This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
The Montgomery Inverse and Its Applications
August 1995 (vol. 44 no. 8)
pp. 1064-1065
ASCII Text
x 
 
Burton S. Kaliski, "The Montgomery Inverse and Its Applications," IEEE Transactions on Computers, vol. 44, no. 8, pp. 1064-1065, August, 1995.
 
 
BibTex
x
 
@article{ 10.1109/12.403725,
author = {Burton S. Kaliski},
title = {The Montgomery Inverse and Its Applications},
journal ={IEEE Transactions on Computers},
volume = {44},
number = {8},
issn = {0018-9340},
year = {1995},
pages = {1064-1065},
doi = {http://doi.ieeecomputersociety.org/10.1109/12.403725},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - The Montgomery Inverse and Its Applications
IS - 8
SN - 0018-9340
SP1064
EP1065
EPD - 1064-1065
A1 - Burton S. Kaliski,
PY - 1995
VL - 44
JA - IEEE Transactions on Computers
ER -
 

Abstract— The Montgomery inverse of b modulo a is b−12n mod a, where n is the number of bits in a. The right-shifting binary algorithm for modular inversion is shown naturally to compute the new inverse in fewer operations than the ordinary modular inverse. The new inverse facilitates recent work by Koç on modular exponentiation and has other applications in cryptography.

[1] S. R. Duss\' eand B. S Kaliski Jr.,“A cryptographic library for the motorola DSP 56000,”inProc. Advances in Cryptology—Eurocrypt '90, New York, 1990.
[2] T. ElGamal, A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms IEEE Trans. Information Theory, vol. 31, no. 4, pp. 469-472, 1985.
[3] S. Even,“Systolic modular multiplication,” A.J. Menezes and S.A. Vanstone, eds., Advances in Cryptology’90., pp. 619-624,New York: Springer-Verlag, 1991.
[4] A. Guyot,“OCAPI: Architecture of a VLSI coprocessor for the GCD and the extended GCD of large numbers,” Proc. 10th IEEE Symp. Computer Arithmetic, pp. 226-231, 1991.
[5] D. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, Mass., 1998.
[6] Ç.K. Koç,“High-radix and bit recoding techniques for modular exponentiation,” Int’l J. Computer Mathematics, vol. 40, nos. 3-4, pp. 139-156, 1987.
[7] D. Laurichesse and L. Blain,“Optimized implementation of RSA cryptosystem,” Computers&Security, vol. 10, no. 3, pp. 263-267, May 1991.
[8] J.L. Massey,“Cryptography: Fundamentals and applications,” Advanced Technology Seminars,Zurich, Switzerland, Feb. 1993.
[9] P.L. Montgomery,“Modular multiplication without trial division,” Mathematics of Computation, vol. 44, no. 170, pp. 519-521, 1985.
[10] Nat’l Inst. of Standards and Technology (NIST), FIPS Publication 186: Digital Signature Standard. May19, 1994.
[11] S.N. Parikh and D.W. Matula,“A redundant binary Euclidean GCD algorithm,” Proc. 10th IEEE Symp. Computer Arithmetic, pp. 220-225, 1991.
[12] J.-J. Quisquater and C. Couvreur,“Fast decipherment algorithm for RSA public-key cryptosystem,” Electronics Letters, vol. 18, no. 21, pp. 905-907, 1982.
[13] R.L. Rivest,A. Shamir, and L.A. Adleman,"A Method for Obtaining Digital Signatures and Public Key Cryptosystems," Comm. ACM, vol. 21, pp. 120-126, 1978.
[14] M. Shand and J. Vuillemin, “Fast Implementations of RSA Cryptography,” Proc. 11th IEEE Symp. Computer Arithmetic, pp. 252-259, 1993.
[15] J. Stein,“Computational problems associated with Racah algebra,” J. Comp. Phys., vol. 1, pp. 397-405, 1967.

Citation:
Burton S. Kaliski, "The Montgomery Inverse and Its Applications," IEEE Transactions on Computers, vol. 44, no. 8, pp. 1064-1065, Aug. 1995, doi:10.1109/12.403725
Usage of this product signifies your acceptance of the Terms of Use.