Prime Proof Protocol and the Case for Finite Field Cryptography (G12b)
NIST 186-5 and other standards are slowly edging away from finite field based cryptography. The discrete logarithm problem over alternate groups have become more popular due to perceptions of improved efficiency, both in speed and size. Both efficiencies are derived from one hypothesis: the number field sieve for index calculus only applies to finite field based systems and once run, breaks the entire system. In this talk I will discuss reasons why we may be premature in discarding finite field based cryptography. These reasons range from quantum resistance differences to new protocols to improve finite field system security.