The Rabin cryptosystem revisited

The Rabin public-key cryptosystem is revisited with a focus on the problem of identifying the encrypted message unambiguously for any pair of primes. In particular, a deterministic scheme using quartic reciprocity is described that works for primes congruent 5 modulo 8, a case that was still open. Both theoretical and practical solutions are presented. The Rabin signature is also reconsidered and a deterministic padding mechanism is proposed.Comment: minor review + introduction of a deterministic scheme using quartic reciprocity that works for primes congruent 5 modulo

Analysis of BCNS and Newhope Key-exchange Protocols

Lattice-based cryptographic primitives are believed to offer resilience against attacks by quantum computers. Following increasing interest from both companies and government agencies in building quantum computers, a number of works have proposed instantiations of practical post-quantum key-exchange protocols based on hard problems in lattices, mainly based on the Ring Learning With Errors (R-LWE) problem. In this work we present an analysis of Ring-LWE based key-exchange mechanisms and compare two implementations of Ring-LWE based key-exchange protocol: BCNS and NewHope. This is important as NewHope protocol implementation outperforms state-of-the art elliptic curve based Diffie-Hellman key-exchange X25519, thus showing that using quantum safe key-exchange is not only a viable option but also a faster one. Specifically, this thesis compares different reconciliation methods, parameter choices, noise sampling algorithms and performance

АНАЛОГ RSA-КРИПТОСИСТЕМЫ В КВАДРАТИЧНЫХ ФАКТОРИАЛЬНЫХ КОЛЬЦАХ

In the article, the analogue of a RSA-cryptosystem in general quadratic unique factorization domains is obtained. A scheme of digital signature on the basis of the generalized RSA cryptosystem is suggested. The analogue of Wiener’s theorem on low private key is obtained. We prove the equivalence of the problems of generalized RSA-modulus factorization and private key search when the domain of all algebraic integer elements of the quadratic field is Euclidean. A method to secure the generalized RSA-cryptosystem of the iterated encryption cracking is proposed.Цель данной работы заключается в построении аналога RSA-криптосистемы в квадратичных факториальных кольцах. В работе предложен алгоритм построения электронной цифровой подписи. Доказан аналог поиска секретного ключа и факторизации модуля криптосистемы в случае, когда целые алгебраические элементы поля образуют Евклидово кольцо. Даны ограничения на параметры криптосистемы для защиты от метода повторного цифрования. Так же проведено исследование скорости работы и взлома полученной криптосистемы

Practical improvements to class group and regulator computation of real quadratic fields

We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying the double large prime strategy, an improved structured Gaussian elimination strategy, and the use of Bernstein's batch smoothness algorithm. We achieve a significant speed-up and are able to compute the ideal class group structure and the regulator corresponding to a number field with a 110-decimal digit discriminant

Integration of post-quantum cryptography in the TLS protocol (LWE Option)

Dissertação de mestrado em Computer ScienceWith the possibility of quantum computers making an appearance, possibly capable of breaking several well established and widespread crytposystems (especially those that implement public key cryptography), necessity has arisen to create new cryptographic algorithms which remain safe even against adversaries using quantum computers. Several algorithms based on different mathematical problems have been proposed which are considered to be hard to solve with quantum computers. In recent years, a new lattice-based mathematical problem called Learning With Errors (and its variant Ring - Learning With Errors) was introduced, and several cryptosystems based on this problem were introduced, some of which are becoming practical enough to compete with traditional schemes that have been used for decades. The primary focus in this work is the implementation of two Ring - Learning With Errors based schemes (one key exchange mechanism and one digital signature scheme) on the TLS protocol via the OpenSSL library as a way of checking their overall viability in real-world scenarios, by comparing them to classical schemes implementing the same functionalities.Com a possibilidade do surgimento dos primeiros computadores quânticos, possivelmente capazes de quebrar muitos dos cripto-sistemas bem difundidos e considerados seguros, tornou-se necessário tomar precauções com a criação de novas técnicas criptográficas que visam manter as suas propriedades de segurança mesmo contra adversários que usem computadores quânticos. Existem já muitas propostas de algoritmos baseados em problemas matemáticos distintos que são considerados difíceis de resolver recorrendo a computadores quânticos. Recentemente, foi introduzido um novo problema baseado em reticulados denominado de Learning With Errors (e a sua variante Ring - Learning With Errors), e consequentemente foram propostos vários cripto-sistemas baseados nesse problema, alguns dos quais começam já a ser utilizáveis ao ponto de poderem ser comparados com os esquemas clássicos usados há décadas. O foco principal neste trabalho é a implementação de dois esquemas baseados no problema Ring - Learning With Errors (mais precisamente, um esquema de troca de chaves e uma assinatura digital) no protocolo TLS através da sua integração no OpenSSL como forma de verificar a sua viabilidade em contextos reais, comparando-os com esquemas clássicos que implementem as mesmas funcionalidades

Similar operation template attack on RSA-CRT as a case study

A template attack, the most powerful side-channel attack methods, usually first builds the leakage profiles from a controlled profiling device, and then uses these profiles to recover the secret of the target device. It is based on the fact that the profiling device shares similar leakage characteristics with the target device. In this study, we focus on the similar operations in a single device and propose a new variant of the template attack, called the similar operation template attack (SOTA). SOTA builds the models on public variables (e.g., input/output) and recovers the values of the secret variables that leak similar to the public variables. SOTA’s advantage is that it can avoid the requirement of an additional profiling device. In this study, the proposed SOTA method is applied to a straightforward RSA-CRT implementation. Because the leakage is (almost) the same in similar operations, we reduce the security of RSA-CRT to a hidden multiplier problem (HMP) over GF(q), which can be solved byte-wise using our proposed heuristic algorithm. The effectiveness of our proposed method is verified as an entire prime recovery procedure in a practical leakage scenario