Modular arithmetic performs integer arithmetic that wraps around a fixed modulus, so numbers are treated as equivalent if they differ by a multiple of that modulus.
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- In modular arithmetic operations are reduced modulo a chosen integer, giving a finite set of residues with well-defined addition and multiplication. Properties of these residue systems, especially over primes, are central to number theory.
- Public-key cryptography, hash constructions and proof systems rely on modular operations over large numbers and finite fields. It is a foundational tool across cryptography.