A course in number theory and cryptography
A course in number theory and cryptography
Algebraic aspects of cryptography
Algebraic aspects of cryptography
Efficient Multiplier Architectures for Galois Fields GF(24n)
IEEE Transactions on Computers
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Parallel Multiplication in GF(2^k) usingPolynomial Residue Arithmetic
Designs, Codes and Cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
An alternative class of irreducible polynomials for optimal extension fields
Designs, Codes and Cryptography
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In this paper we present a new hardware modular multiplication algorithm over the finite extension fields GF(pk) where p 2k. We use an alternate polynomial representation of the field elements and a Lagrange like interpolation technique. We describe our algorithm in terms of matrix operations and point out some properties of the matrices that can be used to improve the hardware design. The proposed algorithm is highly parallelizable and seems well suited for hardware implementation of elliptic curve cryptosystems.