Paul C. van Oorschot

Paul C. van Oorschot coauthored the Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone. Its treatment connects cryptographic constructions with explicit mathematical algorithms and stated assumptions, rather than describing encryption only as a black box. The number-theoretic chapter includes algorithms for modular square roots, while the public-key chapter gives RSA cryptosystem and Rabin cryptosystem constructions.^[ref]

For a concrete special case, if $p\equiv 3(\mathrm{mod}4)$ is prime and $a$ is a nonzero square modulo $p$, a square root is $a^{(p+1)/4}\mathrm{mod}p$. This illustrates how assumptions on an integer modulus determine which algorithm and correctness argument apply.