How can modular multiplication and exponentiation be performed in C#?

Question

If I know parameter a, k and p then how do I calculate this in C#?

s=a*k^-1 mod p

Its for cryptographic purpose and I'm new. Please don't feel offended if the question is not appropriate.

Please note that k^-1 is the modular inverse of k (mod p) and not power operator.

Yes **k^-1** means modular inverse of **k** *mod p). @ArtjomB. — Milon Sarker, May 04 '15 at 12:10
How big are `a`, `k` and `p`? The question is whether an int would suffice or a BigInteger would be needed. — Artjom B., May 04 '15 at 12:17
`a,k and p` would be as big as `long` variable can take. sorry. @ArtjomB. — Milon Sarker, May 04 '15 at 12:41

score 2 · Accepted Answer · edited May 23 '17 at 12:17

Since the question is about modular inverse, I suppose it will benefit the seeker to look at another SO question.

Crux of the answer is -

Net 4.0+ implements BigInteger with a special modular arithmetics function ModPow (which produces “X power Y modulo Z”), you don't need a third-party library to emulate ModInverse. If m is a prime, all you need to do is to compute:

In C# as per MSDN documentation this is defined as

public static BigInteger ModPow(
    BigInteger value,
    BigInteger exponent,
    BigInteger modulus
)

Using this we can do something like to calculate inverse of the k modulo p like

BigInteger bi= ModPow(k, -1, p );
int b= (int) bi;
s= (a* bi )%p;

using `ModPow(k, -1, p )` will cause an `ArgumentOutOfRangeException` to be thrown indicating that `exponent is negative`. [BigInteger.ModPow Method Exceptions](https://msdn.microsoft.com/en-us/library/system.numerics.biginteger.modpow(v=vs.110).aspx#Anchor_1) — Etor Madiv, Apr 23 '17 at 16:30

score -4 · Answer 2 · answered May 04 '15 at 11:34

-4

public static double DoMath(double a, double k, double p)

    {
        return (a * Math.Pow(k, -1)) % p;
    }

answered May 04 '15 at 11:34

Bogdan Banciu

169
1
6

`k^-1` is a modular inverse, which is not the same as `Math.Pow(k, -1)`. – Artjom B. May 04 '15 at 12:14

How can modular multiplication and exponentiation be performed in C#?

2 Answers2