Cryptographic algorithms with secure bit lengths are the basic building blocks for good cryptographic devices. For economical reasons the bit lengths often must not be larger than needed. In order to find a suitable bit length for RSA, one has to know how expensive in terms of money and time it is to factor a
large integer. What are the best algorithms, designs and parameters for a
machine that performs this task? We will discuss several ideas for hardware designs for the relation collection step of the general number field sieve in order to attack this question.