Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
Function field sieve method for discrete logarithms over finite fields
Information and Computation
The Special Function Field Sieve
SIAM Journal on Discrete Mathematics
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Massively Parallel Computation of Discrete Logarithms
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three
IEEE Transactions on Computers
A comparison of MNT curves and supersingular curves
Applicable Algebra in Engineering, Communication and Computing
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Algorithms and Arithmetic Operators for Computing the ηT Pairing in Characteristic Three
IEEE Transactions on Computers
Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Experiments on the linear algebra step in the number field sieve
IWSEC'07 Proceedings of the Security 2nd international conference on Advances in information and computer security
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
Key length estimation of pairing-based cryptosystems using ηT pairing
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
A tutorial on high performance computing applied to cryptanalysis
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Breaking pairing-based cryptosystems using ηT pairing over GF(397)
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The ηT pairing on supersingular curves over GF(3n) is particularly popular since it is efficiently implementable. Taking into account the Menezes-Okamoto-Vanstone (MOV) attack, the discrete logarithm problem (DLP) in GF(36n) becomes a concern for the security of cryptosystems using ηT pairings in this case. In 2006, Joux and Lercier proposed a new variant of the function field sieve in the medium prime case, named JL06-FFS. We have, however, not yet found any practical implementations on JL06-FFS over GF(36n). Therefore, we first fulfill such an implementation and we successfully set a new record for solving the DLP in GF(36n), the DLP in GF(36·71) of 676-bit size. In addition, we also compare JL06-FFS and an earlier version, named JL02-FFS, with practical experiments. Our results confirm that the former is several times faster than the latter under certain conditions.