Low-Complexity Bit-Parallel Systolic Montgomery Multipliers for Special Classes of GF(2^m)
IEEE Transactions on Computers
IEEE Transactions on Computers
High-speed hardware implementations of Elliptic Curve Cryptography: A survey
Journal of Systems Architecture: the EUROMICRO Journal
Montgomery Residue Representation Fault-Tolerant Computation in GF(2k)
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Efficient Modular Arithmetic in Adapted Modular Number System Using Lagrange Representation
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
A versatile Montgomery multiplier architecture with characteristic three support
Computers and Electrical Engineering
On efficient pairings on elliptic curves over extension fields
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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We present a new multiplication algorithm for the implementation of elliptic curve cryptography (ECC) over the finite extension fields GF(pk) where p is a prime number greater than 2k. In the context of ECC we can assume that p is a 7-to-10-bit number, and easily find values for k which satisfy: p 2k, and for security reasons log2 脳 k 驴 160. All the computations are performed within an alternate polynomial representation of the field elements which is directly obtained from the inputs. No conversion step is needed. We describe our algorithm in terms of matrix operations and point out some properties of the matrices that can be used to improve the design. The proposed algorithm is highly parallelizable and seems well adapted to hardware implementation of elliptic curve cryptosystems.