Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A subexponential algorithm for discrete logarithms over all finite fields
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Function field sieve method for discrete logarithms over finite fields
Information and Computation
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
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: 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
IFIP/Sec '93 Proceedings of the IFIP TC11, Ninth International Conference on Information Security: Computer Security
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
An Analytic Approach to Smooth Polynominals over Finite Fields
ANTS-III Proceedings of the Third 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
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Short Signatures from the Weil Pairing
Journal of Cryptology
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Applications to cryptography of twisting commutative algebraic groups
Discrete Applied Mathematics
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
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Solving a 676-bit discrete logarithm problem in GF(36n)
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
The number field sieve in the medium prime case
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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
Improving the complexity of index calculus algorithms in elliptic curves over binary fields
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
On polynomial systems arising from a weil descent
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Factor-4 and 6 (de)compression for values of pairings using trace maps
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Hi-index | 0.00 |
In this paper, we study the application of the function field sieve algorithm for computing discrete logarithms over finite fields of the form ${\mathbb {F}}_{q^n}$ when q is a medium-sized prime power. This approach is an alternative to a recent paper of Granger and Vercauteren for computing discrete logarithms in tori, using efficient torus representations. We show that when q is not too large, a very efficient L(1/3) variation of the function field sieve can be used. Surprisingly, using this algorithm, discrete logarithms computations over some of these fields are even easier than computations in the prime field and characteristic two field cases. We also show that this new algorithm has security implications on some existing cryptosystems, such as torus based cryptography in T30, short signature schemes in characteristic 3 and cryptosystems based on supersingular abelian varieties. On the other hand, cryptosystems involving larger basefields and smaller extension degrees, typically of degree at most 6, such as LUC, XTR or T6 torus cryptography, are not affected.