On effective computations in subsemigroups of affine Cremona semigroup and implentations of new postquantum multivariate cryptosystems

Multivariate cryptography (MC) together with Latice Based, Hash based, Code based and Superelliptic curves based Cryptographies form list of the main directions of Post Quantum Cryptography.Investigations in the framework of tender of National Institute of Standardisation Technology (the USA) indicates that the potential of classical MC working with nonlinear maps of bounded degree and without the usage of compositions of nonlinear transformation is very restricted. Only special case of Rainbow like Unbalanced Oil and Vinegar digital signatures is remaining for further consideration. The remaining public keys for encryption procedure are not of multivariate. nature. The paper presents large semigroups and groups of transformations of finite affine space of dimension n with the multiple composition property. In these semigroups the composition of n transformations is computable in polynomial time. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of these protocols rests on the complexity of the word decomposition problem, Finally presented algebraic protocols expanded to cryptosystems of El Gamal type which is not a public key system.

Efficient GeMSS Based Ring Signature Scheme

The ring signature scheme has an important usage area of public key crypto-system. It can be used for e-voting, as well as leaking information without revealing identity within a group. However, most of these systems relies on traditional crypto-systems which are not secure against quantum computing related attacks. Multivariate cryptography is one of the most popular research areas on quantum resilient crypto-systems. In this work, we propose an efficient ring signature scheme based on GeMSS, where we achieve smaller signature size and faster verification time with respect to other alternatives.

On Public-key Cryptosystem Based on the Problem of Solving a Non-Linear System of Polynomial Equations

The basic idea behind multivariate cryptography is to choose a system of polynomials which can be easily inverted (central map). After that one chooses two affine invertible maps to hide the structure of the central map. Fellows and Koblitz outlined a conceptual key cryptosystem based on the hardness of POSSO. Let Fp s be a finite field of p s elements, where p is a prime number, and s ∈ N, s ≥ 1. In this paper, we used the act of GLn (Fp s ) on the set F n p s and the transformations group, to present the public key cryptosystems based on the problem of solving a non-linear system of polynomial equations

Fuzzy Matching Template Attacks on Multivariate Cryptography: A Case Study

Multivariate cryptography is one of the most promising candidates for post-quantum cryptography. Applying machine learning techniques in this paper, we experimentally investigate the side-channel security of the multivariate cryptosystems, which seriously threatens the hardware implementations of cryptographic systems. Generally, registers are required to store values of monomials and polynomials during the encryption of multivariate cryptosystems. Based on maximum-likelihood and fuzzy matching techniques, we propose a template-based least-square technique to efficiently exploit the side-channel leakage of registers. Using QUAD for a case study, which is a typical multivariate cryptosystem with provable security, we perform our attack against both serial and parallel QUAD implementations on field programmable gate array (FPGA). Experimental results show that our attacks on both serial and parallel implementations require only about 30 and 150 power traces, respectively, to successfully reveal the secret key with a success rate close to 100%. Finally, efficient and low-cost strategies are proposed to resist side-channel attacks.