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, (\u27naturally\u27) 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

bitcoin.BitMint: Reconciling Bitcoin with Central Banks

The sweeping success of the original (2008) bitcoin protocol proves that digital currency has arrived. The mounting opposition from the financial establishment indicates an overshoot. We propose to tame bitcoin into bitcoin.BitMint: keeping the bitcoin excitement -- fitted into real world security, stability and fraud concerns. The basic idea is to excise the bitcoin money generation formula, and otherwise apply bitcoin essentially “as is” over digital coins which are redeemable by the mint that minted them. This will preserve the bitcoin assured anonymity. The new bitcoin.BitMint solution will benefit from bitcoin’s double-spending prevention, and would otherwise enjoy all the benefits associated with money in a digital form. bitcoin.BitMint will allow traders to invest in US$, gold, or any other commodity while practicing their trade in cyberspace, anonymously, securely, and non-speculatively. This “mint-in-the-middle” protocol will allow law enforcement authorities to execute a proper court order to enforce the disclosure of a suspected fraudster, but the community of honest traders will trade with robust privacy as offered by the original bitcoin protocol. We envision interlinked bitcoin.BitMint trading environments, integrated via an InterMint protocol: a framework for the evolution of a cascaded super currency – global and highly stable

Finger Printing Data

By representing data in a unary way, the identity of the bits can be used as a printing pad to stain the data with the identity of its handlers. Passing data will identify its custodians, its pathway, and its bona fide. This technique will allow databases to recover from a massive breach as the thieves will be caught when trying to use this \u27sticky data\u27. Heavily traveled data on networks will accumulate the \u27fingerprints\u27 of its holders, to allow for a forensic analysis of fraud attempts, or data abuse. Special applications for the financial industry, and for intellectual property management. Fingerprinting data may be used for new ways to balance between privacy concerns and public statistical interests. This technique might restore the identification power of the US Social Security Number, despite the fact that millions of them have been compromised. Another specific application regards credit card fraud. Once the credit card numbers are \u27sticky\u27 they are safe. The most prolific application though, may be in conjunction with digital money technology. The BitMint protocol, for example, establishes its superior security on \u27sticky digital coins\u27. Advanced fingerprinting applications require high quality randomization. The price paid for the fingerprinting advantage is a larger data footprint -- more bits per content. Impacting both storage and transmission. This price is reasonable relative to the gained benefit

AI Resistant (AIR) Cryptography

highlighting a looming cyber threat emanating from fast developing artificial intelligence. This strategic threat is further magnified with the advent of quantum computers. AI and quantum-AI (QAI) represent a totally new and effective vector of cryptanalytic attack. Much as modern AI successfully completes browser search phrases, so it is increasingly capable of guessing a rather narrow a-priori list of plausible plaintexts. This guessing is most effective over device cryptography where the message space is limited. Matching these guesses with the captured ciphertext will greatly accelerate the code breaking process. We never faced such a plaintext-originated attack on a strategic level, and never had to prepare for it. Now we do. Proposing to apply a well-known martial art tactics: using the opponent\u27s strength against them: constructing ciphertexts that would provide false answers to the AI attacker and lead them astray. We are achieving this defensive measure by pivoting away from the norm of small, known-size key and pattern-loaded ciphers. Using instead large keys of secret size, augmented with ad-hoc unilateral randomness of unbound limits, and deploying a pattern-devoid algorithm with a remarkably low computational burden, so it can easily handle very large keys. Thereby we achieve large as desired unicity distances. This strategy has become feasible just when the AI threat looms. It exploits three new technologies coming together: (i) non-algorithmic randomness, (ii) very large and inexpensive memory chips, and (iii) high throughout communication networks. These pattern-devoid, randomness rich ciphers also turn up to be an important option in the toolbox NIST prepares to meet the quantum challenge. Avoiding the computational load of mainstay ciphers, AIR-cryptography presents itself as the ciphers of choice for medical, military and other battery-limited devices for which data security is paramount. In summary: we are pointing out a fast emerging cyber challenges, and laying out a matching cryptographic answer

Artificial Intelligence Assisted Innovation

Artificial Intelligence Assisted Innovation (AIAI) is a technology designed to improve innovation productivity by helping human innovators with all the support tasks that kindle the creative spark, and also with sorting out innovative propositions for their merit. Innovation activity is mushrooming and hence innovative history is an ever growing data accumulation. AIAI identified a universal innovation map, which is processed like the tape in a Turing machine, only here in the Innovation Turing machine, marking an innovation pathway. By mapping innovative history onto these maps, one enables the growing record of innovation history to guide current innovation as to merit, expected cost, estimated duration, etc. Using Monte Carlo and Discriminant Analysis, an Artificial Innovation Assistant runs a dialog with the human innovator with a net effect of accelerated innovation. Users of AIAI are expected to exhibit a commanding lead over innovators guided only by their creativity

