## Section: New Results

### Factoring oracles

Participants : François Morain, Benjamin Smith, Guénaël Renault.

Integer factoring is an old topic, and the situation is as follows: in the classical world, we think integer factoring is hard and the algorithms we have are quite powerful though of subexponential complexity and factoring numbers with several hundred bits; whereas in the quantum world, it is assumed to be easy (i.e., there exists a quantum polynomial time algorithm) but never experienced and the record is something like a few bits. F. Morain, helped by B. Smith and G. Renault studied the theoretical problem of factoring integers given access to classical oracles, like the Euler totient function. They were able to give some interesting classes of numbers that could tackled, The manuscript [18] is currently being refereed.