Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.

Abstract. We present the hash-based signature scheme XMSS. It is the first provably (forward) secure and practical signature scheme with minimal security requirements: a pseudorandom and a second preimage resistant (hash) function family. Its signature size is reduced to less than 25% compared to the best provably secure hash based signature scheme.

Abstract. We propose a new algorithm for computing authentication paths in the Merkle signature scheme. Compared to the best algorithm for this task, our algorithm reduces the worst case running time considerably.

Abstract. The Merkle signature scheme (MSS) is an interesting alternative for well established signature schemes such as RSA, DSA, and ECDSA. The security of MSS only relies on the existence of cryptographically secure hash functions. MSS has a good chance of being quantum computer resistant. In this paper, we propose CMSS, a variant of MSS, with reduced private key size, key pair generation time, and signature generation time. We demonstrate that CMSS is competitive in practice by presenting a highly efficient implementation within the Java Cryptographic Service Provider FlexiProvider. We present extensive experimental results and show that our implementation can for example be used to sign messages in Microsoft Outlook.

We propose GMSS, a new variant of the Merkle signature scheme. GMSS is the first Merkle-type signature scheme that allows a cryptographically unlimited (2 80 ) number of documents to be signed with one key pair. Compared to recent improvements of the Merkle signature scheme, GMSS reduces the signature size as well as the signature generation cost.