Cryptology and Information Security

Leader of the group Cryptology and Information Security (PNA5): Ronald Cramer.

Cryptology deals with mathematical techniques for design and analysis of algorithms and protocols for digital security in the presence of malicious adversaries. For example, encryption and digital signatures are used to construct private and authentic communication channels, which are instrumental to secure Internet transactions. Another example of increasing importance 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. Advancing our understanding of secure communications and secure computation are among the primary goals in cryptology.

It is fascinating and promising that the connection between cryptology and fields such as algebra, number theory, geometry, combinatorics, complexity theory, formal methods, quantum physics and information theory is in the process of becoming still deeper than ever before.

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.

Focal points in the research of PNA5 are:

• Mathematical cryptology: problems in cryptology that can ultimately be formulated in terms of standard (computational) mathematics.
  This includes for instance our recent fundamental work on algebraic geometric aspects of efficient information theoretically secure multi-party computation as well as secure multi-party linear algebra, number theoretical and combinatorial aspects of (special purpose) secret sharing schemes. Clearly, it also includes cryptanalysis as in the ongoing Number Field Sieve Project for factoring large integers, which is relevant to the security of the widely used RSA cryptosystem, our cryptanalysis of several crypto-systems based on combinatorial group theory, and lower bounds on algebraic complexity of cryptographically relevant functions.
• Security analysis of highly composed security systems: models and composability theorems, the interaction between formal methods and universal composability, theoretical issues in complexity-based cryptography.
• Public-key cryptography: encryption schemes withstanding chosen ciphertext attacks, digital signatures, identity-based cryptography, practical secure multi-party protocols for specific problems, (non-interactive) zero-knowledge.
• Quantum cryptography and information theory: quantum oblivious transfer, secret key establishment from correlated randomness by public discussion, privacy amplification, secret sharing and secure multi-party computation, alternative (non-complexity-theoretic) security enablers such as (quantum) bounded storage model and perfectly secure message transmission.
• Computational Number Theory and Discrete tomography: the algorithmic study of number theory problems (including the Number Field Sieve and other well-known computational problems, such as ones related to the Riemann hypothesis), algorithms for reconstruction of objects from projections.

This group is part of the cluster Probability, Networks and Algorithms (PNA).

Members
Ronald Cramer, Willemien Ekkelkamp, Serge Fehr, Robbert de Haan, Dennis Hofheinz,
Otto Johnston, Eike Kiltz, Mikkel Kroigaard, Arjen Lenstra, Krzysztof Pietrzak, Herman te Riele, Marc Stevens, Andrey Timofeev, Tomas Toft.

Group publications
Publications in CWI repository

Seminars and more information
http://www.cwi.nl/crypto