A Hardware-Efficient Elliptic Curve Cryptographic Architecture over GF (p)

Algorithm 3

Binary modular inversion (IBMI) algorithm.

	Input:
	Output: , satisfying
	Step 1: ;
	Step 2: if ( is even) {
	;
	if (r is odd) ;
	else if (r is negative) ;
	else ;
	}
	Step 3: if ( is even) {
	;
	if (s is odd) ;
	else if (s is negative) ;
	else;
	}
	Step 4: if (u and are odd) {
	if() ;
	else ;
	}
	Step 5: if () {
	if () {return ; }
	else { return .}
	}
	else if () {
	if () {return ; }
	else {return .}
	}
	else {go to step2.}