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19 January 1999

Date: Tue, 19 Jan 1999 14:29:41 +0100
From: Mok-Kong Shen <mok-kong.shen@stud.uni-muenchen.de>
Organization: Studenten; LRZ; Universitaet Muenchen
To: aucrypto@suburbia.net
Subject: AUCRYPTO: Some Thoughts on the Design of a Proposed Stream Cipher

I. INTRODUCTION.
While the general tendency of modern developments in cryptography has been towards block ciphers of increasingly larger key length, with, e.g., AES demanding a minimum of 128 bits, a recent agreement of the Wassenaar countries to restrict export of crypto products to those having key length not exceeding 56 bits will invariably lead to a more or less long-durated very undesirable situation where innocent and law-obeying people outside of the 33 signatory nations will have only relatively weak ciphers at their disposal that are insufficient to offer an adequate level of security of their private confidential communications (either with themselves or with people of the 33 countries). For eventually illegally imported strong crypto products could have problems of general availability, cost, maintenance, integrity (virus/bugs implanted by malicious agencies) and, last but not least, legal issues. (The maintenance and integrity issues apply also to crypto archives having stuffs that have been legally imported before regulations come into force.) On the other hand, their countries are on the average fairly poor in scientific and technical know-how currently, so that it would be extremely difficult to bring up there in short terms an adequate crypto infrastructure comparable to that of the technically superior export-regulating nations.

One viable way for people in the said technically underdeveloped region to escape from the dilemma appears to be to resort to superencipherment, i.e. an encryption system consisting of a combination of an easily implementable algorithm with a sufficiently good 56-bit algorithm (which can be legally obtained from the 33 countries) with the hope that the resulting strength will exceed the computational capability of the mighty eavesdroppers.

It is the purpose of this paper to present some preliminary ideas on the realization of such an easily implementable complementary algorithm in the form of a stream cipher having the property that its keystream can be easily generated by both partners of a given communication connection without involving any problems of transport and secure storage, thus possessing the advantages of immunity to
(whatever) export controls and of simplicity of handling by (eventually unsophisticated) users of the encryption scheme. (This is to be contrasted, in particular, with keystreams obtained from physical random processes, which normally incur severe management problems of transport and secure storage.)

II. RAW MATERIALS FOR OBTAINING KEYSTREAMS.

For good cryptological security of a stream cipher, the keystream generated should be hard to infer, i.e. it should be difficult for the analyst to predict any bit of the keystream from the other bits. As is well-known, this very crucial problem is unfortunately extremely difficult to deal with. We regret (as the reader may have foreseen from our introduction) not being able to offer any satisfactory solution to that in the present paper. Instead we suggest to appeal to the admittedly crude (imprecise) heuristic argument that by rendering each bit of the keysteam somehow to be a sufficiently complex (complicated) function of a sufficiently large set of independent and sufficiently random values (variables) the dependency of any bit from the other bits of the entire sequence obtained can be made to be arbitrarily small so as to be beyond the inference capability of the analyst.

Assuming that the above heuristic argument can be accepted and noting that the dependency can be expressed in terms of auto-correlations, we suggest using the following coarse plan to generate keystreams for our purpose: Start with some more or less random raw materials (sequences of bits/bytes) that are easily available albeit inherently poor (i.e. comparatively strongly auto-correlated) and apply a sequence of suitably chosen refining processes (to be treated in the next section) aimed to reduce the correlations such that the end-stage output will be of satisfactory quality (progressive refinement).

Conceptually this is akin to obtaining potable water from a muddy source through employing a series of differeent filtering and disinfecting processes, with each augmenting the functionality of the others such that the end product will hopefully be sufficiently free of ingredients that are detrimental to human health.

Thus said, we shall presently look for ensembles of fluctuating quantities that can be easily and perfectly leagally acquired by both communication partners in identical copies independent of geographical locations and that are apparently in some sense random, i.e. roughly speaking non-systematic, disordered and without a discernable periodicity. The following materials suggest themselves:

> 1. Natural language texts (books, news, public documents, etc.)

> 2. Artificial language texts (source programs, digit sequences of transcendental numbers, postcript files, etc.)

> 3. Sequences of data (physical measurements, economic time series, telephone numbers, results of numerical computations (with identical input, algorithms and computational accuracy), scientific data bases, etc.)

> 4. Other digitalized materials (voice, sound, photos, pictures, graphics, satellite and medical images, binary program files, etc.)

