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11
votes
Accepted
P with integer factorization oracle
I don't have an answer to you question, but I know that a similar notion has very recently been studied, under the name of "angel-based security."
The first paper studying this concept is Prabhakaran …
9
votes
Consequences of Factoring being in P?
RSA is one of the most important encryption/signature schemes which breaks if FACTORING is in P. However, there are many more. …
10
votes
Adding integers represented by their factorization is as hard as factoring? Reference request
I'm not aware of a reference, but I think I came up with a proof:
Assume you have an oracle $\mathcal{O}$ which, on input two factored numbers
$x = \prod_{i=1}^n p_i^{\alpha_i}$
and
$y = \prod_{i= …
5
votes
Adding integers represented by their factorization is as hard as factoring? Reference request
The answer below is based on the discussions here: https://math.stackexchange.com/questions/54580/factoring-some-integer-in-the-given-interval. … In this answer, I will provide a deterministic polynimial-time Karp reduction from factoring to factoring the sum of two integers represented by their factorizations. …