Cryptanalysis of Álvarez et al. key exchange scheme

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.

[1]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[2]  Amr M. Youssef,et al.  Cryptanalysis of a Public Key Encryption Scheme Using Ergodic Matrices , 2011, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[3]  Amr M. Youssef,et al.  Cryptanalysis of ‘key agreement scheme based on generalised inverses of matrices’ , 1997 .

[4]  Ciaran Mullan.  Cryptanalysing variants of Stickel's key agreement scheme , 2011, J. Math. Cryptol..

[5]  Francisco Martínez,et al.  Cryptographic Applications of 3x3 Block Upper Triangular Matrices , 2012, HAIS.

[6]  Alfred Menezes,et al.  The Discrete Logarithm Problem in GL(n, q) , 1997, Ars Comb..

[7]  Leandro Tortosa,et al.  A Non-abelian Group Based on Block Upper Triangular Matrices with Cryptographic Applications , 2009, AAECC.

[8]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[9]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

[10]  E. Dawson,et al.  Generalised inverses in public key cryptosystem design , 1998 .

[11]  Francisco Ferrández,et al.  Applying quick exponentiation for block upper triangular matrices , 2006, Appl. Math. Comput..

[12]  Jorge Luis Villar,et al.  Cryptanalysis of a key exchange scheme based on block matrices , 2014, Inf. Sci..

[13]  Ciaran Mullan,et al.  Some Results in Group-Based Cryptography , 2011 .

[14]  V. Varadharajan,et al.  Public Key distribution in matrix rings , 1984 .

[15]  Vladimir Shpilrain.  Cryptanalysis of Stickel's Key Exchange Scheme , 2008, CSR.

[16]  Leandro Tortosa,et al.  Analysis and design of a secure key exchange scheme , 2009, Inf. Sci..