T-Proof: Secure Communication via Non-Algorithmic Randomization

shared random strings are either communicated or recreated algorithmically in “pseudo” mode, thereby exhibiting innate vulnerability. Proposing a secure protocol based on unshared randomized data, which therefore can be based on ‘white noise’ or other real-world, non algorithmic randomization. Prospective use of this T-Proof protocol includes proving possession of data to a party in possession of same data. The principle: Alice wishes to prove to Bob that she is in possession of secret data s, known also to Bob. They agree on a parsing algorithm, dependent on the contents of s, resulting in breaking s into t distinct, consecutive sub-strings (letters). Alice then uses unshared randomization procedure to effect a perfectly random transposition of the t substrings, thereby generating a transposed string s’. She communicates s’ to Bob. Bob verifies that s’ is a permutation of s based on his parsing of s to the same t substrings, and he is then persuaded that Alice is in possession of s. Because s’ was generated via a perfectly randomized transposition of s, a cryptanalyst in possession of s’ faces t! s- candidates, each with a probability of 1/t! (what’s more: the value of t, and the identity of the t sub-strings is unknown to the cryptanalyst). Brute force cryptanalysis is the fastest theoretical strategy. T-Proof can be played over s, mixed with some agreed upon nonce to defend against replay options. Unlike the competitive solution of hashing, T-Proof does not stand the risk of algorithmic shortcut. Its intractability is credibly appraise

A LeVeL Paying Field: Cryptographic Solutions towards Social Accountability and Financial Inclusion

Thousands of digital money protocols compete for attention; the vast majority of them are a minor variation of the Satoshi Nakamoto 2008 proposal. It is time to extract the underlying principles of the Bitcoin revolution and re-assemble them in a way that preserves its benefits and gets rid of its faults. BitMint*LeVeL is a move in this direction. It upholds the fundamental migration of money from hidden bank accounts to cryptographically protected publicly exposed digital coins; it enables a cyber version of peer-to-peer cash transactions. Bitcoin and its variants rely on a fixed public/private key algorithm. Being \u27fixed\u27 turns it into a resting target for advanced cryptanalysis. The LeVeL protocol assigns each coin holder to pick their own public/private key algorithm. An attacker would have to compromise all the algorithms used by all previous coin owners -- a substantial security upgrade relative to Bitcoin. LeVeL applies to self-referential money like Bitcoin or fiat currency, and to other-referential money, serving as a claim check for assets, like gold or fiat currency. Bitcoin decentralization is groundbreaking but it gives too much aid and comfort to wrongdoers. BitMint*LeVeL re-imagines decentralization via the notion of the InterMint: Money is minted by many smoothly interchangeable mints competing for traders. Lastly, BitMint*LeVeL is built on top of the original BitMint protocol which was implemented in the legacy banking system, and thus it offers a smooth migration into cyberspace. 1.2 Billion people around us have no bank account, but do have cell phones. The LeVeL offers social accountability and financial inclusion

Integer Arithmetic without Arithmetic Addition

Revisiting long established conventions has proven very fertile in many a case. Let’s then revisit the premise that arithmetic must be constructed with the arithmetic addition as its foundation. Here we explore an arithmetic realm over integers without invoking the quintessential operation of addition. We propose an arithmetic constructed over a fundamental mapping of one set of integers into another. We start and focus here on mapping an arbitrary number of integers to a single integer, and further limit our investigation to a mapping procedure that views the input integers as a set of conflicting answers to a binary question, and attempt to figure out the single integer that best reflects the combined “wisdom” of the input answers. Thereby we construct the proposed arithmetic as ground tool for discriminant analysis. On the other end, the many-to-one mapping suggests this arithmetic as a fundamental hashing function, and the complexity of data loss suggests a new primitive for asymmetric cryptography. This arithmetic evolved from practical algorithms used by the author in his engineering practice, where the original name was BiPSA: Binary Polling Scenario Analysis. For continuity purposes we carry on the name. This article focuses on the skeleton arithmetic. Applications and substantiation will follow

Pattern Devoid Cryptography

Pattern-loaded ciphers are at risk of being compromised by exploiting deeper patterns discovered first by the attacker. This reality offers a built-in advantage to prime cryptanalysis institutions. On the flip side, the risk of hidden math and faster computing undermines confidence in the prevailing cipher products. To avoid this risk one would resort to building security on the premise of lavish quantities of randomness. Gilbert S. Vernam did it in 1917. Using modern technology, the same idea of randomness-based security can be implemented without the inconvenience associated with the old Vernam cipher. These are Trans Vernam Ciphers that project security through a pattern-devoid cipher. Having no pattern to lean on, there is no pattern to crack. The attacker faces (i) a properly randomized shared cryptographic key combined with (ii) unilateral randomness, originated ad-hoc by the transmitter without pre-coordination with the recipient. The unlimited unilateral randomness together with the shared key randomness is set to project as much security as desired up to and including Vernam levels. Assorted Trans Vernam ciphers (TVC) are categorized and reviewed, presenting a cogent message in favor of a cryptographic pathway where transmitted secrets are credibly secured against attackers with faster computers and better mathematicians