| package org.bouncycastle.math.ec; |
| |
| import java.math.BigInteger; |
| |
| public class ECAlgorithms |
| { |
| public static ECPoint sumOfTwoMultiplies(ECPoint P, BigInteger a, |
| ECPoint Q, BigInteger b) |
| { |
| ECCurve c = P.getCurve(); |
| if (!c.equals(Q.getCurve())) |
| { |
| throw new IllegalArgumentException("P and Q must be on same curve"); |
| } |
| |
| // Point multiplication for Koblitz curves (using WTNAF) beats Shamir's trick |
| if (c instanceof ECCurve.F2m) |
| { |
| ECCurve.F2m f2mCurve = (ECCurve.F2m)c; |
| if (f2mCurve.isKoblitz()) |
| { |
| return P.multiply(a).add(Q.multiply(b)); |
| } |
| } |
| |
| return implShamirsTrick(P, a, Q, b); |
| } |
| |
| /* |
| * "Shamir's Trick", originally due to E. G. Straus |
| * (Addition chains of vectors. American Mathematical Monthly, |
| * 71(7):806-808, Aug./Sept. 1964) |
| * <pre> |
| * Input: The points P, Q, scalar k = (km?, ... , k1, k0) |
| * and scalar l = (lm?, ... , l1, l0). |
| * Output: R = k * P + l * Q. |
| * 1: Z <- P + Q |
| * 2: R <- O |
| * 3: for i from m-1 down to 0 do |
| * 4: R <- R + R {point doubling} |
| * 5: if (ki = 1) and (li = 0) then R <- R + P end if |
| * 6: if (ki = 0) and (li = 1) then R <- R + Q end if |
| * 7: if (ki = 1) and (li = 1) then R <- R + Z end if |
| * 8: end for |
| * 9: return R |
| * </pre> |
| */ |
| public static ECPoint shamirsTrick(ECPoint P, BigInteger k, |
| ECPoint Q, BigInteger l) |
| { |
| if (!P.getCurve().equals(Q.getCurve())) |
| { |
| throw new IllegalArgumentException("P and Q must be on same curve"); |
| } |
| |
| return implShamirsTrick(P, k, Q, l); |
| } |
| |
| private static ECPoint implShamirsTrick(ECPoint P, BigInteger k, |
| ECPoint Q, BigInteger l) |
| { |
| int m = Math.max(k.bitLength(), l.bitLength()); |
| ECPoint Z = P.add(Q); |
| ECPoint R = P.getCurve().getInfinity(); |
| |
| for (int i = m - 1; i >= 0; --i) |
| { |
| R = R.twice(); |
| |
| if (k.testBit(i)) |
| { |
| if (l.testBit(i)) |
| { |
| R = R.add(Z); |
| } |
| else |
| { |
| R = R.add(P); |
| } |
| } |
| else |
| { |
| if (l.testBit(i)) |
| { |
| R = R.add(Q); |
| } |
| } |
| } |
| |
| return R; |
| } |
| } |