the same as or similar to a receiver  242  of demodulator system  202  of  FIG. 2B . 
     
       
         
           
             
               
                 
                   ( 
                   
                     
                       
                         H 
                       
                     
                     
                       
                         D 
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   X 
                   n 
                 
               
               = 
               
                 ( 
                 
                   
                     
                       
                         S 
                         
                           
                             ( 
                             
                               1 
                               - 
                               L 
                             
                             ) 
                           
                           ⁢ 
                           n 
                         
                       
                     
                   
                   
                     
                       
                         T 
                         
                           L 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                       
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
     
     The receiver is configured to extract a data file ( ), which according to some embodiments is representative of the data file (X n ) from a list of potential list source codes. The above method allows list source codes to be deployed in practice using well known linear code constructions, such as Reed-Solomon or low-density parity-check (LDPC), for example. 
     Additionally, the method is valid for general linear codes and holds for any pair of full rank matrices H and D with dimensions (n−k)×n and k×n, respectively, such that rank([H T  D T ] T )=n. In particular, the method makes use of known linear code constructions to design secrecy schemes. 
     Information-Theoretic Metric 
     An exemplary information-theoretic metric (ϵ-symbol secrecy (μ ϵ )) for characterizing and optimizing the system and associated methods disclosed above is also herein provided. In particular, ϵ-symbol secrecy (μ ϵ ) characterizes the amount of information leaked about specific symbols of a data file (X n ) given an encoded version of the data file (X n ). Such is especially applicable to secrecy schemes that do not provide absolute symbol secrecy (μ 0 ), such as the improved scheme and the two-phase secure communication scheme discussed above. 
     Generally, the metrics ϵ-symbol secrecy (μ ϵ ) and absolute symbol secrecy (μ 0 ) can be used in conjunction with process  500  and process  600  for achieving a desired level of secrecy. Absolute symbol secrecy (μ 0 ) and ϵ-symbol secrecy (μ ϵ ) can be defined as follows: 
     Absolute symbol secrecy (μ 0 ) of a code C n  is represented by: 
                 μ   0     ⁡     (     n     )       =     max   ⁢       {           t   n     :     I   ⁡     (       X     (   𝒥   )       ;     Y     nR   n         )         =   0     ,     ∀     𝒥   ∈       𝒥   n     ⁡     (   t   )             }     .             
Absolute symbol secrecy (μ 0 ) of a sequence of codes C n  is represented by:
 
μ 0 =lim inf n→∞ μ 0 (   n ).
 
In contrast, ϵ-symbol secrecy (μ ϵ ) of a code C n  is represented by:
 
                 μ   ϵ     ⁡     (     n     )       =     max   ⁢       {       t   n     :         1   t     ⁢     I   ⁡     (       X     (   𝒥   )       ;     Y     nR   n         )         ≤     ϵ   ⁢           ⁢     ∀     𝒥   ∈       𝒥   n     ⁡     (   t   )                 }     .             
Additionally, ϵ-symbol secrecy (μ ϵ ) of a sequence of codes C n  is represented by:
 
     
       
         
           
             
               μ 
               ϵ 
             
             = 
             
               
                 
                   lim 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   inf 
                 
                 
                   n 
                   → 
                   ∞ 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   μ 
                   ϵ 
                 
                 ⁡ 
                 
                   ( 
                   
                     n 
                   
                   ) 
                 
               
             
           
         
       
         
         
           
             where ϵ&lt;H(X). 
           
         
       
    
     Given a data file X n  and its corresponding encryption Y, ϵ-symbol secrecy (μ ϵ ) can be computed as a largest fraction t/n such that at most ϵ bits can be inferred from any t-symbol subsequence of data file X n . 
     C n  can be either a code or a sequence of codes (i.e. list source code) for a discrete memory-less source X with a probability distribution p(x) that achieves a rate list pair (R, L). Additionally, Y nRn  is a corresponding codeword for a list-source encoded data file ƒ n (X n ) created by C n . Furthermore, I n (t) is a set of all subsets of {(1, . . . , n] of size t, i.e., J∈I n (t) J⊆{1, . . . , n} and |J|=t. Additionally, X (J)  is a set of symbols of data file X n  indexed by elements in set J⊆{1, . . . , n}. 
     It is assumed that a passive, but computationally unbounded, eavesdropper only has access to the list-source encoded message ƒ n (X n )=Y nRn . It is also assumed that based on an observation of Y nRn  the eavesdropper will attempt to determine what is in data file X n . In addition, it is assumed that source statistics and list source code used are universally known, i.e., eavesdropper A has access to a distribution px n (X n ) of symbol sequences produced by a source and C n . 
     An amount of information an eavesdropper can gain about particular sequence of source symbols (X (J) ; Y nRn ) by observing a list-source encoded message (Y nR     n   ) can be computed or mechanical information I have list on previous page. In particular, for ϵ=0, a meaningful bound on what is a largest fraction of input symbols that is perfectly hidden can be computed. 
     For example, a list source code C n  capable of achieving a rate-list pair (R, L) comprises an ϵ-symbol secrecy (μ ϵ ), of 
             0   ≤     μ   ∈     ≤     min   ⁢       {       L   ⁢           ⁢   log   ⁢          X            H   ⁡     (   X   )       -   ϵ         ,   1     }     .             
In particular, with
 
