Cryptographic methods and apparatus using word-wise...

Details Cryptographic methods and apparatus using word-wise... Cryptographic methods and apparatus using word-wise...

2006-05-23

2006-05-23

Darrow, Justin T. (Department: 2132)

Cryptography

Particular algorithmic function encoding

C708S135000, C708S491000

Reexamination Certificate

active

07050579

ABSTRACT:
Cryptographic methods and apparatus are provided for determination of multiplicative inverses. A Montgomery radix is selected based on a wordsize, permitting word-wise Montgomery multiplication. Using word-wise Montgomery multiplication, methods and apparatus determine various multiplicative inverses with reduced computation time.

REFERENCES:
patent: 6088453 (2000-07-01), Shimbo
patent: 6795553 (2004-09-01), Kobayashi et al.
C.K. Koc et al., “Analyzing and Comparing Montgomery Multiplication Algorithms,” IEEE Micro 16:26-33 (Jun. 1996).
B. S. Kaliski, Jr., “The Montgomery Inverse and Its Applications,”IEEE Transactions on Computers 44:1064-1065 (Aug. 1995).
P. L. Montgomery, “Modular Multiplication Without Trial Division,”Mathematics of Computation 44:519-521 (Apr. 1985).
ç. K. Koç et al., “Analyzing and Comparing Montgomery Multiplication Algorithms,”IEEE Micro 16:26-33 (Jun. 1996).
Menezes, et al.,Handbook of Applied Cryptography, p. 600-603 (CRC Press 1997).
S. Even, “Systolic Modular Multiplication,”Advances in Cryptology, Lecture Notes in Computer Science 537:619-624 (Springer Verlag 1990).
Bosselaers et al., “Comparison of Three Modular Reduction Functions,” Crypto '93, pp. 175-186 (1993).
Koc et al., “Carry-save Adders for Computing the Products AB Modulo N,” Electronics Letters 26:899-900 (Jun. 21, 1990).
C.K. Koc., “Montgomery Reduction with Even Modulus,” IEEE Proc.-Compt. Digit Tech., 141:314-316 (Sep. 5, 1994).
Paar et al., “Fast Arithmetic Architectures for Public-Key Algorithms over Galois Fields GF((2n)m),” Eurocrypt '97, p. 363-378 (May 11, 1997).
Leu et al., “A Scalable Low-Complexity Digit-Serial VLSI Architecture for RSA Cryptosystem.” SiPS 99 IEEE Workshop on Signal Processing Systems, p. 586-595 (1999).
Bartee et al., “Computation with Finite Fields,” Information and Control 6:79-98 (1963).
C.D. Walter, “Faster Modular Multiplication by Operand Scaling,” Advances in Cryptology: Lecture Notes in Computer Science 576:313-323 (1992).
Bajard, et al., “An RNS Montgomery Modular Multiplication Algorithm,” IEEE Trans. on Computers, 47:766-776 (Jul. 1998).
Koc et al., “Montgomery Multiplication in GF(2k),” Designs, Codes and Cryptography, 14:57-69 (Apr. 1998).
G.B. Agnew et al., “Arithmetic Operations in GF(2m),” Journal of Cryptology, p. 3-13 (1993).

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