Elliptic curves in cryptography
Elliptic curves in cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Analysis and design of a secure key exchange scheme
Information Sciences: an International Journal
A Non-abelian Group Based on Block Upper Triangular Matrices with Cryptographic Applications
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Cryptanalysis of Stickel's key exchange scheme
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Cryptographic applications of 3x3 block upper triangular matrices
HAIS'12 Proceedings of the 7th international conference on Hybrid Artificial Intelligent Systems - Volume Part II
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
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Alvarez et al., Information Sciences 179 (12) (2009) proposed a new key exchange scheme where the secret key is obtained by multiplying powers of block upper triangular matrices whose elements are defined over Z"p. In this note, we show that breaking this system with security parameters (r,s,p) is equivalent to solving a set of 3(r+s)^2 linear equations with 2(r+s)^2 unknowns in Z"p, which renders this system insecure for all the suggested practical choices of the security parameters.