Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Journal of Cryptology
Constructive problems for irreducible polynomials over finite fields
Proceedings of the third Canadian workshop on Information theory and applications
Low-Energy Digit-Serial/Parallel Finite Field Multipliers
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Irreducible trinomials over finite fields
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes
Designs, Codes and Cryptography
Fast Combinatorial RNS Processors for DSP Applications
IEEE Transactions on Computers
Exponentiation in Finite Fields: Theory and Practice
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
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
Efficient standard basis Reed-Solomon encoder
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 06
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Recently, there has been a lot of interest on cryptographic applications based on fields GF(pm), for pGF(pm) multipliers architectures, where p is odd. We present designs which trade area for performance based on the number of coefficients that the multiplier processes at one time. Families of irreducible polynomials are introduced to reduce the complexity of the modulo reduction operation and, thus, improved the efficiency of the multiplier. We, then, specialize to fields GF(3m) and provide the first cubing architecture presented in the literature. We synthesize our architectures for the special case of GF(397) on the XCV1000-8-FG1156 and XC2VP20-7-FF1156 FPGAs and provide area/performance numbers and comparisons to previous GF(3m) and GF(2m) implementations. Finally, we provide tables of irreducible polynomials over GF(3) of degree m with 2 ≤ m ≥ 255.