Related papers: A Continued Fraction-Hyperbola based Attack on RSA…

Wiener's attack is a well-known polynomial-time attack on a RSA cryptosystem with small secret decryption exponent d, which works if d<n^{0.25}, where n=pq is the modulus of the cryptosystem. Namely, in that case, d is the denominator of…

Extending the classical Legendre's result, we describe all solutions of the inequality |x - a/b| < c/b^2 in terms of convergents of continued fraction expansion of x. Namely, we show that a/b = (rp_{m+1} +- sp_m) / (rq_{m+1} +- sq_m) for…

In this paper, we present attacks on three types of RSA modulus when the least significant bits of the prime factors of RSA modulus satisfy some conditions. Let $p,$ and $q$ be primes of the form $p=a^{m_1}+r_p$ and $q=b^{m_2}+r_q$…

The basic properties of RSA cryptosystems and some classical attacks on them are described. Derived from geometric properties of the Euler functions, the Euler function rays, a new ansatz to attack RSA cryptosystems is presented. A…

After attacking the RSA by injecting fault and corresponding countermeasures, works appear now about the need for protecting RSA public elements against fault attacks. We provide here an extension of a recent attack based on the public…

We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that…

This work presents a novel, black-box software-based countermeasure against physical attacks including power side-channel and fault-injection attacks. The approach uses the concept of random self-reducibility and self-correctness to add…

Rivest-Shamir-Adleman (RSA) cryptosystem uses modular multiplication for encryption and decryption. So, performance of RSA can be drastically improved by optimizing modular multiplication. This paper proposes a new parallel, high-radix…

This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…

The Rank metric decoding problem is the main problem considered in cryptography based on codes in the rank metric. Very efficient schemes based on this problem or quasi-cyclic versions of it have been proposed recently, such as those in the…

Lo and Ko in [1] have developed some attacks on the cryptosystem called AlphaEta [2], claiming that these attacks undermine the security of AlphaEta for both direct encryption and key generation. In this paper, we show that their arguments…

Persistent Fault Attack (PFA) is a recently proposed Fault Attack (FA) method in CHES 2018. It is able to recover full AES secret key in the Single-Byte-Fault scenario. It is demonstrated that classical FA countermeasures, such as Dual…

This paper proposes an alternative approach to formally establishing the correctness of the RSA public key cryptosystem. The methodology presented herein deviates slightly from conventional proofs found in existing literature. Specifically,…

DAGS scheme is a key encapsulation mechanism (KEM) based on quasi-dyadic alternant codes that was submitted to NIST standardization process for a quantum resistant public key algorithm. Recently an algebraic attack was devised by Barelli…

Block ciphers are in widespread use since the 1970s. Their iterated structure is prone to numerous round invariant attacks for example in Linear Cryptanalysis (LC). The next step is to look at non-linear polynomial invariants cf.…

Rank Decoding (RD) is the main underlying problem in rank-based cryptography. Based on this problem and quasi-cyclic versions of it, very efficient schemes have been proposed recently, such as those in the ROLLO and RQC submissions, which…

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of R\'edei rational functions. We then…

We introduce DM-RSA (Dual Modulus RSA), a variant of the RSA cryptosystem that employs two distinct moduli symmetrically to enhance security. By leveraging the Chinese Remainder Theorem (CRT) for decryption, DM-RSA provides increased…

Backdoors on federated learning will be diluted by subsequent benign updates. This is reflected in the significant reduction of attack success rate as iterations increase, ultimately failing. We use a new metric to quantify the degree of…

We propose a generalization of an RSA-like scheme based on R\'edei rational functions over the Pell hyperbola. Instead of a modulus which is a product of two primes, we define the scheme on a multi-factor modulus, i.e. on a product of more…