                 μ   ϵ     ⁡     (     C   n     )       =     μ     ϵ   ,   n                               I   ⁡     (       X     (   𝒥   )       ;     Y     nR   n         )       =       ⁢       H   ⁡     (     X     (   𝒥   )       )       -     H   ⁡     (       X     (   𝒥   )       |     Y     nR   n         )                     =       ⁢         n   ⁢           ⁢     μ     ϵ   ,   n       ⁢     H   ⁡     (   X   )         -     H   ⁡     (       X     (   𝒥   )       |     Y     nR   n         )         ≤                     ⁢     n   ⁢           ⁢     μ     ϵ   ,   n       ⁢   ϵ             .     
     ⁢   Therefore     ,     
     ⁢         μ     ϵ   ,   n       ⁡     (       H   ⁡     (   X   )       -   ϵ     )       ≤       1   n     ⁢     H   ⁡     (       X     (   𝒥   )       |     Y     nR   n         )         ≤       L   n     ⁢   log   ⁢          x        .               
an ϵ-symbol secrecy (μ ϵ ) of
 
             0   ≤     μ   ∈     ≤     min   ⁢     {       L   ⁢           ⁢   log   ⁢          X            H   ⁡     (   X   )       -   ϵ         ,   1     }             
is achieved by taking n→∞.
 
     An upper-bound for a maximum average amount of information that an eavesdropper can gain from a message encoded with a list source code C n  with symbol secrecy μ ϵ,n  can also be computed. In particular, for a list source code C n  discrete memory-less source X, and any ϵ such that 0≤ϵ≤H(X), 
                   1   n     ⁢     I   ⁡     (       X   n     ;     Y     nR   n         )         ≤       H   ⁡     (   X   )       -       μ     ϵ   ,   n       ⁡     (       H   ⁡     (   X   )       -   ϵ     )           ,         
where μ ϵ,n =μ ϵ (C n ).
 
     Alternatively, if μ ϵ,n =t/n, JϵI n (t) and J′={1, . . . , n}\J, then 
     
       
         
           
             
               
                 
                   1 
                   n 
                 
                 ⁢ 
                 
                   I 
                   ⁡ 
                   
                     ( 
                     
                       
                         X 
                         n 
                       
                       ; 
                       
                         Y 
                         
                           nR 
                           n 
                         
                       
                     
                     ) 
                   
                 
               
               ≤ 
               
                 
                   t 
                   n 
                 
                 ⁢ 
                 
                   ( 
                   
                     ϵ 
                     + 
                     
                       
                         1 
                         t 
                       
                       ⁢ 
                       
                         I 
                         ⁡ 
                         
                           ( 
                           
                             
                               X 
                               
                                 ( 
                                 𝒥 
                                 ) 
                               
                             
                             ; 
                             
                               
                                 Y 
                                 
                                   nR 
                                   n 
                                 
                               
                               | 
                               
                                 X 
                                 
                                   ( 
                                   𝒥 
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
               
               ≤ 
               
                 
                   
                     μ 
                     
                       ϵ 
                       , 
                       n 
                     
                   
                   ⁢ 
                   ϵ 
                 
                 + 
                 
                   
                     
                       ( 
                       
                         n 
                         - 
                         t 
                       
                       ) 
                     
                     n 
                   
                   ⁢ 
                   
                     H 
                     ⁡ 
                     
                       ( 
                       X 
                       ) 
                     
                   
                 
               
             
             = 
             
               
                 H 
                 ⁡ 
                 
                   ( 
                   X 
                   ) 
                 
