Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Extending the GHS Weil Descent Attack
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th 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
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Compression in Finite Fields and Torus-Based Cryptography
SIAM Journal on Computing
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
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
Public-key cryptosystems based on cubic finite field extensions
IEEE Transactions on Information Theory
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We give an overview on twisting commutative algebraic groups and applications to discrete log-based cryptography. We explain how discrete log-based cryptography over extension fields can be reduced to cryptography in primitive subgroups. Primitive subgroups in turn are part of a general theory of tensor products of commutative algebraic groups and Galois modules (or twists of commutative algebraic groups), and this underlying mathematical theory can be used to shed light on discrete log-based cryptosystems. We give a number of concrete examples, to illustrate the definitions and results in an explicit way.