On the (In)Security of Cryptography in the Quantum Era
The advent of quantum computing poses significant challenges to modern cryptographic systems. This thesis examines two fundamental quantum algorithms - Grover’s unstructured search algorithm and Shor’s factorization algorithm - and their implications for cryptographic security. Grover’s algorithm provides a quadratic speedup over classical brute-force search, reducing the effective security of symmetric key ciphers and hash functions by approximately half. We analyze its application to AES-128 encryption and hash function collision attacks, demonstrating how quantum circuit implementations of cryptographic primitives enable practical attacks. Shor’s algorithm offers an exponential speedup for integer factorization and discrete logarithm problems, posing a threat to widely-used public-key cryptosystems such as RSA.