Question

我一直在努力将ECDH实现到我的iOS项目中，并且在我的代码中有一个小的逻辑错误用于点乘法。从使用NIST列表示例测试（“Link”）我知道我的double方法和我的add方法正常工作（使用各种曲线测试）但不知何故我无法让实际的乘法算法工作。这是乘法代码：

- (NSArray *)multiplyPX:(BigInteger *)P_X PY:(BigInteger *)P_Y andD:(BigInteger *)D
{
    BigInteger *ZERO = [[BigInteger alloc] initWithInt32:0];
    BigInteger *curveA = [[BigInteger alloc] initWithString:@"ffffffff00000001000000000000000000000000fffffffffffffffffffffffc" radix:16];

    //Getting the binary representation of the D value
    NSString *dBinary = [D toRadix:2];

    //Creating new Point Q = 0;
    BigInteger *Qx = ZERO;
    BigInteger *Qy = ZERO;

    //For every binary digit in D do "point doubling" & if dBinary[i] == 1 do "point addition"
    for (int i = [dBinary length]-1; i >= 0; i++) {

        //Check that you don't divide by 0
        if (![Qy isEqual:ZERO]) {

            //Point Doubling
            NSArray *arr = [self pointDoublingWithXp:Qx andYp:Qy andA:curveA];
            Qx = [arr objectAtIndex:0];
            Qy = [arr objectAtIndex:1];

        }
            //If dBinary[i] == 1
        if ([dBinary characterAtIndex:i] == 49) {

            //Point Addition
            NSArray *arr = [self pointAdditionWithXp:P_X andYp:P_Y andXq:Qx andYq:Qy];
            Qx = [arr objectAtIndex:0];
            Qy = [arr objectAtIndex:1];

        }
    }

    return [[NSArray alloc] initWithObjects:Qx, Qy, nil];
}

这里点加法＆amp;点倍增加。

- (NSArray *)pointAdditionWithXp:(BigInteger *)xp andYp:(BigInteger *)yp andXq:(BigInteger *)xq andYq:(BigInteger *)yq
{
    BigInteger *ONE = [[BigInteger alloc] initWithInt32:1];
    BigInteger *TWO = [[BigInteger alloc] initWithInt32:2];

    BigInteger *slope = [[yq sub:yp] multiply:[[xq sub:xp] inverseModulo:p] modulo:p];
    BigInteger *xout = [[[[slope exp:TWO modulo:p] sub:xq] sub:xp] multiply:ONE modulo:p];
    BigInteger *yout = [[yp negate] multiply:ONE modulo:p];
    yout = [yout add:[slope multiply:[xp sub:xout] modulo:p]];

    return [[NSArray alloc] initWithObjects:xout, yout, nil];
}

- (NSArray *)pointDoublingWithXp:(BigInteger *)xp andYp:(BigInteger *)yp andA:(BigInteger *)a
{
    BigInteger *ONE = [[BigInteger alloc] initWithInt32:1];
    BigInteger *TWO = [[BigInteger alloc] initWithInt32:2];
    BigInteger *THREE = [[BigInteger alloc] initWithInt32:3];

    BigInteger *slope = [[[[xp multiply:xp] multiply:THREE] add:a] multiply:[[yp multiply:TWO] inverseModulo:p]];

    BigInteger *xout = [[[slope multiply:slope] sub:[xp multiply:TWO]] multiply:ONE modulo:p];

    BigInteger *yout = [[[yp negate] add:[slope multiply:[xp sub:xout]]] multiply:ONE modulo:p];

    return [[NSArray alloc] initWithObjects:xout, yout, nil];
}

我真的不知道在开始时如何处理Q点，也许这就是错误。

但无论如何，非常感谢你。 :)
安东

ECC点乘法算法

0 个答案: