Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Proceedings on Advances in cryptology---CRYPTO '86
A cryptographic library for the Motorola DSP56000
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Comparison of three modular reduction functions
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
The Special Function Field Sieve
SIAM Journal on Discrete Mathematics
More on Squaring and Multiplying Large Integers
IEEE Transactions on Computers
Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Arithmetic Operations in the Polynomial Modular Number System
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
New modular multiplication algorithms for fast modular exponentiation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Modular number systems: beyond the mersenne family
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Faster $\mathbb{F}_p$-Arithmetic for Cryptographic Pairings on Barreto-Naehrig Curves
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
| Hi-index | 14.98 |
In 1999, Solinas introduced families of moduli called the generalized Mersenne numbers (GMNs), which are expressed in low-weight polynomial form, p = f(t), where t is limited to a power of 2. GMNs are very useful in elliptic curve cryptosystems over prime fields since modular reduction by a GMN requires only integer additions and subtractions. However, since there are not many GMNs and each GMN requires a dedicated implementation, GMNs are hardly useful for other cryptosystems. Here, we modify GMN by removing restriction on the choice of t and restricting the coefficients of f(t) to 0 and \pm1. We call such families of moduli low-weight polynomial form integers (LWPFIs). We show an efficient modular multiplication method using LWPFI moduli. LWPFIs allow general implementation and there exist many LWPFI moduli. One may consider LWPFIs as a trade-off between general integers and GMNs.