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Families of nested completely regular codes and distance-regular graphs
Cryptanalysis of a noncommutative key exchange protocol
1. | Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Zürich, Switzerland |
References:
[1] |
R. Álvarez, F. Martinez, J. Vicent and A. Zamora, A new public key cryptosystem based on matrices, in 6th WSEAS Int. Conf. Inform. Secur. Privacy, Tenerife, Spain, 2007. |
[2] |
R. Álvarez, L. Tortosa, J. Vicent and A. Zamora, Analysis and design of a secure key exchange scheme, Inform. Sci., 179 (2009), 2014-2021.
doi: 10.1016/j.ins.2009.02.008. |
[3] |
M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Westview Press, 1969. |
[4] |
N. Courtois, A. Klimov, J. Patarin and A. Shamir, Efficient algorithms for solving overdefined systems of multivariate polynomial equations, in Advances in Cryptology - EUROCRYPT 2000 (ed. B. Preneel), Springer, Berlin, 2000, 392-407.
doi: 10.1007/3-540-45539-6_27. |
[5] |
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Trans. Inf. Theory, IT-22 (1976), 644-654. |
[6] |
T. ElGamal, A public-key cryptosystem and a signature scheme based on discrete logarithms, IEEE Trans. Inf. Theory, 31 (1985), 469-472.
doi: 10.1109/TIT.1985.1057074. |
[7] |
J.-C. Faugère, A new efficient algorithm for computing Gröbner bases (F4), J. Pure Appl. Algebra, 139 (1999), 61-88.
doi: 10.1016/S0022-4049(99)00005-5. |
[8] |
J. Hoffstein, J. Pipher and J. H. Silverman, NTRU: A ring-based public key cryptosystem, in Algorithmic Number Theory, 1998, 267-288.
doi: 10.1007/BFb0054868. |
[9] |
G. Maze and C. Monico and J.Rosenthal, Public key cryptography based on semigroup actions, Adv. Math. Commun., 1 (2007), 489-507.
doi: 10.3934/amc.2007.1.489. |
[10] |
G. Micheli, J. Rosenthal and P. Vettori, Linear spanning sets for matrix spaces, preprint, arXiv:1409.3020 |
[11] |
G. Micheli and M. Schiavina, A general construction for monoid-based knapsack protocols, Adv. Math. Commun., 8 (2014), 343-358.
doi: 10.3934/amc.2014.8.343. |
[12] |
D. Naccache and J. Stern, A new public key cryptosystem, in Advances in Cryptology, EUROCRYPT, 1997, 27-36.
doi: 10.1007/3-540-69053-0_3. |
[13] |
D. Naccache and J. Stern, A new public key cryptosystem based on higher residues, in Proc. 5th ACM Conf. Computer Commun. Secur., San Francisco, 1998, 59-66.
doi: 10.1145/288090.288106. |
[14] |
H. K. Pathak and M. Sanghi, Public key cryptosystem and a key exchange protocol using tools of non-abelian groups, Int. J. Comput. Sci. Engin., 2 (2010), 1029-1033. |
[15] |
D. Pointcheval, Rabin cryptosystem, in Encyclopedia of Cryptography and Security, Springer, 2011, 1013-1014.
doi: 10.1007/978-1-4419-5906-5_151. |
[16] |
R. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM, 21 (1978), 120-126.
doi: 10.1145/359340.359342. |
[17] |
Slavin, Public key cryptography using matrices, available at http://www.patentgenius.com/patent/7184551.html, 2007. |
[18] |
R. Steinwandt and A. S. Corona, Cryptanalysis of a 2-party key establishment based on a semigroup action problem, Adv. Math. Commun., 5 (2011), 87-92.
doi: 10.3934/amc.2011.5.87. |
[19] |
M. I. G. Vasco, A. L. Pérez del Pozo, P. T. Duarte and J. L. Villar, Cryptanalysis of a key exchange scheme based on block matrices, Inf. Sc., 276 (2014), 319-331.
