Rabin fingerprint

The Rabin fingerprinting scheme is a method for implementing fingerprints using polynomials over a finite field. It was proposed by Michael O. Rabin.

Given an n-bit message m₀,...,m_n-1, we view it as a polynomial of degree n-1 over the finite field GF(2).

We then pick a random irreducible polynomial ${\displaystyle p(x)}$ of degree k over GF(2), and we define the fingerprint of the message m to be the remainder ${\displaystyle r(x)}$ after division of ${\displaystyle f(x)}$ by ${\displaystyle p(x)}$ over GF(2) which can be viewed as a polynomial of degree k-1 or as a k-bit number.

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