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from libnum import *
from gmpy2 import log2
from Crypto.Util.number import bytes_to_long, long_to_bytes
s = "012abc"
s2n(s), bytes_to_long(s.encode()) # (52987856773731, 52987856773731)
n2s(num), long_to_bytes(num) # ('012abc', b'012abc')
s_num = s2n(s)
len_in_bits(num), log2(num) # (46, mpfr('45.590727008691232'))
s2b(s), "".join([bin(ord(c)) for c in s])[2:] # ('001100000011000100110010011000010110001001100011', '1100000b1100010b1100100b11000010b11000100b1100011')
s_bin = s2b(s)
b2s(s_bin), "".join([chr(int(s_bin[i:i+8], 2)) for i in range(0, len(s_bin), 8)]) # ('012abc', '012abc')
from libnum import *
from gmpy2 import log2
from Crypto.Util.number import bytes_to_long, long_to_bytes
s = "012abc"
s2n(s), bytes_to_long(s.encode()) # (52987856773731, 52987856773731)
n2s(num), long_to_bytes(num) # ('012abc', b'012abc')
s_num = s2n(s)
len_in_bits(num), log2(num) # (46, mpfr('45.590727008691232'))
s2b(s), "".join([bin(ord(c)) for c in s])[2:] # ('001100000011000100110010011000010110001001100011', '1100000b1100010b1100100b11000010b11000100b1100011')
s_bin = s2b(s)
b2s(s_bin), "".join([chr(int(s_bin[i:i+8], 2)) for i in range(0, len(s_bin), 8)]) # ('012abc', '012abc')
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(b'012abc', '012abc')
获取素数 ¶
primes(n)获取不大于 n 的所有素数generate_primes(n)获取长度为 n bits 的素数factorize(n)分解质因数
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little_num = 101
littlelittle_num = 11
to_be_factorized = 564587462423644586312345678908654325263456667
primes(little_num), generate_prime(littlelittle_num), factorize(to_be_factorized)
little_num = 101
littlelittle_num = 11
to_be_factorized = 564587462423644586312345678908654325263456667
primes(little_num), generate_prime(littlelittle_num), factorize(to_be_factorized)
Out[36]:
([2,
3,
5,
7,
11,
13,
17,
19,
23,
29,
31,
37,
41,
43,
47,
53,
59,
61,
67,
71,
73,
79,
83,
89,
97,
101],
1733,
{264547984673890083312604955351805711413: 1, 13093: 1, 163: 1})
当然，大数分解质因数还得看 factordb 。
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factorize(8699621268124163273600280057569065643071518478496234908779966583664908604557271908267773859706827828901385412151814796018448555312901260592)
factorize(8699621268124163273600280057569065643071518478496234908779966583664908604557271908267773859706827828901385412151814796018448555312901260592)
factordb¶
安装指令：
pip3 install factordb-python使用场景：命令行中使用，分解大整数，之中存储了大量的已知的分解的整数，也就是说相当于只是在查表，所以很快。
对于上面的大数：
8699621268124163273600280057569065643071518478496234908779966583664908604557271908267773859706827828901385412151814796018448555312901260592
yafu 分解失败；libnum 分解了 6 min 还在跑；
sage 分解用时 53 s 左右：
2^4 * 3^2 * 31 * 61 * 223 * 4013 * 281317 * 4151351 * 339386329 * 370523737 * 5404604441993 * 26798471753993 * 25866088332911027256931479223 * 64889106213996537255229963986303510188999911
factordb 很快就给出了答案：
$ factordb 86996212681241632736002800575690656430715184784
96234908779966583664908604557271908267773859706827828901385412151814796018448555312901260592
2 2 2 2 3 3 31 61 223 4013 281317 4151351 339386329 370523737 5404604441993 26798471753993 25866088332911027256931479223 64889106213996537255229963986303510188999911