Is it possible to decipher a ciphertext, in RSA with small primes (two 128-bit factors) when we only have ciphertext $c$, private exponent $d$ and public exponent $e=65537$ to crack it? I try hard on this question but I couldn't find $N$.
First try, I write the code to find factors of $ed-1$ and find it on factordb and try to find out $p$ and $q$ but it doesn't help at all
from itertools import chain, combinations def powerset(iterable): s = list(iterable) return chain.from_iterable(combinations(s, r) for r in range(len(s)+1)) def another_set(all, subset): for s in subset: all.remove(s) return tuple(all) from functools import reduce factors = [2,2,13,17,17,137,263,397, 11119,99181,12203,12330780871,94976914459050383474573,663887747473781762461237] all = powerset(factors) for subset in all: p = subset q = another_set(factors.copy(), p) p = reduce((lambda x, y: x * y), p, 1) q = reduce((lambda x, y: x * y), q, 1) if isPrime(p+1) and isPrime(q+1): print(p+1,q+1)
d.bit_length()? From your code I think it's 255-bit (343…229, equivalently 0x4b…c5), but can't be sure. $\endgroup$