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Results tagged with factoring
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user 495
11
votes
Accepted
Reference for Levin's optimal factoring algorithm ?
Here is a quote from lectures notes given by Blum on SECURITY and CRYPTOGRAPHY:
Leonid LEVIN's OPTIMAL NUMBER-SPLITTING (FACTORING) ALGORITHM. … Here is Levin's optimal factoring algorithm:
The OPTIMAL-SPLIT ALGORITHM:
BEGIN
Enumerate all algorithms in order of size, lexicographically within each size. …
- 21.1k
1
vote
An NP-complete variant of factoring.
This is an informal efficient deterministic reduction idea (and may be incomplete):
Fractran is a Turing-complete programming language. A suitably defined bounded-version of Fractran programs should …
- 21.1k
9
votes
Accepted
What NP-complete problems are most similar to integer factoring?
The textbook of Computational Complexity: Modern Approach, by Arora and Barak gives such example:
They define the decision problem Integer Factoring on input of three positive integers,
$\text{Integer … Factoring} = \{\langle L, U, N \rangle \;|\; (\exists \text{ a prime } p \in \{L, \ldots, U\})[p | N]\}$. …
- 21.1k
3
votes
Consequences of Factoring being in P?
A major consequence of Factoring being in $P$ is that multiplication (of two equal size integers) is not one-way function. …
- 21.1k