Related papers: A Continued Fraction-Hyperbola based Attack on RSA…
The following submission constitutes a guide and an introduction to a collection of articles submitted as a Ph.D. dissertation at the University of Gda\'nsk. In the dissertation, we study the fundamental limitations within the selected…
In this paper we study the existing CRT-RSA countermeasures against fault-injection at-tacks. In an attempt to classify them we get to achieve deep understanding of how they work. We show that the many countermeasures that we study (and…
The security of the RSA cryptosystem is based on the intractability of computing Euler's totient function phi(n) for large integers n. Although deriving phi(n) deterministically remains computationally infeasible for cryptographically…
The MinRank (MR) problem is a computational problem that arises in many cryptographic applications. In Verbel et al. (PQCrypto 2019), the authors introduced a new way to solve superdetermined instances of the MinRank problem, starting from…
The most important characteristic of a Quantum Key Distribution (QKD) protocol is its security against third-party attacks, and the potential countermeasures available. While new types of attacks are regularly developed in the literature,…
We examine a natural but improper implementation of RSA signature verification deployed on the widely used Diebold Touch Screen and Optical Scan voting machines. In the implemented scheme, the verifier fails to examine a large number of the…
Ciminion and Hydra are two recently introduced symmetric key Pseudo-Random Functions for Multi-Party Computation applications. For efficiency, both primitives utilize quadratic permutations at round level. Therefore, polynomial system…
In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on…
Many variants of RSA cryptosystem exist in the literature. One of them is RSA over polynomials based on Galois approach. In standard RSA modulus is product of two large primes whereas in the Galois approach author considered the modulus as…
In this paper, we present a deterministic attack on (EC)DSA signature scheme, providing that several signatures are known such that the corresponding ephemeral keys share a certain amount of bits without knowing their value. By eliminating…
The Ring Learning-With-Errors (RLWE) problem shows great promise for post-quantum cryptography and homomorphic encryption. We describe a new attack on the non-dual search RLWE problem with small error widths, using ring homomorphisms to…
We show that for a fixed integer $n \neq \pm2$, the congruence $x^2 + nx \pm 1 \equiv 0 \pmod{\alpha}$ has the solution $\beta$ with $0 < \beta < \alpha$ if and only if $\alpha/\beta$ has a continued fraction expansion with sequence of…
Establishing the security of continuous-variable quantum key distribution against general attacks in a realistic finite-size regime is an outstanding open problem in the field of theoretical quantum cryptography if we restrict our attention…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…
Due to the nature of applications such as critical infrastructure and the Internet of Things etc. side channel analysis attacks are becoming a serious threat. Side channel analysis attacks take advantage from the fact that the behavior of…
We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Ap\'ery in his proof of the irrationality of $\zeta(3)$. We show in particular that this can be applied to a…
In this paper we give a polynomial time algorithm to compute $\varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer. This provides a new insight in the very important problem of factoring an RSA…
In this paper, we study applications of Bernstein-Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it,…
We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to…
In recent years, several hacking attacks have broken the security of quantum cryptography implementations by exploiting the presence of losses and the ability of the eavesdropper to tune detection efficiencies. We present a simple attack of…