A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A More Compact Representation of XTR Cryptosystem
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
The number field sieve in the medium prime case
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
The function field sieve in the medium prime case
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
SP 800-57. Recommendation for Key Management, Part 1: General (revised)
SP 800-57. Recommendation for Key Management, Part 1: General (revised)
Public-key cryptosystems based on cubic finite field extensions
IEEE Transactions on Information Theory
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The security of pairing-based cryptosystems relies on the hardness of the discrete logarithm problems in elliptic curves and in finite fields related to the curves, namely, their embedding fields. Public keys and ciphertexts in the pairing-based cryptosystems are composed of points on the curves or values of pairings. Although the values of the pairings belong to the embedding fields, the representation of the field is inefficient in size because the size of the embedding fields is usually larger than the size of the elliptic curves. We show factor-4 and 6 compression and decompression for the values of the pairings with the supersingular elliptic curves of embedding degrees 4 and 6, respectively. For compression, we use the fact that the values of the pairings belong to algebraic tori that are multiplicative subgroups of the embedding fields. The algebraic tori can be expressed by the affine representation or the trace representation. Although the affine representation allows decompression maps, decompression maps for the trace representation has not been known. In this paper, we propose a trace representation with decompression maps for the characteristics 2 and 3. We first construct efficient decompression maps for trace maps by adding extra information to the trace representation. Our decompressible trace representation with additional information is as efficient as the affine representation is in terms of the costs of compression, decompression and exponentiation, and the size.