               
               - 
               
                 
                   
                     μ 
                     
                       ϵ 
                       , 
                       n 
                     
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         H 
                         ⁡ 
                         
                           ( 
                           X 
                           ) 
                         
                       
                       - 
                       ϵ 
                     
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
     A rate-list function (R, L) with ϵ-symbol secrecy (μ ϵ ) can be related to the upper bound if list source code C n  achieves a point (R′, L) with 
               μ   ϵ     =     L   ⁢           ⁢   log   ⁢          X            H   ⁡     (   X   )       -   ϵ               
for some ϵ, where
 
               R   i     =         lim     n   →   ∞       ⁢       1   n     ⁢     H   ⁡     (     Y     nR   n       )       ⁢     R   ′         =     lim   ⁢           ⁢   n   ⁢     1   n     ⁢     H   ⁡     (     Y     nR   n       )                 
and R′=R(L).
 
With δ&gt;0 and n sufficiently large,
 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       n 
                     
                     ⁢ 
                     
                       H 
                       ⁡ 
                       
                         ( 
                         
                           Y 
                           
                             nR 
                             n 
                           
                         
                         ) 
                       
                     
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         1 
                         n 
                       
                       ⁢ 
                       
                         I 
                         ⁡ 
                         
                           ( 
                           
                             
                               X 
                               n 
                             
                             ; 
                             
                               Y 
                               
                                 nR 
                                 n 
                               
                             
                           
                           ) 
                         
                       
                     
                     ≥ 
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     
                       H 
                       ⁡ 
                       
                         ( 
                         X 
                         ) 
                       
                     
                     - 
                     
                       
                         μ 
                         ϵ 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             H 
                             ⁡ 
                             
                               ( 
                               X 
                               ) 
                             
                           
                           - 
                           ϵ 
                         
                         ) 
                       
                     
                     + 
                     δ 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       H 
                       ⁡ 
                       
                         ( 
                         X 
                         ) 
                       
                     
                     - 
                     
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       log 
                       ⁢ 
                       
                          
                         x 
                          
                       
                     
                     + 
                     
                       δ 
                       . 
                     
                   
                 
               
             
           
         
       
     
