Algebraic properties of cryptosystem PGM
Journal of Cryptology
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
New Public Key Cryptosystem Using Finite Non Abelian Groups
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Group factorizations in cryptography
Group factorizations in cryptography
Towards a Uniform Description of Several Group Based Cryptographic Primitives
Designs, Codes and Cryptography
Attacking a public key cryptosystem based on tree replacement
Discrete Applied Mathematics
Minimal logarithmic signatures for classical groups
Designs, Codes and Cryptography
A new cramer-shoup like methodology for group based provably secure encryption schemes
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
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The public key cryptosystem MST1 has been introduced by Magliveras et al. [12] (Public Key Cryptosystems from Group Factorizations. Jatra Mountain Mathematical Publications). Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify `wild-like' logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We present tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree 驴 5. Hence, basing a key generation procedure on the assumption that totally-non-transversal logarithmic signatures are `wild like' seems critical. We also discuss the problem of recognizing `weak' totally-non-transversal logarithmic signatures, and demonstrate that another proposed key generation procedure based on permutably transversal logarithmic signatures may produce weak keys.