Deterministic factoring with oracles
نویسندگان
چکیده
Can we factor an integer $$N$$ unconditionally, in deterministic polynomial time, given the value of its Euler totient $$\varphi (N)$$ ? We show that this can be done under certain size conditions on prime factors . The key technique is lattice basis reduction using LLL algorithm. Among our results, if has a $$p > \sqrt{N}$$ , then recover $$p$$ time also shed some light analogous factorization problems oracles for sum-of-divisors function, Carmichael’s and order oracle used Shor’s quantum factoring
منابع مشابه
Deterministic factoring with oracles
We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer $N$ unconditionally, in deterministic polynomial time, given the value of the Euler totient $(\varphi(N)$? We show that this can be done, under certain size conditions on the prime factors of $N$. The key technique is lattice basis reduction using the LLL algor...
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2021
ISSN: ['1432-0622', '0938-1279']
DOI: https://doi.org/10.1007/s00200-021-00521-8