Probabilistic Multivariate Cryptography

The field of cryptography has seen enormous changes ever since the invention of Public Key Cryptography by Diffie and Hellman. The algorithms for complex problems like integer factorization, Discrete Logarithms and Elliptic Curve Discrete Logarithms have improved tremendously making way for attackers to crack cryptosystems previously thought were unsolvable. Newer Methods have also been invented like Lattice based cryptography, Code based cryptography, Hash based cryptography and Multivariate cryptography. With the invention of newer public Key cryptosystems, the signature systems making use of public key signatures have enabled authentication of individuals based on public keys. The Key Distribution mechanisms including the Key Exchange protocols and Public Key infrastructure have contributed to the development of algorithms in this area. This chapter also surveys the developments in the area of identity Based Cryptography, Group Based Cryptography and Chaos Based Cryptography.

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Multivariate Cryptography

Multivariate Public Key Cryptosystems - Advances in Information Security ◽

10.1007/978-1-0716-0987-3_2 ◽

2020 ◽

pp. 7-23

Author(s):

Jintai Ding ◽

Albrecht Petzoldt ◽

Dieter S. Schmidt

Keyword(s):

Multivariate Cryptography

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Revisiting the Minrank Problem on Multivariate Cryptography

Information Security Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-030-65299-9_22 ◽

2020 ◽

pp. 291-307

Author(s):

Yacheng Wang ◽

Yasuhiko Ikematsu ◽

Shuhei Nakamura ◽

Tsuyoshi Takagi

Keyword(s):

Multivariate Cryptography

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Efﬁcient GeMSS Based Ring Signature Scheme

Malaysian Journal of Computing and Applied Mathematics ◽

10.37231/myjcam.2020.3.1.41 ◽

2020 ◽

Vol 3 (1) ◽

pp. 38-42

Author(s):

Murat Demircioglu Demircioglu ◽

Sedat Akleylek Akleylek ◽

Murat Cenk

Keyword(s):

Quantum Computing ◽

Public Key ◽

Signature Scheme ◽

Ring Signature ◽

Multivariate Cryptography ◽

Research Areas ◽

Verification Time ◽

Usage Area

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.

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Efficient implementation for QUAD stream cipher with GPUs

Computer Science and Information Systems ◽

10.2298/csis121102040t ◽

2013 ◽

Vol 10 (2) ◽

pp. 897-911 ◽

Cited By ~ 4

Author(s):

Satoshi Tanaka ◽

Takashi Nishide ◽

Kouichi Sakurai

Keyword(s):

Provable Security ◽

Stream Cipher ◽

Computational Cost ◽

Polynomial Systems ◽

Efficient Implementation ◽

Multivariate Polynomial ◽

Multivariate Cryptography ◽

Parallel Arithmetic ◽

Np Complete ◽

Multivariate Systems

QUAD stream cipher uses multivariate polynomial systems. It has provable security based on the computational hardness assumption. More specifically, the security of QUAD depends on hardness of solving non-linear multivariate systems over a finite field, and it is known as an NP-complete problem. However, QUAD is slower than other stream ciphers, and an efficient implementation, which has a reduced computational cost, is required. In this paper, we propose an efficient implementation of computing multivariate polynomial systems for multivariate cryptography on GPU and evaluate efficiency of the proposal. GPU is considered to be a commodity parallel arithmetic unit. Moreover, we give an evaluation of our proposal. Our proposal parallelizes an algorithm of multivariate cryptography, and makes it efficient by optimizing the algorithm with GPU.

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

Physico-mathematical modelling and informational technologies ◽

10.15407/fmmit2021.32.050 ◽

2021 ◽

pp. 27-31

Author(s):

Vasyl Ustimenko ◽

Oleksandr Pustovit

Keyword(s):

Bounded Degree ◽

N Transformations ◽

Decomposition Problem ◽

Multivariate Cryptography ◽

Public Keys ◽

The Family ◽

The Usa ◽

Composition Property ◽

Superelliptic Curves ◽

Nonlinear Maps

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.

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