Cryptanalysis of matrix conjugation schemes

Myasnikov, Alex D.; Ushakov, Alexander

doi:10.1515/jmc-2012-0033

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…A second way to attack the present protocol would be to find a polynomial time algorithm to solve the algebraic generalized symmetric decomposition. As some simpler OWTF based on algebraic conjugation were successfully cryptanalyzed [38,39], it was mandatory to find very hard functions. We presented earlier (see Definition (5)) a stronger version, the blind general symmetric decomposition problem (BGSDP).…”

Section: Protocol Securitymentioning

confidence: 99%

Post-Quantum Cryptography: generalized ElGamal cipher over GF(251^8)

Hecht

2017

TAAI

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Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks by means of for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). Other aspects are the backdoors discovered in deterministic random generators or recent advances in solving some instances of DLP. The use of alternative algebraic structures like non-commutative or non-associative partial groupoids, magmas, monoids, semigroups, quasigroups or groups, are valid choices for these new kinds of protocols. In this paper, we focus in an asymmetric cipher based on a generalized ElGamal non-arbitrated protocol using a non-commutative general linear group. The developed protocol forces a hard subgroup membership search problem into a non-commutative structure. The protocol involves at first a generalized Diffie-Hellman key interchange and further on the private and public parameters are recursively updated each time a new cipher session is launched. Security is based on a hard variation of the Generalized Symmetric Decomposition Problem (GSDP). Working with GF (251 8 ) a 64-bits security is achieved, and if GF ( 251 16 ) is chosen, the security rises to 127-bits. An appealing feature is that there is no need for big number libraries as all arithmetic if performed in Z 251 and therefore the new protocol is particularly useful for computational platforms with very limited capabilities like smartphones or smartcards.

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Section: Protocol Securitymentioning

confidence: 99%

Post-Quantum Cryptography: generalized ElGamal cipher over GF(251^8)

Hecht

2017

TAAI

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“…(xiv) In 2014, Myasnikov and Ushakov [36] cryptanalyzed the authentication scheme proposed by Shpilrain and public key encryption to use the hardness of the Conjugacy Search Problem in noncommutative monoids. A heuristic algorithm, was devised by those to solve these problems and declared that these protocols are anxious.…”

Section: Introductionmentioning

confidence: 99%

Novel Noncommutative Cryptography Scheme Using Extra Special Group

Kumar

Saini

2017

Security and Communication Networks

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Noncommutative cryptography (NCC) is truly a fascinating area with great hope of advancing performance and security for high end applications. It provides a high level of safety measures. The basis of this group is established on the hidden subgroup or subfield problem (HSP). The major focus in this manuscript is to establish the cryptographic schemes on the extra special group (ESG). ESG is showing one of the most appropriate noncommutative platforms for the solution of an open problem. The working principle is based on the random polynomials chosen by the communicating parties to secure key exchange, encryption-decryption, and authentication schemes. This group supports Heisenberg, dihedral order, and quaternion group. Further, this is enhanced from the general group elements to equivalent ring elements, known by the monomials generations for the cryptographic schemes. In this regard, special or peculiar matrices show the potential advantages. The projected approach is exclusively based on the typical sparse matrices, and an analysis report is presented fulfilling the central cryptographic requirements. The order of this group is more challenging to assail like length based, automorphism, and brute-force attacks.

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An ECC with Probable Secure and Efficient Approach on Noncommutative Cryptography

Kumar

Saini

2019

Advances in Intelligent Systems and Computing

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Cryptanalysis of matrix conjugation schemes

Cited by 5 publications

References 11 publications

Post-Quantum Cryptography: generalized ElGamal cipher over GF(251^8)

Post-Quantum Cryptography: generalized ElGamal cipher over GF(251^8)

Novel Noncommutative Cryptography Scheme Using Extra Special Group

An ECC with Probable Secure and Efficient Approach on Noncommutative Cryptography

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