     As a result, R′≤H(X)−L log|X|. In general, the value of n may be chosen according to the delta in the above equation and will depend upon the characteristics of the source. In practice, the length of the code will be determined by security and efficiency constraints. 
     In some embodiments, uniformly distributed data files (X n ) using MDS codes have been shown to achieve ϵsymbol secrecy (μ ϵ ) bounds. In other embodiments, absolute symbol secrecy (μ 0 ) can be achieved through use of the improved scheme, as disclosed above, with an MDS parity check matrix H and a uniform i.i.d. source X in F q . With the source X being uniform and i.i.d., no source coding is necessary. 
     In particular, if H is a parity check matrix of an (n, k, d) MDS and a source X is uniform and i.i.d., the improved scheme is capable of achieving an upper bound μ 0 =L, where L=k/n. For example, if (1) H is a parity check matrix of a (n, k, n−k+1) MDS code C over F q , (2) x∈C, and (3) a set J∈I n (k) of k positions of x (denoted by x (J) ) are fixed, for any other codeword in z∈C we have z (J)  x (J)  since the minimum distance of C is n−k+1. Additionally, since C (J) {x (J) ∈F k   q : xϵC), |C (J) |=|C|=q k . Accordingly, C (J)  contains all possible combinations of k symbols. Since the aforementioned holds for any coset of H, an upper bound of μ 0 =L is achieved where L=k/n. 
     List Source Codes for General Source Models 
     Information-theoretic approaches to secure cryptosystems, particularly secrecy, traditionally make one fundamental assumption, namely that a data file (X n ) (i.e., plaintext source), a key, and noise of a physical channel (e.g., communication channel) over which an encoded and/or encrypted form of the data file (X n ) and the key are transmitted, are substantially uniformly distributed. Here, uniformity is used to indicate that the file, key, or physical channel has equal or close to equal likelihood of all possible different outcomes. The uniformity assumption implies that, before the message is sent, the attacker has no reason to believe that any possible message, key, or channel noise is more likely than any other possible message, key, or channel noise. In practice, the data file (X n ), the key, and the noise of the physical channel are not always substantially uniformly distributed, specifically in secure cryptosystems. For example, user passwords are rarely chosen perfectly at random. Additionally, packets produced by layered-protocols are not uniformly distributed, i.e., they usually do not contain headers that follow a pre-defined structure. In failing to take into account non-uniform distributions (hereinafter, “non-uniformity”), security of a supposedly secure cryptosystem can be significantly decreased. 
     Non-uniformity, in general, poses several threats. In particular, non-uniformity (1) significantly decreases an effective key length of any security scheme, and (2) makes a secure cryptosystem vulnerable to correlation attacks. The foregoing is most severe, for example, when multiple, distributed correlated sources are being encrypted since one source might reveal information about the other. As a result, in order to guarantee security in distributed data collection and transmission, non-uniformity should be accounted for in secure cryptosystems. 
     The secrecy scheme systems and associated methods for enabling secure communications described above assume uniformization, with the uniformization being performed as part of compression (i.e., encoding and/or encrypting) of a data file (X n ), and are therefore most suitable for i.i.d. sources. The compression, for example, does not lead to sufficient guarantees in the way of uniformization. Even slight deviations from uniformization can have considerable effects. As a result, for more general sources (i.e., non-i.i.d. source models), slightly different secrecy scheme systems and associated methods should be used. In particular, using the above-described systems and associated methods with non-i.i.d. sources (e.g., a first order Markov sequence where probability distribution for an nth random variable is a function of a previous random variable in the sequence) can result in a more convoluted analysis since multiple list source encoded messages (i.e., encoded messages resulting from non-i.i.d. source models) can reveal information about each other. If the encoding and encryption process  500  of  FIG. 5  were to be applied over multiple blocks of source symbols (i.e., data file(s) (X n )) in a non-i.i.d. source, for example, and the encoded and encrypted multiple blocks of source symbols are decoded and decrypted according to process  600  of  FIG. 6 , for example, the list of potential list source codes from extracted data file(s) ( ), which according to some embodiments is representative of the data file(s) (X n ) from a list of potential list source codes, will not necessarily grow if the multiple blocks of source symbols are correlated. 
     For example, given an output X=X 1 , . . . , X n  of n correlated source symbols (i.e., data file(s) (X n )), and using the improved scheme described above, an eavesdropper can observe a coset valued sequence of random elements {H(sn(X))}, with H being a parity check matrix. Since X is a correlated source of symbols, there is no reason to expect that a coset valued sequence will not be correlated. For example, if X forms a Markov chain, the coset valued sequence will be function of the Markov chain. Although the coset valued sequence will not, in general, form a Markov chain itself, the coset valued sequence will still comprise correlations. These correlations can reduce size of a list of potential list source codes (e.g., from an extracted data file(s) ( )) that an eavesdropper must search through in determining a representative data file(s) (X n ) and, consequently, decrease the effectiveness of the improved scheme. Reducing or eliminating these correlations, for example, can counteract the decrease in effectiveness of the improved scheme. 
