06088453 is referenced by 50 patents and cites 6 patents.

A scheme for performing high speed Montgomery division within the Montgomery space. Montgomery division Y=B.multidot.A.sup.-1 .multidot.2.sup.n mod N for a positive integer N, a positive integer A which is relatively prime with respect to N and satisfying 0.ltoreq.A.ltoreq.N, a positive integer B, and an integer n which is satisfying n.gtoreq.L where L is a bit length of N in binary expression, is performed by obtaining a Montgomery inverse X=A.sup.-1 .multidot.2.sup.2n mod N from inputs A and N, and obtaining the Montgomery division Y=B.multidot.X.multidot.2.sup.-n mod N from the Montgomery inverse X and inputs B and N. Montgomery inverse X=A.sup.-1 .multidot.2.sup.2n mod N for a positive integer N, a positive integer A which is relatively prime with respect to N and satisfying 0.ltoreq.A<N, and an integer n which satisfies n.gtoreq.L where L is a bit length of N in binary expression, is determined by obtaining an intermediate result C=A.sup.-1 .multidot.2.sup.k mod N and a parameter k satisfying L.ltoreq.k.ltoreq.2L from inputs A and N, and obtaining the Montgomery inverse X=C.multidot.2.sup.2n-k mod N from the intermediate result C and the parameter k and input N.

Title
Scheme for computing Montgomery division and Montgomery inverse realizing fast implementation
Application Number
9/13209
Publication Number
6088453
Application Date
January 26, 1998
Publication Date
July 11, 2000
Inventor
Atsushi Shimbo
Tokyo
JP
Agent
Oblon Spivak McClelland Maier & Neustadt P C
Assignee
Kabushiki Kaisha Toshiba
JP
IPC
G06F 15/00
G06F 7/52
H04L 9/28
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