For example, encryption schemes and digital signatures are used to construct private and authentic communication channels (``uni-lateral security,'' security against malicious outsiders). These are instrumental to secure Internet transactions and payments, mobile telephony and much more. Another example is secure computation, which in principle enables an arbitrary computation to be distributed among the processors in a network so that computations remain secret and are performed correctly, even if a certain quorum of the network is under full control by an adversary (``multi-lateral security,'' security among mutually distrusting parties or parties with conflicting interests). Besides being a versatile theoretical primitive, potential real-life applications are myriad and include secure cooperation in the absence of trust, auctions, privacy-protecting data-mining and-benchmarking. Notable examples that fit neither category include secure positioning and searching encrypted data.

The research in the Cryptology Group is driven partly by questions such as: How reliable are the cryptographic methods in use today, really? Can they be made more secure and/or more efficient? Which are possible (minimal) assumptions under which security can be provided? Post-quantum cryptography: what to do if and when life-size quantum computers come into existence, and, hence, today's standards for secure communication are rendered insecure? Can large-scale secure computations be made practical?

In search for answers to these questions, the research is organized around the following (partially overlapping) themes. First, communication security beyond the horizon: post-quantum security (crypto from geometry of numbers, information-theoretic methods), leakage-resilience and tamper-resistant cryptography. Second, theory: secure computation, composability, public key cryptography. Third, alternative models: quantum cryptography and -information theory, bounded storage model, noisy channels. Fourth, cryptanalysis and applications to information security: number-theoretic (number field sieve, elliptic curve discrete logarithms), hash-functions, security of public key infrastructures.

In addition, there is special focus on interplays with algebra, number theory, geometry, combinatorics, probability theory, complexity theory, formal methods, quantum physics and information theory, as advances in modern cryptology increasingly rely on deeper understanding of these interplays.

The PNA5 theme was established on June 1, 2004. The group conducts fundamental and application-oriented research in cryptology and information security with a broad basis in mathematics and computer science.