Esquema de Acordo de Chaves de Conferência Baseado em um Problema de Funções Quadráticas de Duas Variáveis
Resumo
Estabelecimento de chave de conferência é o processo de determinação de uma chave comum compartilhada entre três ou mais participantes. Se neste processo, todos os participantes influenciam a chave a ser gerada, temos um esquema de acordo de chaves de conferência. No presente trabalho, propomos um esquema de acordo de chaves de conferência que apresenta vantagens significativas sobre os atuais esquemas existentes, como: 1. acordo de chaves de conferência em uma única rodada e com quantidade linear de mensagens publicadas; 2. combinação de duas chaves de conferência em uma única rodada e com número constante de mensagens publicadas; 3. renovação de chaves de conferência em uma única rodada e com única mensagem publicada. O esquema proposto é resiliente face a cenários de ataques clássicos, mas é vulnerável a ataques executados por um atacante capaz de calcular o logaritmo discreto, sendo, portanto, vulnerável a ataques usando Computação Quântica.Referências
Al-Riyami, S. S. and Paterson, K. G. (2003). Tripartite Authenticated Key Agreement Protocols from Pairings, pages 332–359. Springer Berlin Heidelberg, Berlin, Heidelberg.
Ateniese, G., Steiner, M., and Tsudik, G. (2000). New multiparty authentication services and key agreement protocols. IEEE Journal on Selected Areas in Communications, 18(4):628–639.
Barker, E., Chen, L., Roginsky, A., and Smid, M. (2013). Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography (NIST Special Publication 800-56A, Revision 2). National Institute of Standards and Technology.
Barua, R., Dutta, R., and Sarkar, P. (2003). Extending joux’s protocol to multi party key agreement. IACR Cryptology ePrint Archive, 2003:62.
Boneh, D. and Silverberg, A. (2002). Applications of multilinear forms to cryptography. Contemporary Mathematics, 324:71–90.
Chunsheng, G. (2015a). Multilinear maps using ideal lattices without encodings of zero. Cryptology ePrint Archive, Report 2015/023. http://eprint.iacr.org/2015/023.
Chunsheng, G. (2015b). Multilinear maps using ideal lattices without encodings of zero. Diffie, W. and Hellman, M. (1976). New directions in cryptography. IEEE Trans. Inf. Theor., 22(6):644–654.
Diffie, W., Van Oorschot, P. C., and Wiener, M. J. (1992). Authentication and authenticated key exchanges. Designs, Codes and Cryptography, 2(2):107–125.
ElGammal, T. The first ten years of public-key cryptograph. Proceedings of the IEEE, 76.
ElGammal, T. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31.
Garg, S., Gentry, C., and Halevi, S. (2013). Candidate Multilinear Maps from Ideal Lattices, pages 1–17. Springer Berlin Heidelberg, Berlin, Heidelberg.
Hilbert, D. (1902). Mathematical problems. Bull. Amer. Math. Soc., 8(10):437–479.
Hu, Y. and Jia, H. (2016). Cryptanalysis of ggh map. In Proceedings of the 35th Annual International Conference on Advances in Cryptology — EUROCRYPT 2016 - Volume 9665, pages 537–565, New York, NY, USA. Springer-Verlag New York, Inc.
Joux, A. (2000). A One Round Protocol for Tripartite Diffie–Hellman, pages 385–393. Springer Berlin Heidelberg, Berlin, Heidelberg.
Lee, Y.-R., Lee, H.-S., and Lee, H.-K. (2004). Multi-party authenticated key agreement protocols from multi-linear forms. Applied Mathematics and Computation, 159(2):317 – 331.
Manders, K. L. and Adleman, L. (1978). Np-complete decision problems for binary quadratics. Journal of Computer and System Sciences, 16(2):168 – 184.
Matijasevi?c, J. V. (1970). The diophantineness of enumerable sets (russian). Dokl. Akad. Nauk SSSR, 191:279–282.
Matsumoto, T., Takashima, Y., and Ima, H. On seeking smart public-key distribution systems. The Transactions of the IECE of Japan, E69.
