Joye M, Paillier P: GCD-free algorithms for computing modular inverses. Proceedings of 5th International Workshop on Cryptographic Hardware and Embedded Systems (CHES '03), September 2003, Cologne, Germany, Lecture Notes in Computer Science 2779: 243-253.
Google Scholar
Schönhage A, Strassen V: Schnelle Multiplikation großer Zahlen. Computing 1971, 7: 281-292. 10.1007/BF02242355
Article
MATH
Google Scholar
GNU Multiple Precision Arithmetic Library manual, http://www.swox.com/gmp/gmp-man-4.1.2.pdf
Hankerson DR, Menezes AJ, Vanstone SA: Guide to Elliptic Curve Cryptography. Springer, New York, NY, USA; 2004.
MATH
Google Scholar
Menezes AJ, van Oorschot PC, Vanstone SA: Handbook of Applied Cryptography. CRC Press, Boca Raton, Fla, USA; 1996.
Book
Google Scholar
Hars L: Fast truncated multiplication and its applications in cryptography. Proceedings of 7th International Workshop on Cryptographic Hardware and Embedded Systems (CHES '05), August 2005, Edinburgh, Scotland
Google Scholar
Shantz SC: From Euclid's GCD to Montgomery
multiplication to the great divide. In Tech. Rep. TR-2001-95. Sun Microsystems Laboratories, Santa Clara,
Calif, USA; 2001.
Google Scholar
Jedwab J, Mitchell CJ: Minimum weight modified signed-digit representations and fast exponentiation. Electronics Letters 1989,25(17):1171-1172. 10.1049/el:19890785
Article
MATH
Google Scholar
Cohen H, Miyaji A, Ono T: Efficient elliptic curve exponentiation using mixed coordinates. In Proceedings of International Conference on the Theory and Applications of Cryptology and Information Security, Advances in Cryptology (ASIACRYPT '98), October 1998, Beijing, China, Lecture Notes in Computer Science Edited by: Ohta K, Pei D. 1514: 51-65.
Google Scholar
Ercegovac MD, Lang T: Digital Arithmetic. Morgan Kaufmann, San Francisco,
Calif, USA; 2004. chapter 2
Google Scholar
Hars L: Long modular multiplication for cryptographic applications. Proceedings of 6th International Workshop on Cryptographic Hardware and Embedded Systems (CHES '04), August 2004, Cambridge, Mass, USA, Lecture Notes in Computer Science 3156: 44-61. http://eprint.iacr.org/2004/198/
Google Scholar
Knuth DE: The Art of Computer Programming, Volume 2: Seminumerical Algorithms. 3rd edition. Addison-Wesley, Reading, Mass, USA; 1997.
Google Scholar
Stein J: Computational problems associated with Racah algebra. Journal of Computational Physics 1967,1(3):397-405. 10.1016/0021-9991(67)90047-2
Article
MATH
Google Scholar
Brent RP, Kung HT: Systolic VLSI arrays for linear-time GCD computation. In Proceedings of International Conference on Very Large Scale Integration (VLSI' 83), August 1983, Trondheim, Norway Edited by: Anceau V, Aas EJ. 145-154.
Google Scholar
Kaliski BS Jr.: The Montgomery inverse and its applications. IEEE Transactions on Computers 1995,44(8):1064-1065. 10.1109/12.403725
Article
MATH
Google Scholar
Savaş E, Koç ÇK: The Montgomery modular inverse-revisited. IEEE Transactions on Computers 2000,49(7):763-766. 10.1109/12.863048
Article
Google Scholar
Lórencz R: New algorithm for classical modular inverse. Proceedings of 4th International Workshop on Cryptographic Hardware and Embedded Systems (CHES '02), August 2002, Redwood Shores, Calif, USA, Lecture Notes in Computer Science 2523: 57-70.
Google Scholar
Jebelean T: Comparing several GCD algorithms. Proceedings of 11th IEEE Symposium on Computer Arithmetic (ARITH-11 '93), June-July 1993, Windsor, Ontario, Canada 180-185.
Chapter
Google Scholar
Vallée B: Complete Analysis of the Binary GCD Algorithm. 1998, http://citeseer.ist.psu.edu/79809.html
Schroeppel R, Orman H, O'Malley S: Fast key exchange with elliptic
curve systems. In Tech. Rep. 95-03.
Department of Computer Science, The University of
Arizona, Tucson, Ariz, USA; 1995.
Google Scholar
Jebelean T: A double-digit Lehmer-Euclid algorithm for finding the GCD of long integers. Journal of Symbolic Computation 1995,19(1–3):145-157. Technical report version also available ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz 10.1006/jsco.1995.1009
Article
MathSciNet
MATH
Google Scholar
Weber K: The accelerated integer GCD algorithm. ACM Transactions on Mathematical Software 1995,21(1):111-122. 10.1145/200979.201042
Article
MATH
Google Scholar