Discrete Applied Mathematics
The SPARC architecture manual (version 9)
The SPARC architecture manual (version 9)
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Finite Field Multiplier Using Redundant Representation
IEEE Transactions on Computers
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Software Implementation for Finite Field Multiplication in Normal Basis
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
High-Speed Software Multiplication in F2m
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Hardware Implementation of Finite Fields of Characteristic Three
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three
IEEE Transactions on Computers
Efficient Algorithms and Architectures for Field Multiplication Using Gaussian Normal Bases
IEEE Transactions on Computers
Software Multiplication Using Gaussian Normal Bases
IEEE Transactions on Computers
Formulas for cube roots in F3m
Discrete Applied Mathematics
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Implementing cryptographic pairings on smartcards
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Hardware acceleration of the tate pairing in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Security proof of sakai-kasahara's identity-based encryption scheme
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Field inversion and point halving revisited
IEEE Transactions on Computers
IEEE Transactions on Information Theory
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Faster and lower memory scalar multiplication on supersingular curves in characteristic three
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Key length estimation of pairing-based cryptosystems using ηT pairing
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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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Fast arithmetic for characteristic three finite fields is desirable in pairing-based cryptography because there is a suitable family of elliptic curves over having embedding degree 6. In this paper we present some structure results for Gaussian normal bases of , and use the results to devise faster multiplication algorithms. We carefully compare multiplication in using polynomial bases and Gaussian normal bases. Finally, we compare the speed of encryption and decryption for the Boneh-Franklin and Sakai-Kasahara identity-based encryption schemes at the 128-bit security level, in the case where supersingular elliptic curves with embedding degrees 2, 4 and 6 are employed.