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A general construction for monoid-based knapsack protocols
1. | Institut für Mathematik, Winterthurerstrasse 190, Zürich, CH8057, Switzerland, Switzerland |
References:
[1] |
B. Chevallier-Mames, D. Naccache and J. Stern, Linear bandwidth Naccache-Stern encryption, in Security and Cryptography for Networks, 2008, 337-339.
doi: 10.1007/978-3-540-85855-3_22. |
[2] |
W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. Inf. Theory, 22 (1976), 644-654. |
[3] |
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. |
[4] | |
[5] |
M. E. Hellman, An overview of public key cryptography, IEEE Commun. Soc. M., 16 (1978), 24-32.
doi: 10.1109/MCOM.1978.1089772. |
[6] |
J. Hoffstein, J. Pipher and J. H. Silverman, A ring based public key cryptosystem, in Algorithmic Number Theory (ANTS III), (ed. J.P. Buhler), Springer-Verlag, Berlin, 1998, 267-288.
doi: 10.1007/BFb0054868. |
[7] |
S. Kiuchi, Y. Murakami and M. Kasahara, High rate mulitiplicative knapsack cryptosystem (in Japanese), IEICE Tech. Report, ISEC98-26 (1998), 43-50. |
[8] |
S. Kiuchi, Y. Murakami and M. Kasahara, New mulitiplicative knapsack-type public key cryptosystems, IEICE Trans., E84-A (2001), 188-196. |
[9] |
G. Maze, 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] |
R. J. McEliece, A public-key cryptosystem based on algebraic coding theory, DSN Progress Report, 114 (1978), 42-44. |
[11] |
M. Morii and M. Kasahara, New public key cryptosystem using discrete logarithms over GF(P) (in Japanese), IEICE Trans., J71-D (1988), 448-453. |
[12] |
D. Naccache and J. Stern, New public key cryptosystem, in Proceedings of Eurocrypt 97, Springer-Verlag, 1997, 27-36.
doi: 10.1007/3-540-69053-0_3. |
[13] |
T. Okamoto, K. Tamaka and S. Uchiyama, Quantum public key cryptosystem, in Advances in cryptology - CRYPTO 2000, Springer, 2000, 147-165.
doi: 10.1007/3-540-44598-6_9. |
[14] |
J. Patarin, Hidden field equations HFE and isomorphisms of polynomials IP: two new families of asymmetric algorithms, in Advances in Cryptology - EUROCRYPT '96, 1996, 33-48. |
[15] |
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. |
[16] |
M. Rosen, Number Theory in Function Fields, Springer, 2002.
doi: 10.1007/978-1-4757-6046-0. |
[17] |
A. Salomaa, Public Key Cryptography, Springer-Verlag, 1990
doi: 10.1007/978-3-662-02627-4. |
[18] |
V. Shoup, New algorithms for finding irreducible polynomials over finite fields, Math. Comput., 54 (1990), 435-447.
doi: 10.2307/2008704. |
show all references
References:
[1] |
B. Chevallier-Mames, D. Naccache and J. Stern, Linear bandwidth Naccache-Stern encryption, in Security and Cryptography for Networks, 2008, 337-339.
doi: 10.1007/978-3-540-85855-3_22. |
[2] |
W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. Inf. Theory, 22 (1976), 644-654. |
[3] |
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. |
[4] | |
[5] |
M. E. Hellman, An overview of public key cryptography, IEEE Commun. Soc. M., 16 (1978), 24-32.
doi: 10.1109/MCOM.1978.1089772. |
[6] |
J. Hoffstein, J. Pipher and J. H. Silverman, A ring based public key cryptosystem, in Algorithmic Number Theory (ANTS III), (ed. J.P. Buhler), Springer-Verlag, Berlin, 1998, 267-288.
doi: 10.1007/BFb0054868. |
[7] |
S. Kiuchi, Y. Murakami and M. Kasahara, High rate mulitiplicative knapsack cryptosystem (in Japanese), IEICE Tech. Report, ISEC98-26 (1998), 43-50. |
[8] |
S. Kiuchi, Y. Murakami and M. Kasahara, New mulitiplicative knapsack-type public key cryptosystems, IEICE Trans., E84-A (2001), 188-196. |
[9] |
G. Maze, 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] |
R. J. McEliece, A public-key cryptosystem based on algebraic coding theory, DSN Progress Report, 114 (1978), 42-44. |
[11] |
M. Morii and M. Kasahara, New public key cryptosystem using discrete logarithms over GF(P) (in Japanese), IEICE Trans., J71-D (1988), 448-453. |
[12] |
D. Naccache and J. Stern, New public key cryptosystem, in Proceedings of Eurocrypt 97, Springer-Verlag, 1997, 27-36.
doi: 10.1007/3-540-69053-0_3. |
[13] |
T. Okamoto, K. Tamaka and S. Uchiyama, Quantum public key cryptosystem, in Advances in cryptology - CRYPTO 2000, Springer, 2000, 147-165.
doi: 10.1007/3-540-44598-6_9. |
[14] |
J. Patarin, Hidden field equations HFE and isomorphisms of polynomials IP: two new families of asymmetric algorithms, in Advances in Cryptology - EUROCRYPT '96, 1996, 33-48. |
[15] |
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. |
[16] |
M. Rosen, Number Theory in Function Fields, Springer, 2002.
doi: 10.1007/978-1-4757-6046-0. |
[17] |
A. Salomaa, Public Key Cryptography, Springer-Verlag, 1990
doi: 10.1007/978-3-662-02627-4. |
[18] |
V. Shoup, New algorithms for finding irreducible polynomials over finite fields, Math. Comput., 54 (1990), 435-447.
doi: 10.2307/2008704. |
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