Computational records for RSA and finite field Diffie-Hellman

This talk reports on the latest computational records in integer factoring and
finite field discrete logarithms. These hard computational problems underpin the
security of the public-key cryptographic primitives known as RSA and finite
field Diffie-Hellman, which are still the most used public-key cryptographic
primitives in many contexts.

This work required a quite formidable amount of computing power, from various
sources. But beyond that, it is interesting to look at some comparative
insights. First, for the first time, same-size records were computed
simultaneously for integer factoring and discrete logarithms, and this shows
that while the latter is more difficult than the former, the hardness ratio is
much less than commonly expected. A second aspect is the comparison of the
computational cost of this work with previous records of this kind. Thanks to
algorithmic variants and well-chosen parameters, our computations were
significantly less expensive than anticipated based on previous records.