ELLIPTIC CURVE SQUARE COMPUTING DEVICE, GENERATING POLYNOMIAL GENERATOR AND PROGRAM RECORDING MEDIUM THEREFOR

摘要

PROBLEM TO BE SOLVED: To increase the speed of the computations by reducing the number of times of multiplications. SOLUTION: A squaring computation of GF(qn-1) on a quadratic extension field GF(qn)=GF(qn-12) is conducted on GF(qn-1). In a quadratic generating polynomial x2+v1x+v0 on the GF(qn-1) which has basesαandβas solutions to A=A0α+A1βand A2=C0α+C1β, A0-A1, is computed using relationships v0=u2 and u exists GF(qn-1), (u/v1) is multiplied to obtain L5, computes (L5-A0)(L5+A0)→T0, computes (L5-A1)(L5+A1)→T1, computes -v1T0→C0 and -v1T1→C1 and outputs the results.