Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
Hierarchical identity based encryption with constant size ciphertext
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Security analysis of the strong diffie-hellman problem
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Efficient blind and partially blind signatures without random oracles
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Remarks on Cheon's algorithms for pairing-related problems
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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Pairing based cryptography is a new public key cryptographic scheme. An elliptic curve suitable for pairing based cryptography is called a "pairing-friendly" elliptic curve. After Mitsunari, Sakai and Kasahara's traitor tracing scheme and Boneh and Boyen's short signature scheme, many protocols based on pairing-related problems such as the q-weak Diffie-Hellman problem have been proposed. In Eurocrypt 2006, Cheon proposed a new efficient algorithm to solve pairing-related problems and recently the complexity of Cheon's algorithm has been improved by Kozaki, Kutsuma and Matsuo. Due to these two works, an influence of Cheon's algorithm should be considered when we construct a suitable curve for the use of a protocol based on a pairing-related problem. Among known methods for constructing pairing-friendly elliptic curves, ones using cyclotomic polynomials are affected by Cheon's algorithm. In this paper, we study how to reduce a security loss of a cyclotomic family by Cheon's algorithm.