In , Bernstein proposed a circuit-based implementation of the matrix 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 , 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 logarith, 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.
|Title of host publication||Advances in Cryptology - ASIACRYPT 2002 (Proceedings 8th International Conference on the Theory and Application of Cryptology and Information Security, Queenstown, New Zealand, December 1-5, 2002)|
|Place of Publication||Berlin|
|Publication status||Published - 2002|
|Name||Lecture Notes in Computer Science|