Question

I am implementing Schnorr identification protocol.
I have an example from book “Handbook of applied cryptography” example 10.37.
Everything works without one thing.

(p = 48731, q = 433, B = 11444) - public params.
v = 7355 - public Key.
a = 357 - privateKey.
t = 8 - identification certanity,

Protocol Actions

A choses r = 274 and sends to B x = B^r mod p = 37123.
B sends to A e ( 1 <=e <= 2^t), e = 129.
A sends to B y = (ae + r) mod q. - this doesn't work. should be 255.
B comutes z = ((B^y)(V^e)) mod p. if z == x then identity is ok.

So, i have problem with (ae + r) mod q, should 255 and I have 429.
code :

BigInteger ae = a.multiply(e);
ae = ae.mod(q);
y = ae.add(r);      
y = y.mod(q);

result y = 429
if i ll compute

BigInteger ae = a.multiply(e); 
y = ae.add(r);      
y = y.mod(q);

result is the same.

Please help me.
Thanks.

Answer 1

q=433 is incorrect, it should be divisor of p-1. Correct value is 443.