doi: 10.1016/j.ins.2013.11.009. |
show all references
References:
[1] |
R. Álvarez, F. Martinez, J. Vicent and A. Zamora, A new public key cryptosystem based on matrices, in 6th WSEAS Int. Conf. Inform. Secur. Privacy, Tenerife, Spain, 2007. |
[2] |
R. Álvarez, L. Tortosa, J. Vicent and A. Zamora, Analysis and design of a secure key exchange scheme, Inform. Sci., 179 (2009), 2014-2021.
doi: 10.1016/j.ins.2009.02.008. |
[3] |
M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Westview Press, 1969. |
[4] |
N. Courtois, A. Klimov, J. Patarin and A. Shamir, Efficient algorithms for solving overdefined systems of multivariate polynomial equations, in Advances in Cryptology - EUROCRYPT 2000 (ed. B. Preneel), Springer, Berlin, 2000, 392-407.
doi: 10.1007/3-540-45539-6_27. |
[5] |
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Trans. Inf. Theory, IT-22 (1976), 644-654. |
[6] |
T. ElGamal, A public-key cryptosystem and a signature scheme based on discrete logarithms, IEEE Trans. Inf. Theory, 31 (1985), 469-472.
doi: 10.1109/TIT.1985.1057074. |
[7] |
J.-C. Faugère, A new efficient algorithm for computing Gröbner bases (F4), J. Pure Appl. Algebra, 139 (1999), 61-88.
doi: 10.1016/S0022-4049(99)00005-5. |
[8] |
J. Hoffstein, J. Pipher and J. H. Silverman, NTRU: A ring-based public key cryptosystem, in Algorithmic Number Theory, 1998, 267-288.
doi: 10.1007/BFb0054868. |
[9] |
G. Maze and C. Monico and J.Rosenthal, Public key cryptography based on semigroup actions, Adv. Math. Commun., 1 (2007), 489-507.
doi: 10.3934/amc.2007.1.489. |
[10] |
G. Micheli, J. Rosenthal and P. Vettori, Linear spanning sets for matrix spaces, preprint, arXiv:1409.3020 |
[11] |
G. Micheli and M. Schiavina, A general construction for monoid-based knapsack protocols, Adv. Math. Commun., 8 (2014), 343-358.
doi: 10.3934/amc.2014.8.343. |
[12] |
D. Naccache and J. Stern, A new public key cryptosystem, in Advances in Cryptology, EUROCRYPT, 1997, 27-36.
doi: 10.1007/3-540-69053-0_3. |
[13] |
D. Naccache and J. Stern, A new public key cryptosystem based on higher residues, in Proc. 5th ACM Conf. Computer Commun. Secur., San Francisco, 1998, 59-66.
doi: 10.1145/288090.288106. |
[14] |
H. K. Pathak and M. Sanghi, Public key cryptosystem and a key exchange protocol using tools of non-abelian groups, Int. J. Comput. Sci. Engin., 2 (2010), 1029-1033. |
[15] |
D. Pointcheval, Rabin cryptosystem, in Encyclopedia of Cryptography and Security, Springer, 2011, 1013-1014.
doi: 10.1007/978-1-4419-5906-5_151. |
[16] |
R. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM, 21 (1978), 120-126.
doi: 10.1145/359340.359342. |
[17] |
Slavin, Public key cryptography using matrices, available at http://www.patentgenius.com/patent/7184551.html, 2007. |
[18] |
R. Steinwandt and A. S. Corona, Cryptanalysis of a 2-party key establishment based on a semigroup action problem, Adv. Math. Commun., 5 (2011), 87-92.
doi: 10.3934/amc.2011.5.87. |
[19] |
M. I. G. Vasco, A. L. Pérez del Pozo, P. T. Duarte and J. L. Villar, Cryptanalysis of a key exchange scheme based on block matrices, Inf. Sc., 276 (2014), 319-331.
doi: 10.1016/j.ins.2013.11.009. |
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