The SPARC architecture manual (version 9)
The SPARC architecture manual (version 9)
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
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
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
An Algorithm for the nt Pairing Calculation in Characteristic Three and its Hardware Implementation
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Software Implementation of Arithmetic in
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Some efficient algorithms for the final exponentiation of ηT pairing
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
Efficient GF(pm) arithmetic architectures for cryptographic applications
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Explicit formulas for efficient multiplication in F36m
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Universal ηT pairing algorithm over arbitrary extension degree
WISA'07 Proceedings of the 8th international conference on Information security applications
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
SP 800-57. Recommendation for Key Management, Part 1: General (revised)
SP 800-57. Recommendation for Key Management, Part 1: General (revised)
Multi-core Implementation of the Tate Pairing over Supersingular Elliptic Curves
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
On the efficiency and security of pairing-based protocols in the type 1 and type 4 settings
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Key length estimation of pairing-based cryptosystems using ηT pairing
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
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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The ηTpairing in characteristic threeis implemented by arithmetic in GF(3)={0,1,2}. Harrison et al.reported an efficient implementation of the GF(3)-addition by usingseven logical instructions (consisting of AND, OR, and XOR) withthe two-bit encoding { (0,0) →0, (0,1) →1, (1,0) → 2}. It has not yet been proven whether seven is the minimum numberof logical instructions for the GF(3)-addition. In this paper, weshow many implementations of the GF(3)-addition using only sixlogical instructions with different encodings such as { (1,1)→0, (0,1) →1, (1,0) →2 } or { (0,0) →0, (0,1)→1, (1,1) →2 }. We then prove that there is noimplementation of the GF(3)-addition using five logicalinstructions with any encoding of GF(3) by two bits. Moreover, weapply the new GF(3)-additions to an efficient softwareimplementation of the ηTpairing.The running time of the ηTpairing over GF(3509), that is considered to be realizedas 128-bit security, using the new GF(3)-addition with the encoding{ (0,0) →0, (0,1) →1, (1,1) →2 } is 16.3milliseconds on an AMD Opteron 2.2-GHz processor. This isapproximately 7% faster than the implementation using the previousGF(3)-addition with seven logical instructions.