A method of exchanging digital public-key verification data whereby a first computing
entity (102) enables a second computing entity (104) to obtain probabilistic
evidence that a given public-key number n is the product of exactly two odd primes
p and q, not known to the second party, whose bit lengths (l(p), l(q)) differ by
not more than d bits. The method provides an efficient proof of knowledge protocol
for demonstrating Monte-Carlo evidence that a number n is the product of two odd
primes of roughly equal size. The evidence is shown "in the dark", which means
that the structure is verified without the prime factors of n disclosed. The cost
of a proof amounts to 12klog2 n multiplications of integers of size
of n where k is the number of the iterations in the proof and relates to an error
probability bounded by max(k, 24/n1/4).
