Cryptographic Math Tool

Modular arithmetic calculator for cryptography learning

Select Operation

Calculator

+
mod
Result:4

Step-by-Step Solution

1Calculate: 17 + 13 = 30
2Apply modulus: 30 mod 26
3Result: 4

Common Cryptographic Values

RSA Common Exponents

e = 3e = 17e = 65537

Common Primes

2, 3, 5, 7, 1113, 17, 19, 2329, 31, 37, 41

Euler's Totient

For prime p: phi(p) = p - 1For p*q: phi(n) = (p-1)(q-1)

Key Formulas

Modular Arithmetic

(a + b) mod m = ((a mod m) + (b mod m)) mod m(a * b) mod m = ((a mod m) * (b mod m)) mod m

Modular Inverse

a * a^-1 = 1 (mod m)Exists only if gcd(a, m) = 1

Fermat's Little Theorem

a^(p-1) = 1 (mod p) for prime pa^p = a (mod p)

Euler's Theorem

a^phi(n) = 1 (mod n)if gcd(a, n) = 1

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