 Next up, Jean-Sébastien Corral, speaking about numbers of the four p squared q and p q. He has five, six minutes. Yes, in that talk I'm going to give some evidence that p q and p squared q are probably not an artifact job. This is a joint work, but that is like that from where the score is initial. A traditional way of evaluating the present sense consists in analyzing the variance. This methodology is often adopted by the block-cycler community, and it consists in analyzing ground-constructed versions of the block-cycler. And for the case of factorization problems, the evaluation consists in increasingly difficult factorization challenges. And instead of that, it may be interesting to find a new notion of factorization to which our moduli would not be equally resistant. The most natural way to generalize factorization is to ask the factorizer to extract some knowledge about what factor rather than to reveal it. And so we can invent a new notion of factorization called information theoretic factorization, which generalizes the usual factorization by elevating some binary string, L of q of one factor q, that directly raises this factor beyond any reasonable roots. And a result in that p squared q is not an artifact job with respect to that definition, that notion of factorization, but pq seems to be out. And it's very easy to factor p squared q under that notion of factorization. Instead, we take the original symbol of p squared q relative to some prime, so you define a binary string of L and you take the original symbol relative to some prime p i. And because of the multiplicative properties of the original symbol, this sequence is only specific to q and does not depend on p. So you can extract knowledge about one factor. And it's possible to show that under the assumption that the function L behaves as a random oracle, the uncertainty about q vanishes for a sufficiently long string L of q. But of course, this result does not enter any of today's p squared q schemes because inverting L of q is an important point. That's it.