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modular exponentiation

Raising a number to a large power and taking the remainder — the core arithmetic behind RSA.

Modular exponentiation computes (base raised to exponent) modulo some number, kept feasible by squaring and reducing at each step rather than forming the astronomically large full power. RSA encryption and signing are essentially one big modular exponentiation with a secret exponent. Because the secret is the exponent, the operation must run in constant time — its duration must not leak which bits the key contains.