Um, actually your ststement is mistaken.
It is not that MATLAB won't accept a negative exponent. It is that vpi/powermod won't accept that. If powermod was not written to do so, then you cannot make it behave in that way. Ok, I'll admit that had I thought of it when I wrote that code, I should probably have done so. So sue me. :)
I wrote minv after I wrote powermod, and did not think at the time to simply wrap it into powermod.
The simple solution is to use a fix like this:
negpowermod = @(a,d,n) minv(powermod(a,abs(d),n),n);
so, for a negative exponent d, negpowermod will do the powermod computation, then compute the modular inverse.
a = 23;
d = 17;
n = 137;
negpowermod(a,d,n)
ans =
96
Did it work? Of course.
mod(96*powermod(23,17,137),137)
ans =
1
Note that not ALL integers will have a modular multiplicative inverse with respect to any given modulus, so that negative exponent can fail. In that case, the result will be empty. Thus:
minv(2,10)
ans =
1×0 empty double row vector
The failure will arise when the two are not relatively co-prime, as I recall.
