TWINKLE

TWINKLE is a hypothetical integer factorization device described in 1999 by Adi Shamir and purported to be capable of factoring 512-bit integers. The name is an acronym of "The Weizmann Institute Key Locating Engine". It is also a pun on the twinkling LEDs used in the device.
The goal of TWINKLE is to implement the sieving step of the Number Field Sieve algorithm, which is the fastest known algorithm for factoring large integers. The sieving step, at least for 512-bit and larger integers, is the most time consuming step of NFS. It involves testing a large set of numbers for B-'smoothness', i.e., absence of a prime factor greater than a specified bound B.
What is remarkable about TWINKLE is that it is not a purely digital device. It gets its efficiency by eschewing binary arithmetic for an "optical" adder which can add hundreds of thousands of quantities in a single clock cycle.
The key idea used is "time-space inversion". Conventional NFS sieving is carried...