     One method for reducing correlations is to use large block lengths of source symbols as an input to the list-source code. This requires an increase of the length of the message used for encryption. For example, if X 1 , X 2 , . . . , X N  are N blocks of source symbols produced by a Markov source (i.e., a stationary Markov chain M, together with a function ƒ: S→Γ that maps states S in the Markov chain to letters in a fine alphabet Γ) such that X i ∈ data file (X n ) and p(X 1 , . . . , X N )=p(X 1 )p(X 2 |X 1 ) . . . p(X N |X N-1 ), instead of encoding each block individually, a transmitter, which can be the same as or similar to transmitter  230  of  FIG. 2A , can compute a plurality of binary codewords Y nNR , where Y nNR =ƒ(X 1 , . . . , X N ). This approach (hereinafter, “non-i.i.d. source model approach”) has a disadvantage of requiring long block lengths and a potentially high implementation complexity. However, the non-i.i.d. source model approach does not necessarily have to be performed independently over multiple blocks of source symbols (i.e., processing can be performed in parallel. An alternative non-i.i.d. source model approach for reducing coset valued sequence correlations of source symbols, particularly when individual sequences X i  are already substantially large, is to define Y 1 =ƒ(X 1 , X 2 ), Y 2 =ƒ(X 2 , X 3 ), . . . , and so forth. Thus, in one approach, a security scheme may be used on a single message at a time, so that encryption and encoding can be done in a single step. In another approach, the scheme may be used on a combination of multiple messages that are encrypted together, so that both encoding and encryption are done simultaneously. 
     In another approach, when probabilistic encryption is required over multiple blocks of source symbols, source encoded symbols (e.g., of the improved scheme) can be combined with an output of a pseudorandom number generator (PRG) before being multiplied by parity check matrix H to provide necessary randomization of an output. In another approach, an initial seed of the PRG can be transmitted to a receiver, which can be the same as or similar to a receiver  240  of  FIG. 2B , in phase II of the two-phase communication scheme. 
     It is to be appreciated that although the secrecy scheme systems and associated methods for enabling secure communications described in conjunction with  FIGS. 1-6  are stated at being most suitable for i.i.d. source models, for example, the secrecy scheme systems and associated methods can be applied to non-i.i.d. source models. 
     In at least one embodiment, techniques and features described herein may be used to allow a large portion of a file (e.g., a list coded unencrypted portion) to be securely distributed and cached in a network. The large file portion will not be able to be decoded/decrypted until both the encrypted portion of the file and the key are received. In this manner, much of the content of the file can be distributed (e.g., pre-caching of content) before the keys are distributed, which can be advantageous in many different scenarios. 
     Referring to  FIG. 7 , shown is a block diagram of an example processing system  700  that may be used to implement the exemplary systems and associated methods discussed above in conjunction with  FIGS. 1-6 . In one embodiment, the processing system  700  may be implemented in a mobile communications device, for example, but it is not so limited. 
     The processing system  700  may, for example, comprise processor(s)  710 , a volatile memory  720 , a user interface (UI)  730  (e.g., a mouse, a keyboard, a display, touch screen and so forth), a non-volatile memory block  750 , and an encoding/encryption/decryption/tuning block  760  (collectively, “components”) coupled to a BUS  740  (e.g., a set of cables, printed circuits, non-physical connection and so forth). The BUS  740  can be shared by the components for enabling communication amongst the components. 
     The non-volatile memory block  750  may, for example, store computer instructions, an operating system and data. In one embodiment, the computer instructions are executed by the processor(s)  710  out of volatile memory  720  to perform all or part of the processes described herein (e.g., processes  500  and  600 ). The encoding/encryption/decryption/tuning block  760  may, for example, comprise a list-source encoder, encryption/decryption circuitry, and security level tuning for performing the systems, associated methods, and processes described above in conjunction with  FIGS. 1-6 . 
     It is to be appreciated that the various illustrative blocks, modules, processing logic, and circuits described in connection with processing system  700  may be implemented or performed with a general purpose processor, a content addressable memory, a digital signal processor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), any suitable programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof, designed to perform the functions described herein. 
     The techniques described herein are not limited to the specific embodiments described. Elements of different embodiments described herein may be combined to form other embodiments not specifically set forth above. Other embodiments not specifically described herein are also within the scope of the claims. 
     For example, it is to be appreciated that the processes described herein (e.g., processes  500  and  600 ) are not limited to use with the hardware and software of  FIG. 7 . In particular, the processes may find applicability in any computing or processing environment and with any type of machine or set of machines that is capable of running a computer program. In some embodiments, the processes described herein may be implemented in hardware, software, or a combination of the two. In other embodiments, the processes described herein may be implemented in computer programs executed on programmable computers/machines that each includes a processor, a non-transitory machine-readable medium or other article of manufacture that is readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and one or more output devices. Program code may be applied to data entered using an input device to perform any of the processes described herein and to generate output information. 
     It is also to be appreciated that the processes described herein are not limited to the specific examples described. For example, the processes described herein (e.g., processes  500  and  600 ) are not limited to the specific processing order of  FIGS. 5 and 6 . Rather, any of the processing blocks of  FIGS. 5 and 6  may be re-ordered, combined or removed, performed in parallel or in serial, as necessary, to achieve the results set forth above. 
     Processing blocks in  FIGS. 5 and 6 , for example, may be performed by one or more programmable processors executing one or more computer programs to perform the functions of the system. All or part of the system may be implemented as, special purpose logic circuitry (e.g., an FPGA (field programmable gate array) and/or an ASIC (application-specific integrated circuit)). 
     Having described preferred embodiments, which serve to illustrate various concepts, structures and techniques that are the subject of this disclosure, it will now become apparent to those of ordinary skill in the art that other embodiments incorporating these concepts, structures and techniques may be used. Accordingly, it is submitted that that scope of the patent should not be limited to the described embodiments but rather should be limited only by the spirit and scope of the following claims.