Re: Finding n mod p^(D-1) given A=g^n mod p^D

On Tue, Apr 27, 2021 at 12:56 PM Bill Allombert
<[email protected]> wrote:

> >
> > Conjecture 1: dlog(p,g,A,D) mod p^(D-1) = n mod p^(D-1)
>
> Your function is not defined for all (p,g,A,D).
> Otherwise this follows from the definition of the Iwasawa logarithm.
>

Thanks for the answer.

We believe there are few counterexamples to the congruence
if g is p-th power and dlog is successfully computed by pari:

? p=113;D=3;X0=(p+2);g=Mod(2,p^D)^p;A=g^X0;X1=dlog1(p,g,A,D);
? [((X1-X0)%p^(D-1)==0),((X1-X0)%p^(D-2)==0)]
%13 = [0, 1]