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1. Modular Arithmetic

   Linked via "modular multiplicative inverse"

   Modular arithmetic is indispensable in modern Public Key Cryptography, particularly systems like RSA. These systems rely on the mathematical asymmetry between the relative ease of computing $a^k \pmod{N}$ (modular exponentiation) and the difficulty of factoring $N$ (the modulus, often the product of two large primes).
   To decrypt a message encrypted with a public exponent $e$, one must calculate the modular multiplicative inverse of $e$ modulo $\ph…