Fluctuation and Noise Letters Vol. 4, No. 2 (2004) C1 C5 c World Scientific Publishing Company NON-REKLE DT ENCRYPTION WITH CLSSICL INFORMTION LSZLO. KISH and SWMINTHN SETHURMN Texas &M University, Department of Electrical Engineering College Station, TX 77843-3128, US Received 12 May 2004 Revised 9 June 2004 ccepted 9 June 2004 Secure encryption of data is one of the most important parts of information technology and major concern of data security, military, defense and homeland security applications. The main aim of the paper is to propose a new way of approach to encryption. We propose a new possible approach [1] to encryption, which could be a fast, simple, inexpensive, robust, flexible, and mobile way of data encryption for absolutely secure data transmission by using classical digital information. The Eavesdropper is allowed to know the received signal thus the method has a higher level of protection than that of quantum encryption. Factorization algorithms do not help to break the code. Proper scrambling operators, which are necessary for the method, are study of current research. Keywords: Classical information; encryption. 1. Introduction Secure encryption of data is one of the most important parts of information technology and major concern of data security, military, defense and homeland security applications. So far, there is no secure practical way to encrypt the data. Depending on the type of encryption, if the Third Party (Eavesdropper) acquires enough knowledge about how the encryption is made and/or about the key, the Eavesdropper can decode the encrypted message. The general opinion is that classical information systems, either digital or analog, are not suitable for absolutely secure data encryption. This is the reason why governments, defense and funding agencies have been spending billions of dollars for the research of quantum encryption which has the potential to reach absolutely secure encryption. However, the performance of data transfer via quantum encryption is very poor, expensive and extremely slow. The reason for these deficiencies is the fact that quantum encryption requires generating, handling and detecting of single photons (or other particles) and that requirement implies short transfer distance (<one mile) or the need of a large number of repeaters which makes the system slow, expensive, fragile, less flexible and less mobile. Moreover, it usually needs at least two parallel information channels, a quantum one and a classical one. C1
C2 L.. Kish & S. Sethuraman The method proposed in this paper offers a fast, simple, inexpensive, robust, flexible, and mobile way of data encryption for absolutely secure data transmission by using classical digital information. The speed of transfer depends on the level of security and practically unbreakable encryption can be reached at a relatively high speed. The absolute security is supported by the following facts: (i) (ii) There are no shared secret keys or public keys to share between the Sender and the Receiver. The encoding keys are random and they exist only locally and temporarily. They are kept at the stations where they are generated and terminated after use. Therefore, the Eavesdropper has no way to acquire the actual encoding key, unless it has a physical access to the encoder or the decoder. (iii) nybody, including the Eavesdropper, is allowed to know the all details of the process how the encryption is made. (iv) The actual encoding key is random and it is changing for each message. Thus, the Eavesdropper is unable to succeed by using statistical analysis of the transmitted signals. 2. Description of the Method Table 1 illustrates how the method works. The arrows show the direction of signal transmission. Let us suppose that we have two data scrambling operators which satisfy the following relation: =. (1) (1) In the first step, the message u(t), and the random number sequence (seed) for the scrambling operator are generated. (2) Then the encoded signal is generated and sent to the Receiver through a channel which can be a public classical channel. The Eavesdropper cannot decode the message, even if he knows the operation because it is scrambled by an unknown random sequence. (3) The Receiver generates the random number sequence (seed) for the scrambling operator, then uses on the received message and generates. Then he sends back to the Sender. (4) The Sender receives the signal and removes the operator by applying its inverse on this signal. = u(t), in accordance with Eq. (1). Then the Sender sends the signal u(t) back to the Receiver. The Sender does not need the random seed for the operator any more, so he deletes it to secure non-breakability. (5) The Receiver decodes this signal by applying the inverse of operation thus he gets u(t) = u(t). The Receiver does not need the random seed for the operator any more, so he deletes it to secure non-breakability.
Non-breakable Simple Encryption with No Key to Share C3 Table. 1. Scheme of absolute secure data transfer by a public classical channel. The Eavesdropper is allowed to know almost everything except the seeds (random number sequences) used by the operators and. S T E P Sender Signal Transferred (Eavesdropper knows) Receiver 1) Message: u(t) Generates seed for: 2) u(t) u(t) u(t) 3) Generates seed for: 4) u(t) = u(t) u(t) u(t) 5) Deletes seed for: u(t) = u(t) Deletes seed for: Keeps: u(t) O P E R T O R S = R P = R P = R P = R P
C4 L.. Kish & S. Sethuraman The remaining part of the description is to identify what kind of scrambling operators can provide the non-breakability. The first condition, which is necessary for the basic operation of the method, is described by Eq. (1). However, this is not enough for nonbreakability. For example, let us imagine that the data sequence and the seeds consist of numbers +1 and -1 (instead of numbers zero and 1). Then the operators can be simply the multiplication by the seeds. Equation (1) holds and the encryption functions with division by the seeds used as inverse operators. However, it is easily breakable. Observing the signals in phase 2 and 3 (see Table 1) makes it very easy to determine the operator and its inverse. Thus after observing the signal in phase 4, it can be easily decoded. The necessary non-breakability condition for an operator C used with the present method is the following. The observation of a particular signal x(t) and the signal C x(t) obtained by the operation should not make it possible to determine how the operator will act on a different signal y(t) provided y(t) is statistically independent of x(t). In conclusion: The knowledge of x(t), C x(t) and y(t) should not be enough to determine C y(t). (2) Equation (1) and Condition 2 look like they are not easy to satisfy at the same time and the search for satisfactory operations is currently going on. In the rest of the paper, we show a simple operator below which may satisfy both Eq. (1) and Condition 2. Let us continue to work with data sequences containing +1 and -1 numbers only. Let the operator C be defined as follows: C = P C R C (3) where the operator P C makes a random permutation of the location of the data within the signal u(t) (that is, scrambles the variable t); and the operator R C multiplies the elements of the signal by the elements of a random data sequence r C (t). It can be shown that a fairly large subset of these operators satisfy both Eq. (1) and Condition 2. Note, alternative orderings of the permutation and random sequence operators are also relevant. The transferred signals will be completely scrambled and for long data lengths and supposedly there is no way to reconstruct the original message by the Eavesdropper because she has less known parameters than unknown variables and equations to solve. This assumption is still to be confirmed. If this realization works, it would have the following advantages when compared to quantum encryption: The encryption is more secure than quantum encryption because the Eavesdropper can be allowed to be present at the signal receiver and see all the received signals, which cannot be allowed at secure quantum communication. Moreover, the method needs only a single classical channel (quantum encryption needs two channels). Classical communication, so it is many orders of magnitude faster than quantum communication. It is simple, very cheap and can be easily installed at the software level. No maintenance is needed.
Non-breakable Simple Encryption with No Key to Share C5 Finally, it is important to emphasize that the main aim of this paper is to propose a new way of approach to encryption. The proper operators and the exact conditions of their working still have to be found or confirmed. It is also possible that the proposed method has to be expanded for satisfactory performance. For example, one can imagine that the original message is encrypted by different but related operators and these encrypted data are sent to the Receiver, who acts similarly before sending them back. Then the message would be decrypted in a more sophisticated way by combing the operators and the data packages. cknowledgements Valuable discussions with Janos ergou, Suhail Zubairy, Julio Gea anacloche, Deepa Kundur, Minoru Fujishima, Robert Vajtai and Gabe Schmera are appreciated. References [1] L.. Kish and S. Sethuraman, Non-reakable Encryption with Classical Information, Patent Disclosure, Texas &M University, TMU-TEES, May 11, 2004.