Abstract:
We propose an encryption scheme which uses steganography. The encryption algorithm encrypts messages by embedding them in a data stream in such a way that an adversary cannot get information about the messages. Since the embedding is the only computation requires this scheme is optimal in computational efficiency. However, since the size of the data stream is large, this scheme is most beneficial when the cost of bandwidth is less expensive than the cost of computation. The scheme embeds the message as specified by a pseudo random generator. Therefore, the scheme&#39;s security is based on a new weak assumption base on the pseudo random generator which we introduce.

Description:
FIELD OF THE INVENTION  
       [0001]     The presently disclosed system and method relate to the fields of cryptography, steganography and secure communications. In particular, by virtue of present disclosure we accordingly propose a new field which we call analog cryptography.  
       BACKGROUND OF THE INVENTION  
       [0002]     Most encryption schemes are based on some computational assumptions (The only encryption scheme which is not based on any assumption requires the communicating parties to continuously meet and establish a private key). Some of the assumptions are quite strong and might turn out to be false. For example, the RSA encryption scheme is based on the assumption that factoring large composite numbers is computationally infeasible in a reasonable amount of time. However, it was shown that using quantum computers it is possible to factor, making this assumption false with regard to quantum computers. Recently, with the advancement in quantum computation technology, the threat to encryption schemes based on the hardness of factoring assumption increases. Therefore, it is of interest to base encryption schemes on the weakest assumption possible.  
         [0003]     Another important feature in encryption schemes is their computational efficiency. Even the most practical encryption schemes usually are quite costly and require at least one exponentiation. In the scheme presented here we are able to reduce the computation to the minimum. The only computation we require in order to create the ciphertext is embedding the bits of the message in a larger data stream. We are able to achieve this increased efficiency by utilizing bandwidth. In particular, to encrypt the message we embed it into a larger data stream in such a way that an adversary cannot find the embedded message. This is particularly beneficial when the cost of bandwidth is less expensive relative to the cost of computation.  
       BRIEF SUMMARY OF THE INVENTION  
       [0004]     We present an encryption scheme optimal in its computational efficiency which utilizes bandwidth as a resource. This scheme uses steganography in a novel way enabling us to use a weaker than ordinary computational assumption. 
     
    
     DETAILED DESCRIPTION  
       [0000]     The Main Idea:  
         [0005]     The encryption scheme we propose uses steganography in a novel way. Usually, steganography is the art and science of embedding a message in data so that an adversary will not be able to tell whether the data has a message embedded in it or not. Typically a user will use data available from an outside source to embed the message. Therefore, the user will not have the privilege to choose the type of data used. For example, a worker in an office might want to send personal notes to another worker embedding the messages in the data files already distributed at the work place.  
         [0006]     Our encryption scheme uses steganography—embedding a message in data—in a novel way, as encryption. Therefore, unlike other steganographic schemes it is not relevant to our scheme whether the adversary will be able to detect the existence of a message in the data. In fact, the data is sent only for the purpose of embedding, so all data streams will have messages embedded in them. Moreover, the data in our scheme could be created especially for the purpose of embedding messages in it. Therefore, we can choose the data yielding the highest security and efficiency. As in all private key encryption schemes, the message will be embedded in the data so that an adversary who reads the data will not be able to learn information about the message without knowledge of the secret key.  
         [0007]     The data we choose to use for our scheme is data produced from scanning color pictures, or data produced from color pictures taken on a digital camera. The reason this data is most appropriate for our use is because in digital data encoding colors there are usually several data streams representing the same visual image. If these data streams representing the same image cannot be distinguished, the message can be embedded in on such a stream which is randomly chosen from the set. We are then exploiting the entropy available in such data to communicate specific messages without an eavesdropper being able to figure out what the messages are. Indeed statistical tests which are typically used to break steganographic schemes do not perform well in breaking data scanned from color pictures. Moreover, since in our scheme the sender creating the ciphertext can choose which pictures to scan, he can make sure to pick the pictures with the most variability in color which decreases the possibility of finding any statistical patterns in the data.  
         [0008]     The scheme works according to the following steps. The sender and receiver establish an initial secret key. The secret key will contain the information of how the message is embedded in the data. In addition, it will contain a seed for a pseudo random generator which will specify where in the data stream the bits should be embedded.  
         [0000]     Details of Embedding Methods:  
         [0009]     There are several ways to embed a message into data. One good way is to embed it in the low order bits of the data. The size of the message will be small relative to the data. Therefore, not all the low order bits will have messages embedded in them and only a small fraction of them will. This again reduces the possibility of performing statistical attacks on the data, since most statistical attacks succeed only when a large fraction of the bits are used for embedding. In order to decide where in the data to embed the bits we can use a weak pseudo random generator.  
         [0010]     We suggest another method of embedding the messages in pictorial data—embedding the message into the picture itself. For example, it is possible that the domain of pictures will depict people with some facial expressions. The secret key will specify which facial expression is the one which will encode the message as well as where to find the pictographic image bearing this encoded message. One possibility is an expression such as satisfaction. Thus in order to encode the bit zero the picture will denote satisfied people and to encode one it will depict an expression of lack of satisfaction. Since bandwidth is not of concern these pictures can be mixed with other pictures which depict other facial expressions so that an adversary will not be able to guess what the key is. It may be useful in a variation of this idea to use other images of people containing the same expression features as the one bearing the encoded data. (Again realizing bandwidth is not a limiting factor). In this variation, the facial expressions used to encode the messages are satisfaction, drowsiness and possibly other appropriately compatible facial gestures. It would be possible in the previously encoded message to transmit through one or more of the gestures the location data (such as which specific image in a sequence or the coordinates of) the image bearing the encoded message. It would be possible in this scenario to include noise, which is indistinguishable from real data. This noise could consist of other apparently identical satisfied people where the satisfaction feature is used to send encoded messages which determine which people among those which are satisfied actually possess legitimate versus illegitimate (decoy) encoded messages which as a result make the system extremely noisy and random to a would-be attacker. The satisfaction and drowsiness features on other images could, for example, contain the actual encoded message. Thus, it may be possible in this scheme to leverage the use of available bandwidth to add a significantly large amount of randomness, in this way (by obfuscating the true message bearing image segments using this type of random noise). In addition, the adversary will not be able to run any statistical test on the data since currently artificial intelligence is not yet capable of detecting facial expressions as well as people can.  
         [0000]     Details of Pseudo Random Generator:  
         [0011]     Let the data stream have w words in it, s 0 , s 1 , . . . , s w-1  (w is large enough as described later but small enough so that it is within the processing capability of the sender and receiver). For example, a word in the stream can be the digital representation of a scanned picture. The initial seed that the two parties share in their secret key is of length c log w, for some constant c such that wC is not feasibly long (as described below). View this seed as partitioned into c equal length blocks of length log w each −K=K 0 K 1  . . . K c-1 . This seed specifies where the message is to be embedded in the sequence of words in the data stream. When the i th  message is to be sent it is placed in the following location in the word:  
         (       ∑     j   =   0       c   -   1       ⁢       K   j     ⁢     i   j         )     ⁢     mod   ⁢   w         
 
