Method and apparatus for modular inversion for information security and recording medium with a program for implementing the method

摘要

Values X and N of n bits and a parameter t are input, then Y=X2<-t >mod N is calculated, then an extended binary GCD algorithm is executed for Y to obtain S=y<-1>2<k >mod N and k, and R=S2<-(k+t-2n) >is calculated for S, thereby obtaining a Montgomery inverse R=X<-I>2<2n >mod N of X on a residue class ring Z/NZ.