Introduction to finite fields and their applications
Introduction to finite fields and their applications
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
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Exponentiation in Finite Fields: Theory and Practice
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CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
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Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
FPGA design for algebraic tori-based public-key cryptography
Proceedings of the conference on Design, automation and test in Europe
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
On XTR and side-channel analysis
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
A note on the signed sliding window integer recoding and a left-to-right analogue
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Fast irreducibility testing for XTR using a gaussian normal basis of low complexity
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Discrete logarithm variants of VSH
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
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This paper describes several speedups for computation in the order p + 1 subgroup of F*p2 and the order p2 - p + 1 subgroup of F*p6. These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with p = 3 mod 4.