Robinson, J. (1972). Review: Ju. v. matijasevic, a. doohovskoy, enumerable sets are diophantine. J. Symbolic Logic, 37(3):605–606.
Thue, A. (1902). Uber annaherungswerte algebraischer. J. Reine Angew Math, 135:284–305.
Ateniese, G., Steiner, M., and Tsudik, G. (2000). New multiparty authentication services and key agreement protocols. IEEE Journal on Selected Areas in Communications, 18(4):628–639.
Barker, E., Chen, L., Roginsky, A., and Smid, M. (2013). Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography (NIST Special Publication 800-56A, Revision 2). National Institute of Standards and Technology.
Barua, R., Dutta, R., and Sarkar, P. (2003). Extending joux’s protocol to multi party key agreement. IACR Cryptology ePrint Archive, 2003:62.
Boneh, D. and Silverberg, A. (2002). Applications of multilinear forms to cryptography. Contemporary Mathematics, 324:71–90.
Chunsheng, G. (2015a). Multilinear maps using ideal lattices without encodings of zero. Cryptology ePrint Archive, Report 2015/023. http://eprint.iacr.org/2015/023.
Chunsheng, G. (2015b). Multilinear maps using ideal lattices without encodings of zero. Diffie, W. and Hellman, M. (1976). New directions in cryptography. IEEE Trans. Inf. Theor., 22(6):644–654.
Diffie, W., Van Oorschot, P. C., and Wiener, M. J. (1992). Authentication and authenticated key exchanges. Designs, Codes and Cryptography, 2(2):107–125.
ElGammal, T. The first ten years of public-key cryptograph. Proceedings of the IEEE, 76.
ElGammal, T. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31.
Garg, S., Gentry, C., and Halevi, S. (2013). Candidate Multilinear Maps from Ideal Lattices, pages 1–17. Springer Berlin Heidelberg, Berlin, Heidelberg.
Hilbert, D. (1902). Mathematical problems. Bull. Amer. Math. Soc., 8(10):437–479.
Hu, Y. and Jia, H. (2016). Cryptanalysis of ggh map. In Proceedings of the 35th Annual International Conference on Advances in Cryptology — EUROCRYPT 2016 - Volume 9665, pages 537–565, New York, NY, USA. Springer-Verlag New York, Inc.
Joux, A. (2000). A One Round Protocol for Tripartite Diffie–Hellman, pages 385–393. Springer Berlin Heidelberg, Berlin, Heidelberg.
Lee, Y.-R., Lee, H.-S., and Lee, H.-K. (2004). Multi-party authenticated key agreement protocols from multi-linear forms. Applied Mathematics and Computation, 159(2):317 – 331.
Manders, K. L. and Adleman, L. (1978). Np-complete decision problems for binary quadratics. Journal of Computer and System Sciences, 16(2):168 – 184.
Matijasevi?c, J. V. (1970). The diophantineness of enumerable sets (russian). Dokl. Akad. Nauk SSSR, 191:279–282.
Matsumoto, T., Takashima, Y., and Ima, H. On seeking smart public-key distribution systems. The Transactions of the IECE of Japan, E69.
Robinson, J. (1972). Review: Ju. v. matijasevic, a. doohovskoy, enumerable sets are diophantine. J. Symbolic Logic, 37(3):605–606.
Thue, A. (1902). Uber annaherungswerte algebraischer. J. Reine Angew Math, 135:284–305.
Publicado
06/11/2017
Como Citar
KOWADA, Luis Antonio B.; MACHADO, Raphael C. S..
Esquema de Acordo de Chaves de Conferência Baseado em um Problema de Funções Quadráticas de Duas Variáveis. In: SIMPÓSIO BRASILEIRO DE SEGURANÇA DA INFORMAÇÃO E DE SISTEMAS COMPUTACIONAIS (SBSEG), 17. , 2017, Brasília.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2017
.
p. 126-139.
DOI: https://doi.org/10.5753/sbseg.2017.19495.
