On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
A new method for constructing pairing-friendly abelian surfaces
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Compact hardware for computing the tate pairing over 128-bit-security supersingular curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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We show that supersingular Abelian varieties can be used to obtain higher MOV security per bit, in all characteristics, than supersingular elliptic curves. We give a point compression/decompression algorithm for primitive subgroups associated with elliptic curves that gives shorter signatures, ciphertexts, or keys for the same security while using the arithmetic on supersingular elliptic curves. We determine precisely which embedding degrees are possible for simple supersingular Abelian varieties over finite fields and define some invariants that are better measures of cryptographic security than the embedding degree. We construct examples of good supersingular Abelian varieties to use in pairing-based cryptography.