Introduction to algorithms
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
A New Hardware Architecture for Operations in GF(2m)
IEEE Transactions on Computers
Efficient Software Implementation for Finite Field Multiplication in Normal Basis
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
Fast Generation of Pairs (k, [k]P) for Koblitz Elliptic Curves
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Efficient Finite Field Basis Conversion Involving Dual Bases
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Relationship between GF(2^m) Montgomery and Shifted Polynomial Basis Multiplication Algorithms
IEEE Transactions on Computers
Short memory scalar multiplication on koblitz curves
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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The problem of finite field basis conversion is to convert from the representation of a field element in one basis to the representation of the element in another basis. This paper presents new algorithms for the problem that require much less storage than previous solutions. For the finite field GF(2m), for example, the storage requirement of the new algorithms is only O(m) bits, compared to O(m2) for previous solutions. With the new algorithms, it is possible to extend an implementation in one basis to support other bases with little additional cost, thereby providing the desired interoperability in many cryptographic applications.