This book constitutes the refereed proceedings of the Second International Workshop on Post-Quantum Cryptography PQCrypto 2008 held in Cincinnati OH USA in October 2008. The 15 revised full papers presented were carefully reviewed and selected from numerous submissions. Quantum computers are predicted to break existing public key cryptosystems within the next decade. Post-quantum cryptography is a new fast developing area where public key schemes are studied that could resist these emerging attacks. The papers present four families of public key cryptosystems that have the potential to resist quantum computers: the code-based public key cryptosystems the hash-based public key cryptosystems the lattice-based public key cryptosystems and the multivariate public key cryptosystems.