Mathematical breaktroughs can remain unnoticed by the real world if they are not confirmed by record computations. In particular the key sizes used on credit cards are tuned with respect to record computations. This is why I have spent months doing effective implementations, often with people who contribute to the CADO software. I list the records in two groups which are different in nature.
Discrete logarithm in the multiplicative group of F2n when n is prime.
- n=619 Done in November 2012, beating a record of Joux and Lercier in 2003 (no better records for composite n).
- n=809 Done in April 2013, still a record when n is prime altough Joux and respectively Robert Granger, Faruk Gologlu, Gary McGuire, Jens Zumbragel had tackled larger fields when n is composite. Today the record is n=1279 for primes (Kleinjung 2014) and n=9234 for composite numbers (Robert Granger, Thorsten Kleinjung, Jens Zumbragel 2014).
Discrete logarithme in the multiplicative group of Fpn when n < 20.
- Fp2 160 dd (p2 has 160 decimal digits) Done in June 2014, it was the first Fp2 above 100 decimal digits.
- Fp2 180 dd Done in August 2014, it was 260 times faster than the record of Bouvier et al. on a prime field of same size, which is contrary to commun belief that prime fields are easier.
- Fp3 156 dd Announced in October 2015, it beated the record of 120 dd of Joux, Lercier, Smart and Vercauteren realized in 2006.
- Fp4 120 dd (last slide) Announced in October 2015, it was the first record in Fp4 larger than 100 dd.
If you are a student and like the idea to read a mathematical algorithm and implement it in C/C++ or CUDA, please send me a CV !