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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 security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…

Most modern cryptographic systems, such as RSA and the Diffie-Hellman Key Exchange, rely on "trapdoor" mathematical functions that are presumed to be computationally difficult with existing tools. However, quantum computers will be able to…

With photons being the only available candidates for long-distance quantum communication, most quantum cryptographic devices are physically realized as optical systems that operate a security protocol based on the laws of quantum mechanics.…

Recent cryptanalytic attacks have exposed the vulnerabilities of some widely used cryptographic hash functions like MD5 and SHA-1. Attacks in the line of differential attacks have been used to expose the weaknesses of several other hash…

We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an Error…

Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…

These notes are a brief introduction to the RSA algorithm and modular arithmetic. They are intended for an undergraduate audience.

Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have…

A new fault attack, double counting attack (DCA), on the precomputation of $2^t$-ary modular exponentiation for a classical RSA digital signature (i.e., RSA without the Chinese remainder theorem) is proposed. The $2^t$-ary method is the…

The emergence of small computing devices and the integration of processing units into everyday objects has made lightweight cryptography an essential part of the security landscape. Conventional cryptographic algorithms such as AES, RSA,…

Ethereum smart contracts are programs that are deployed and executed in a consensus-based blockchain managed by a peer-to-peer network. Several re-entrancy attacks that aim to steal Ether, the cryptocurrency used in Ethereum, stored in…

The cryptosystem RSA is a very popular cryptosystem in the study of Cryptography. In this article, we explore how the idea of a primitive mth root of unity in a ring can be integrated into the Discrete Fourier Transform, leading to the…

We point out critical deficiencies in lattice-based cryptanalysis of common prime RSA presented in ``Remarks on the cryptanalysis of common prime RSA for IoT constrained low power devices'' [Information Sciences, 538 (2020) 54--68]. To…

The advent of quantum computing poses a critical threat to RSA cryptography, as Shor's algorithm can factor integers in polynomial time. While post-quantum cryptography standards offer long-term solutions, their deployment faces significant…

An improved design of a cryptosystem based on small Ree groups is proposed. We have changed the encryption algorithm and propose to use a logarithmic signature for the entire Ree group. This approach improves security against sequential key…

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…

Today, Internet becomes the essential part of our lives. Over 90 percent of the ecommerce is developed on the Internet. A security algorithm became very necessary for producer client transactions assurance and the financial applications…

We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in…

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…