With the possible exception of the digit sequences of transcendental numbers, these items are mostly fairly strongly auto-correlated. In fact, some well-known methods of analysis are based on the frequency distributions of bigrams, trigrams, etc. of the natural languages in which the plaintext messages are written. In the next section we shall therefore deal with a number of techniques aimed to efficiently reduce the auto-correlations, hopefully leading to keystreams that are
of satisfactory quality for our purpose. (The envisaged, though certainly not fully attainable, goal is of course the white noise, whose auto-correlation function is defined to have the value zero everywhere excepting at a singular point.)

III. TECHNIQUES FOR REDUCING AUTO-CORRELATIONS.

For simplicity of presentation we shall confine ourselves in this section to natural language texts (sequences of characters in 8-bit bytes) as raw materials for obtaining keystreams, since these are very easily available and since the other sources can be treated in essentially the same manner. The following techniques, being largely taken from classical elementary cryptography and readily implementable by persons of modest programming proficiency, appear to be promising candidates for reducing the auto-correlations that are present in the
texts:

> 1. Apply substitutions, e.g. polyalphabetic substitutions of bytes.

> 2. Apply permutations, i.e. transpositions, including reversal.

> 3. Apply homophones, utilizing the fact that the alphabet of the texts is smaller than the full 256 character set.

> 4. Combining two text streams through:

> > a. Bitwise XOR.

> > b. Addition mod 2^32 (assuming 32 bit word length).

> > c. Substitution, e.g. mapping a pair of bytes (or halfbytes), one from each stream, to a pair of bytes (or halfbytes).

> 5. Compression through:

> > a. Commonly available data compression algorithms.

> > b. XORing groups of bits, e.g. 32 bits, i.e. taking their parity.

> 6. Use every second or third character of the texts.

> 7. Apply other simple encryption techniques, e.g. auto-keying applied to a group of words and circular shift of bits in a word.

Note that with (4) an arbitrary number of text streams can be combined and that all techniques can be applied recursively, for example (4b) can be applied after (5b). Thus the proposed scheme for the generation of keystreams can apparently indeed be made to be arbitrarily complex, satisfying the requirement mentioned in our heuristic argument of Section II. Of course, at this point one naturally tends to recall the efficiency issue of processing which is up till now among the essential selection criteria of modern encryption algorithms. However, as the author recently pointed out [1,2], one practical and simple way of coping with the 56-bit limitation is to make use of a new paradigm, namely 'security through inefficiency', i.e. paying the price of some tolerable longer precessing time. This can certainly be justified in a substantial part of civilian applications, e.g. encrypting e-mails, and can evidently be applicable even to certain relatively time-critical encryptions as well, if multiple hardware is available for processing parallel jobs.

IV. MISCELLANEOUS REMARKS.

The 'key', i.e. the secret information to be kept by both communictaion partners, consists of the names or ISBNs of the texts being used and the arbitraily chosen initial offsets from the beginning of the texts. The keystream is preferably to be generated online rather than generated once in great length and used for a
number of subsequent sessions, since otherwise it would have to be securely stored, resulting in substantial management problems. This means that the user keeps a running record of the offsets to the individual texts, i.e. the character positions of the texts after the previous message has been processed. (As a variation one could introduce some amounts of skips after each message processed.) No other informations need be securely stored. (The texts can in fact be freely displayed and read by the user for entertainment when he is not doing encryption.)

Since one's library may contain quite a large number of texts (possibly also of several different languages which is advantageous from the point of view of combination), each having the potential of being combined together to generate the keystreams for encryption, the mere knowledge of the content of the library of the user is virtually useless to the analyst. Simple combinatorical considerations
indicate that an almost unlimited number of keysteams (or equivalently a non-repeating (non-periodic) keystream of practically infinite length) can be generated from a library of non-trivial size. This is to be contrasted with keystreams obtained from one or a few pseudo-random number generators (LFSRs etc. see [3]) that normally have fairly limited period lengths. (For a compound PRNG designed to accept an arbitrarily long seed and produce pseudo-random number sequences of arbitrarily long period lengths, see [4].) In other words, on the assumption that the user commits no procedural errors, the keystream obtained is of 'one-time' nature.

Note: The above said 'one-time' qualification should not be mis-understood by the reader to induce conceptual associations with the one-time pad (OTP). Our proposed scheme is simply a stream cipher. OTP is on the other hand an ideal and purely theoretical concept that is never fully realizable in practice, though it is commonly believed that OTP can be approximated to satisfactory degree through adequately post-processing bit sequences obtained from some physical random processes. (Our comparatively much less ambitious goal, though, is to be able to approximate the white noise well.)

Maurer's universal statistical test [5], being fairly easily implementable, appears to be particularly recommendable for testing the quality of the keystreams obtained with a given design configuration.

More than one offsets can be applied to the same text. This may be useful in the special case where only a single text is availble. (As a matter of interest, we mention that the same technique can be applied to a single record of hardware generated keystream, enabling through combination (with e.g. XOR) of the subquences thus obtained the derivation of a number of different keystreams from the same record.)

It is not necessary to maintain a large library at the user's place. Certain texts may be downloaded from publically accessible servers, if care is taken not to leak thereby sufficient amount of exploitable informations to the analyst as to which texts actually participate in the keystream generation process.

Pi appears to have an advantage over the other transcendental numbers in the present context in that one can compute its digits starting from arbitrarily given offsets, thus dispensing with the need to store its digit sequence (albeit at the price of higher computing cost).

Text file compression software are easily obtainable and not subject to export regulations. Self-implementation of these may however incur some non-trivial programming expenditure. Note that such compressions are reversible (through the corresponding decompression processes). For multi-media applications, a large number of methods, some involving sophisticated mathematical transformations, are available that are irreversible but ensure reproduction of acceptable visual quality (see [6,7]). It should be noted however that in our case we need to care neither reversibility nor satisfactory reproduction. (Likewise we are not concerned at all with error detection/correction of codes.) Hence the extremely simple compression technique of (5b) of Section III appears to be particularly valuable for our purpose. (It may be mentioned that (5b) is utilized in author's humble design WEAK4-EX [8], a stream cipher based on psuedo-random number generation with a 56-bit key as seed.)

We take this opportunity to raise a question that could be of some indirect relevance to our topic: Suppose there are three character strings as follows:

> 1. Purchase 500 million Yens.

> 2. Sell all Microsoft shares.

> 3. Cut UK offer by 7 percent.

Suppose string 1 is the proper message to be communicated. Using (4a) of Section III we obtain a keystream from strings 2 and 3 and XOR it with string 1 to produce the ciphertext, i.e. the result of XORing all three strings together. Suppose now that the analyst has a method to systematically obtain all meaningful possible plaintexts corresponding to the given ciphertext. Then all three character strings above are certainly among the set of candidate plaintexts found. How can he know which is the true message? This ambiguity seems to imply that it may not be unconditionally necessary to strive to achieve a very excellent approximation to the white noise but that certain comparatively inferior quality could be sufficient. The author is ignorant of an answer to this seemingly paradoxical issue and should very much appreciate hints and explanations from the experts.

V. CONCLUSION.

As our title clearly indicates, this paper does not aim to present any finalized design but simply sketches some apparently promising techniques of realizing such. Based on our more or less fuzzy heuristic argument (as given in Section II) alone it is evidently entirely futile to predict which of the techniques (listed in Section III) are efficient and which (eventually recursive) combination out of them will actually lead to an optimal and practically useful stream cipher. Only actual experiments will be able to tell this. However, it is the author's intuitive conviction (partly based on some test results of his WEAK-series of algorithms [1,8,9] that utilize part of the techniques listed in this paper) that the direction we have been persuing is a rewarding one worthy of serious further investigations.

The author wishes to thank CWL for reading a draft of the present paper.

Comments, critiques and suggestions for improvement are sincerely solicited.

M. K. Shen

LITERATURE.

[1] http://www.stud.uni-muenchen.de/~mok-kong.shen/#paper13

[2] http://www.stud.uni-muenchen.de/~mok-kong.shen/#paper17

[3] A. J. Menezes et al., Handbook of Cryptography. CRC Press, 1997.

[4] http://www.stud.uni-muenchen.de/~mok-kong.shen/#paper9

[5] U. M. Maurer, A Universal Statistical Test for Random Bit Generators. J. Cryptology (1992) 5:89-105.

[6] W. Kou, Digital Image Compression. Kluwer, 1995.

[7] V. Bhaskaran, K. Konstantinides, Image and Video Compression Standards. Kluwer, 1995.

[8] http://www.stud.uni-muenchen.de/~mok-kong.shen/#paper16

[9] http://www.stud.uni-muenchen.de/~mok-kong.shen/#paper15