Discrete Logarithm Problem

One-way function strength scales exponentially with prime modulus size, making small-number examples trivial while hundred-digit primes resist all known computational attacks.

The discrete logarithm problem challenges solvers to find the hidden exponent x such that g^x ≡ y (mod p), given generator g, modulus p, and result y.

Modular arithmetic, known colloquially as clock arithmetic, provides the mathematical foundation for discrete logarithm-based cryptography through its wrapping behavior.

Modern cryptography requires numerical procedures exhibiting computational asymmetry—operations trivial to perform forward but computationally infeasible to reverse.

Cryptographic applications of modular arithmetic specifically require prime moduli rather than composite numbers to enable primitive root generation and uniform distribution.

For prime modulus 17, the number 3 serves as a primitive root (generator) possessing the critical property that its powers distribute uniformly across all possible residues.