Historically, computer security is related to both cryptography and access control in operating systems. Cryptography, although mostly applied in the military and diplomacy, was used to protect communication channels and storage facilities (especially the backups). In the seventies there was a breakthrough in cryptography - the invention of public-key cryptography. It started in 1976 when Dime and Hcllman formulated their public-key distribu- tion system and formally defined public-key cryptosystems. Two years later two practical implementations of public-key cryptosystems were published. One was designed by Rivest, Shamir, and Adleman (called the RSA system); the authors based the system on the two "difficult" numerical problems: dis- crete logarithm and factorization. The other invented by Merklc and Hcllman was based on the knapsack problem, which is even "harder" than these used in the RSA system. Since that time cryptography, traditionally seen as the theory of encryption algorithms, has extended its scope enormously. Now it comprises many new areas, namely authentication, digital signature, hash- ing, secret sharing, design and verification of cryptographic protocols, zero knowledge protocols, quantum cryptography, etc.

This work presents recent developments in secure hashing algorithm design. The main part of the work was written when the authors were with the Department of Computer Science, University of New South Wales, Aus- tralian Defence Force Academy, and Babak Sadeghiyan was a PhD student working with Josef Pieprzyk as his supervisor.