Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Modern Computer Algebra
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Efficient Modular Arithmetic in Adapted Modular Number System Using Lagrange Representation
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Explicit formulas for efficient multiplication in F36m
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Delaying mismatched field multiplications in pairing computations
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
A variant of Miller's formula and algorithm
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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Pairings over elliptic curves use fields $\mathbb{F}_{p^k}$ with p *** 2160 and 6 k ≤ 32. In this paper we propose to represent elements in $\mathbb{F}_p$ with AMNS sytem of [1]. For well chosen AMNS we get roots of unity with sparse representation. The multiplication by these roots are thus really efficient in $\mathbb{F}_p$. The DFT/FFT approach for multiplication in extension field $F_{p^k}$ is thus optimized. The resulting complexity of a multiplication in $\mathbb{F}_{p^k}$ combining AMNS and DFT is about 50% less than the previously recommended approach [2].