We perform a special number field sieve discrete logarithm computation in a 1024-bit prime
field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever
reported for prime fields. This computation took a little over two months of calendar time on
an academic cluster using the open-source CADO-NFS software. Our chosen prime p looks
random, and p-1 has a 160-bit prime factor, in line with recommended parameters for the
Digital Signature Algorithm. However, our p has been trapdoored in such a way that the …