[英]BigInteger exponentiation with negative number
How can I do the same as in this python (using sage) code: 我该怎么做与此Python(使用鼠尾草)代码相同:
def elGamalDecrypt(c1, c2, p, x):
return Mod(c2*c1^(-x),p)
with standard Java 7 libraries? 标准的Java 7库? All numbers are
BigInteger
. 所有数字均为
BigInteger
。
I've tried a lot with no avail. 我已经尝试了很多无济于事。 In Python it's really simple and FAST.
在Python中,它非常简单且快速。
The BigInteger class in Java 7 has a modPow
method, which handles modular exponentiation. Java 7中的BigInteger类具有一个
modPow
方法,该方法可处理模块化幂运算。 So, something like the following should work (although I haven't tested it): 因此,类似以下的内容应该可以工作(尽管我还没有测试过):
c2.multiply(c1.modPow(x.negate(), p)).mod(p)
The modPow
method will only accept a negative exponent -x
if c1
and p
are coprime. 如果
c1
和p
为互质数,则modPow
方法仅接受负指数-x
。 (The name p
suggests that p
is prime, and if c1
and p
aren't coprime, c1
would be divisible by p
, and hence the exponentiation would make no sense, so I suspect that this won't be a problem.) (名称
p
表示p
是质数,如果c1
和p
不是互质数,则c1
将被p
整除,因此取幂是没有意义的,因此我怀疑这不会成为问题。)
This should do the same since c2 * c1^-x = c2 / (c1 ^ x)
: 由于
c2 * c1^-x = c2 / (c1 ^ x)
因此应该这样做:
BigInteger elGamalDecrypt(BigInteger c1, BigInteger c2, BigInteger p, int x) {
return c2.divide(c1.pow(x)).mod(p);
}
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