Affiliation: AGS Encryptions Ltd.
Binomial Sieve Series -- a Prospective Cryptographic Tool
A Binomial Sieve Series (BSS) is an infinite monotonic set of natural numbers, b1, b2, .....bn ( bi < b(i+1) ) generated, ('naturally') from any two natural numbers (x, y <= x) . If one repeatedly counts bi elements over the set X= 1,2, ,x (recycled counting) and eliminates each time the element of X that stops each round of counting, then the surviving element of X is y. Every natural number, per any x, is associated with a certain survivor. We prove that per any x all BSS are infinite and approach an equal size, regardless of the identity of the survivor element y. These infinite series (in count and length) have no simple pattern, their disorder is reminiscent of primes. We suggest some intriguing cryptographic applications based on the poor predictability of the next element in each series, combined with good predictability of the computational load to develop the series (by users and by the cryptanalyst). Using x as a shared secret, and a random, per-session, y, Alice and Bob may mark successive messages between them with the next element of the respective BSS, thereby mutually authenticating themselves throughout their conversation. Other cryptographic possibilities are outlined.
Encryption-On-Demand: Practical and Theoretical Considerations
Alice and Bob may develop a spontaneous, yet infrequent need for online confidential exchange. They may be served by an 'encryption-on-demand' (EoD) service which will enable them to communicate securely with no prior preparations, and no after effects. We delineate a possible EoD service, and describe some of its theoretical and practical features. The proposed framework is a website which could tailor-make an encryption package to be downloaded by both Alice and Bob for their ad-hoc use. The downloaded package will include the cryptographic algorithm and a unique key, which may be of any size, since Alice and Bob will not have to enter, or regard the key per se, they would simply use the downloaded page to encrypt and decrypt their data. After their secure exchange both Alice and Bob may ignore, or discard the downloaded software, and restart the same procedure, with a different tailor-made package, exactly when needed. This framework allows for greater flexibility in managing the complexity aspects that ensures security. Alice and Bob will not have to know what encryption scheme they use. The server based tailoring program could pseudo-randomly pick AES, DES, RSA, ECC, select a short, or long key, and otherwise greatly increase the variability that would have to be negotiated by a cryptanalyst. Encryption-on-demand is offered on http://youdeny.com . Features are described.
Proposing a Master One-Way Function
Making an arbitrary binary string fit as a fixed size cipher key (via hashing) one could use an arbitrary string x as both plaintext and key to generate a ciphertext, y defined as "the crypto square of x", while x is the crypto square root of y. Extended to higher powers, this formalism allows for polynomial morphology that combines all one-way functions candidates into a single master function which is at least as intractable as its best ingredient one-way function. The master list has some interesting and useful attributes: at will size for both input and output, controlled forward computational burden, milestone computing, and of course the best practical chance for being one-way.
s(n) An Arithmetic Function of Some Interest, and Related Arithmetic
Every integer n > 0 ? N defines an increasing monotonic series of integers: n1, n2, ...nk, such that nk = nk +k(k-1)/2. We define as s(m) the number of such series that an integer m belongs to. We prove that there are infinite number of integers with s=1, all of the form 2^t (they belong only to the series that they generate, not to any series generated by a smaller integer). We designate them as s-prime integers. All integers with a factor other than 2 are not s-prime (s>1), but are s-composite. However, the arithmetic s function shows great variability, lack of apparent pattern, and it is conjectured that s(n) is unbound. Two integers, n and m, are defined as s-congruent if they have a common s-series. Every arithmetic equation can be seen as an expression without explicit unknowns -- provided every integer variable can be replaced by any s-congruent number. To validate the equation one must find a proper match of such members. This defines a special arithmetic, which appears well disposed towards certain cryptographic applications.
Tailored Key Encryption (TaKE) Tailoring a key for a given pair of plaintext/ciphertext
Abstract. The prevailing cryptographies are attacked on the basis of the fact that only a single element in the key space will match a plausible plaintext with a given ciphertext. Any cryptography that would violate this unique-key assumption, will achieve added security through deniability (akin to One Time Pad). Such cryptography is being described. It is achieved by breaking away from the prevailing notion that the key is a binary string of a fixed length. The described key is random-size non-linear array: a graph constructed from vertices and edges. The binary naming of the vertices and edges, and the configuration are all part of the key. Such keys can take-on most of the necessary complexity, which allows the algorithm itself to be exceedingly simple (a-la Turing Machine).
Essential Shannon Security with Keys Smaller Than the Encrypted Message
To a cryptographer the claim that ?Shannon Security was achieved with keys smaller than the encrypted message" appears unworthy of attention, much as the claim of ?perpetuum mobile? is to a physicist. Albeit, from an engineering point of view solar cells which power satellites exhibit an ?essential perpetuum mobile? and are of great interest. Similarly for Shannon Security, as it is explored in this article. We discuss encryption schemes designed to confound a diligent cryptanalyst who works his way from a captured ciphertext to a disappointing endpoint where more than one otherwise plausible plaintexts are found to be associated with keys that encrypt them to that ciphertext. Unlike some previous researchers who explored this equivocation as a special case of existing schemes, this approach is aimed at devising a symmetric encryption for that purpose per se.
Non-Deforming Digital Watermarks
TaKE cryptography offers subliminal marking of a digital stream so that any tampering, induces an unacceptable distortion of the primary information. Encrypted audio and video streams are decrypted by one key to the original content (e.g. music), and through another key to the digital watermark (e.g. name of legitimate user). Unlike the prevailing methods which are based on distorting the protected contents, or locking it through a digital signature, TaKE -- Tailored Key Encryption -- preserves the integrity of the original stream, and its digital watermarks are inconspicious. Daniel (tm) is a particular TaKE cryptography which also offers an instant and flexible trade off between security level and speed and convenience level. The described method is fast and proper for both high capacity stream, and secrecy sensitive streams..