Hi Bill, On 2017-04-08, 'Bill Cox' via sage-support <sage-support@googlegroups.com> wrote: > I want to test finding the discrete log in the circle group over Z/Zm -- > discrete logs of g^a mod m, where g is a complex number and m is composite. > Can Sage do this for large composite m, say on the order of 2^128 or more, > when m is smooth, containing no prime factors larger than say 1 billion? > > I can get the discrete log in the circle group for prime powers like this: > > sage: F.<a> = FiniteField(23^2, modulus=x^2 + 1) > sage: F.<a> = FiniteField(23^2, modulus=x^2 + 1) > sage: aliceSecret = (1 + a)^13 > sage: sage: aliceSecret.log(1 + a) > 13
Maybe I misunderstand your problem, but can't you simply do exactly the same thing with a quotient ring instead of a finite field? sage: m = 120011^2*12000239*5150237*7200233^2 sage: m 46147940098802341021228029866464641067 sage: R = Integers(m) sage: aliceSecret = R(2)^13 sage: aliceSecret.log(2) 13 sage: aliceSecret = R(19)^11231 sage: aliceSecret.log(19) 11231 Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
