Working on discrete logarithm algorithms for such fields he introduced some concepts which are still used in modern algorithms; in particular the trick used for the descent stage. On one of his students giving a talk on this at IBM Don Coppersmith became intrigued and quickly came up with his L(1/3) algorithm for discrete logarithms in finite fields of characteristic two. This new algorithm rendered the second product obsolete; although actually breaking a 500 bit field took another 10 years.
The he moved onto looking at a new form of cryptography based on elliptic curves. At that time computing the number of points on a curve was hard (although polynomial time), and so he initially settled on supersingular curves. But during a reading group at the University of Waterloo on Burt Kaliski's thesis on group structures for elliptic curves, there came the realization that the Weil pairing could be used to translate the discrete logarithm problem on supersingular elliptic curves to an associated finite field.
Then he turned to looking at arithmetic for elliptic curves defined over GF(2155). But these soon were declared "weak" due to Weil descent attacks. Although, as Alf pointed out, despite intense effort over the last 15 years on such attacks no one is yet able to solve an ECDLP problem over the binary field of 155 bits.
Finally, Scott (and his company Certicom) settled on general ordinary elliptic curves. These were then possible to implement due to many groups having been able to now implement the algorithm to compute the number of points on a curve (an algorithm now included in many algebra systems). Scott evangelized the use of elliptic curves. The products of Certicom were used in products by RIM (now Blackberry), Pitney Bowes and Motorola. Then the NSA endorsed the use of elliptic curves for US government business via the Suite B standard. Scott also helped coordinate the efforts to produce standards in the area, launch conferences (the annual ECC conference was founded by him) and other aspects.
A non-elliptic curve major achievement was the co-authorship of the massive tome which the the Handbook of Applied Cryptography (or HAC to its friends). Scott conceived of the idea and with his co-authors he delivered a book which has been used by countless researchers to understand how cryptographic systems are used in the real world. And the book hardly mentions elliptic curves.
Scott was honored by being a Fellow of the Royal Society of Canada, a Fellow of the IACR (he served for six years on the IACR board of directors), he was also the recipient of the RSA Mathematics award and held the Ontario Premier's Catalyst Award for Lifetime Achievement in Innovation. As well as this he was one of the founding members of the Bristol Crypto groups Industrial Advisory Board.
On a personal note Scott was always a great supporter of young (and old) researchers; he encouraged me to keep working on ECC and I remember fondly the parties held at Scott and Sherry's house during the early ECC conferences in Waterloo. Scott helped encourage people around the world to work in the area, and ECC would not be the public key technology of choice that it is today without Scott's tireless work.
Alfred's talk ended with a picture of Alfred (who was Scott's PhD student) and Scott, along with Scott's PhD supervisor Ron Mullin, and Ron's PhD supervisor Bill Tutte (of Bletchley Park fame).