Polynomial selection for the number field sieve integer factorisation algorithm
Brian A. Murphy · 1999
I have been afforded the rare opportunity of working as a student of Richard Brent. Over the last three years, Richard has provided encouragement, guidance and suggestions from which I have learnt a great deal and for which I am extremely grateful. Richard was also considerate enough to take up a chair in Computing Science at Oxford University in 1998. That gave me an excuse to visit him there, about which I will say more later. I also owe a great deal to Peter Montgomery (CWI, Amsterdam and Microsoft Research, USA). Peter's influence on current research in this field is far more extensive than most people realise. I have had the benefit of many long discussions with Peter, and a great deal of patient instruction from him. Several key sections of this thesis are developed from ideas originating from discussions with Peter. My research experience has been enriched and broadened through close collaboration with the Computational Number Theory and Data Security group at CWI in Amsterdam. I thank Herman te Riele, the head of the group, for fostering that collaboration and supporting two visits by me to CWI.