A Multivariate Encryption Scheme with Rainbow

Yasuda, Takanori; Sakurai, Kouichi

doi:10.1007/978-3-319-29814-6_19

Cited by 24 publications

(5 citation statements)

References 41 publications

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“…The main similarity of the proposed algorithms with the algorithms of multivariate cryptography [16,[18][19][20][21][22][23][24][25][26][27][28] is that both types of algorithms are based on the computational difficulty of solving large systems of quadratic multivariate equations. This determines the similarity of the direct attack on these algorithms.…”

Section: More Realistic Attacks On the Proposed Algorithms Relate To ...mentioning

confidence: 99%

Signature Algorithms with a Hidden Group, Based on Difficulty of Solving Systems of Quadratic Equations

Levina,

Moldovyan,

Moldovyan

et al. 2023

JAIT

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This research introduces two novel algebraic signature algorithms with a hidden group, which are based on the computational difficulty of finding a solution of a large system of quadratic multivariate equations. Like signature algorithms of multivariate cryptography, the developed ones represent interest as post-quantum cryptoschemes, the latter having a significant merit consisting of a 100 or more times smaller size of public key. The introduced algorithms represent interest as candidates for a practical post-quantum signature standard with small sizes for both the signature and the public key. Their security is estimated to be vulnerable to direct attacks using the known algorithms for solving the systems of many quadratic equations. The development of structural attacks exploiting properties of the used algebraic support is estimated as an independent research task composing the next stage of the analysis of the proposed signature algorithms on finite non-commutative associative algebras. Relatively the known algebraic signature algorithms with a hidden group, which are based on the computational difficulty of the so called hidden discrete logarithm problem, the developed signature algorithms differ in the use of the signature verification equations with multiple entry of signature. This feature defines a specific technique for the signature generation. The next peculiarity is the use of algebras of higher dimensions set over the finite fields of smaller orders.

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Section: More Realistic Attacks On the Proposed Algorithms Relate To ...mentioning

confidence: 99%

Signature Algorithms with a Hidden Group, Based on Difficulty of Solving Systems of Quadratic Equations

Levina,

Moldovyan,

Moldovyan

et al. 2023

JAIT

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show abstract

“…3) Multivariate-based DS: Security assumptions in multivariate cryptography are based on the difficulty of solving systems of multivariate polynomials over finite fields (MVP). Rainbow [35] derives its structure from unbalanced Oil and Vinegar (UOV) scheme. To achieve NIST security level I, Rainbow selects the finite-field F q with q elements, m multivariate equations and n variables as the security parameters.…”

Section: Asa On the Security Parameters (Sparam)mentioning

confidence: 99%

Fuzzing+Hardware Performance Counters-Based Detection of Algorithm Subversion Attacks on Post-Quantum Signature Schemes

Chowdhury,

Mahapatra,

Soni

et al. 2022

Preprint

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NIST is standardizing Post Quantum Cryptography (PQC) algorithms that are resilient to the computational capability of quantum computers. Past works show malicious subversion with cryptographic software (algorithm subversion attacks) that weaken the implementations. We show that PQC digital signature codes can be subverted in line with previously reported flawed implementations [1], [2] that generate verifiable, but less-secure signatures, demonstrating the risk of such attacks. Since, all processors have built-in Hardware Performance Counters (HPCs), there exists a body of work proposing a lowcost Machine Learning (ML)-based integrity checking of software using HPC fingerprints. However, such HPC-based approaches may not detect subversion of PQC codes. A miniscule percentage of qualitative inputs when applied to the PQC codes improve this accuracy to 98%. We propose grey-box fuzzing as a preprocessing step to obtain inputs to aid the HPC-based method.

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“…In [38], [37], D. Moody et al and Gu Chunsheng presented some attacks on Simple matrix scheme. Another multivariate public key cryptosystem called SRP was proposed by Yasude et al in 2015 [36]. This cryptosystem combines several multivariate public key cryptosystems into one which seems to prevent some of the known attacks on multivariate cryptosystems.…”

Section: Introductionmentioning

confidence: 99%

A Public Key Cryptosystem Using a Group of Permutation Polynomials

Singh

Sarma

Saikia

2020

Tatra Mountains Mathematical Publications

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In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field Fqm. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m2+3m – 4 left cyclic shifts, 5m2 +3m + 4 xor operations and 7 permutations on bits for decryption.

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A Multivariate Encryption Scheme with Rainbow

Cited by 24 publications

References 41 publications

Signature Algorithms with a Hidden Group, Based on Difficulty of Solving Systems of Quadratic Equations

Signature Algorithms with a Hidden Group, Based on Difficulty of Solving Systems of Quadratic Equations

Fuzzing+Hardware Performance Counters-Based Detection of Algorithm Subversion Attacks on Post-Quantum Signature Schemes

A Public Key Cryptosystem Using a Group of Permutation Polynomials

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