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Cryptography 04 - Fermat's Little Theorem

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Introduction #

  • In the previous article we dove deep into a fundamental topic in number theory and cryptography - modular arithmetic. In this blog, we will look at some interesting Mathematical properties surrounding modular arithmetic, one of them being the fermat’s little theorem.

  • It is a very important topic in public key cryptography as it helps us test whether a number is prime or not, which is essential in generation of large prime numbers that are used in encryption

  • The theorem states that if p is a prime number and a is relatively prime to p, then then a^(p-1) is congruent to 1 (mod p)

  • We can represent this in modular arithmetic as

    \(f(a,b,c) = (a^2+b^2+c^2)^3\)