Analysis of Bernstein's factorization circuit

In [1], Bernstein proposed a-circuit-based implementation of the inatrix step of the number field sieve factorization algorithm. These circuits, offer an asymptotic cost reduction under the measure "construction cost x run time". We evaluate the cost-of these circuits, in agreement with [1], but argue that compared to previously known methods these circuits can factor integers that are 1.17 times larger, rather than 3.01 as claimed (and even this, only under the non-standard -cost measure). We also propose an improved circuit design based on a new mesh routing algorithm, and show that for factorization of.1024-bit integers the matrix step can, under an optimistic assumption, about the matrix size, be completed within a day by a device that costs a few thousand dollars. We-conclude that from a-practical,standpoint; the security of RSA relies exclusively on the hardness of the relation collection step of the number field sieve.