Brier, Éric Ferradi, Houda Joye, Marc Naccache, David
Published in
Journal of Mathematical Cryptology

This paper introduces new prq-based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutation and the Fiat–Shamir transform. In the basic signature scheme, the signer generates multiple RSA-like moduli...

Tomkins, Hayley Nevins, Monica Salmasian, Hadi
Published in
Journal of Mathematical Cryptology

We present a large class of new Zémor-Tillich type hash functions whose target space is the finite group GL2(𝔽pn) for any prime p and power n. To do so, we use a novel group-theoretic approach that uses Tits’ “Ping-Pong Lemma” to outline conditions under which a set of matrices in PGL2(𝔽p((x))) generates a free group. The hash functions we form are...

Joye, Marc
Published in
Journal of Mathematical Cryptology

Due to its shorter key size, elliptic curve cryptography (ECC) is gaining more and more popularity. However, if not properly implemented, the resulting cryptosystems may be susceptible to fault attacks. Over the past few years, several techniques for secure implementations have been published. This paper revisits the ring extension method and its a...

Coron, Jean-Sébastien Gini, Agnese
Published in
Journal of Mathematical Cryptology

At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al. described an attack with complexity 𝓞(22h). In this paper, we describe an improved attack with complexity 𝓞(21.75h).

Bootland, Carl Castryck, Wouter Szepieniec, Alan Vercauteren, Frederik
Published in
Journal of Mathematical Cryptology

We introduce a general framework encompassing the main hard problems emerging in lattice-based cryptography, which naturally includes the recently proposed Mersenne prime cryptosystem, but also problems coming from code-based cryptography. The framework allows to easily instantiate new hard problems and to automatically construct plausibly post-qua...

Chakraborty, Suvradip Alawatugoda, Janaka Rangan, Chandrasekaran Pandu
Published in
Journal of Mathematical Cryptology

We present a new approach to construct several leakage-resilient cryptographic primitives, including leakage-resilient public-key encryption (PKE) schemes, authenticated key exchange (AKE) protocols and low-latency key exchange (LLKE) protocols. To this end, we introduce a new primitive called leakage-resilient non-interactive key exchange (LR-NIKE...

Karmakar, Sudhangshu B.
Published in
Journal of Mathematical Cryptology

Zhang, Liang Feng Safavi-Naini, Reihaneh
Published in
Journal of Mathematical Cryptology

Outsourcing computation has gained significant popularity in recent years due to the development of cloud computing and mobile services. In a basic outsourcing model, a client delegates computation of a function f on an input x to a server. There are two main security requirements in this setting: guaranteeing the server performs the computation co...

Goel, Neha Gupta, Indivar Dass, B. K.
Published in
Journal of Mathematical Cryptology

The concept of the semigroup action problem (SAP) was first introduced by Monico in 2002. Monico explained in his paper that the discrete logarithm problem (DLP) can be generalized to SAP. After defining the action problem in a semigroup, the concept was extended using different mathematical structures. In this paper, we discuss the concept of SAP ...

Karmakar, Sudhangshu B.
Published in
Journal of Mathematical Cryptology

An elementary proof that the equation x2n + y2n = z2n can not have any non-zero positive integer solutions when n is an integer ≥ 2 is presented. To prove that the equation has no integer solutions it is first hypothesized that the equation has integer solutions. The absence of any integer solutions of the equation is justified by contradicting the...