         [0012]     Someone who does not know the key K will have to essentially guess each of w c  possible keys and try them all to see which one holds the new secret key. We choose c so that this computation is not feasible for practical purposes.  
         [0013]     This is a much weaker pseudo random generator than the one which is obtained from one way function assumption. The reason we are able to rely on a much weaker assumption is because the data itself has some randomness. Our scheme is computationally secure in the following sense. If D is the length of the data stream, we consider O(D) to be feasible computation whereas O(Dˆ2) to be infeasible.  
         [0000]     Alternative Embodiment for Analog Steganographic Embedding of Messages  
         [0014]     In an alternative embodiment it may be possible to devise a similar scheme to that proposed, however, it would be a further objective to utilize the inexpensive costs of bandwidth in order to add a high degree of statistical noise. In this regard it would be an additional objective to prevent the adversary from being able to detect the presence of an embedded message. In this approach, we rely on two primary assumptions: 
    1.That the ability of computational means employing AI techniques to discover the presence of analog data within otherwise very noisy analog content to be inferior to that of a human.     2.That we can exploit a sufficiently abundant degree of bandwidth needed to ensure that another human (adversary) will not be capable of scanning the volume of analog contents which may contain the analog message.    
 
         [0017]     In one final variation of this idea, we additionally seek to leverage the inherent noisiness of the analog data in which the analog encoded messages are embedded in order to not only hide the locations or where analog encoded messages are hidden but further so doing to make it possible for analog encoding of these messages to be performed in an automated fashion. For example, one could easily imagine pictographic or videographic contents in which there are so many unusual or anomalous analog features or actions that the inherent noisiness would make it difficult to detect which, if any, analog feature(s) contained an encoded message. In this example this inherent noisiness could be further exploited so as to nearly maximally increase entropy to the point that any statistical patterns which could be detected by an adversary would possess such a low degree of statistical confidence as to make the data of little value. We can achieve this objective by maximally spreading around among a maximally large number and diversity the selection and type of analog components containing a given encoded message.  
         [0000]     Additional Considerations  
         [0000]     It is worthy to note the following:  
         [0018]     1.1. Co-pending patent application entitled “A Multi-User Secure System Utilizing Shared Keys”, by the same authors as the present patent application includes under “Detailed Description” a section describing in high level of detail how a preferred analog cryptographic scheme which is well suited for the application it is used for, i.e., for purposes of key replenishment of shared set keys. It is, however, obvious that such a scheme could be usable within a much more broad-based context as well as being very similar to the methods as herein described. Therefore in order to further elucidate these methods as presently claimed we hereby incorporate by reference co-pending patent application entitled, “A Multi-User Secure System Utilizing Shared Keys”. Conversely, it can be amply appreciated that the methods for analog encrypted data transmission and delivery (as they are presently herein suggested to apply to all kinds of data) would consitute viable alternative key replenishment methodologies (among still others) to preferred embodiment as disclosed in the above referenced patent application.  
         [0019]     2.The present scheme is applicable to any/all kinds of data. However, in the future it is anticipated for a variety of reasons that the relative computational costs of encryption will increase while (as suggested bandwidth costs will increasingly diminish by comparison). This suggests the increasing potential need for high bandwidth, low computational cost encryption and particularly a type of encryption which incorporates forms of complexity which do not evenly scale with increases in processing speed (as is the case with standard factor-based public key encryption).  
         [0020]     3.Quantum Cryptography—As quantum cryptography becomes a practical reality for photonic-based transmissions a need will also arise for fast, efficient yet highly secure encryption methods through which the encryption keys can be securely transmitted in advance of transmission. Once the keys are present (and the fact of their non-interception securely verified) it will be important for the sake of computational efficiency and speed for the scheme to enable the recipient to easily decrypt the message. In addition, once quantum cryptoanalysis becomes a practical realization the use of fundamentally alternative methods such as the analog encryption scheme herein proposed (versus digital factor-based ciphers) will be particularly needed.  
       CONCLUSION  
       [0021]     The scheme proposed here requires less computation than other schemes which use standard pseudo random generators. However, it does rely on the ability to send large amounts of data in an efficient manner. This quite likely is a reasonable assumption since bandwidth is turning out to be inexpensive whereas computation is still costly. In addition, scanning pictures is a task which is easy and inexpensive.