Residue Classes of the PPT Sequence
This work provides pseudorandom sequences for key generation and distribution problems, offering a domain-specific solution with incremental mathematical insights.
The paper tackled the problem of analyzing residue classes of Primitive Pythagorean Triples (PPT) and derived the probability that the smaller odd number in a PPT is divisible by a prime p as 2/(p+1). It showed that sequences derived from these residue classes have excellent randomness properties, with analytical explanations for autocorrelation peaks and off-peak values.
Primitive Pythagorean triples (PPT) may be put into different equivalence classes using residues with respect to primes. We show that the probability that the smaller odd number associated with the PPT triple is divisible by prime p is 2/(p+1). We have determined the autocorrelation function of the Baudhayana sequences obtained from the residue classes and we show these sequences have excellent randomness properties. We provide analytical explanation for the peak and the average off-peak values for the autocorrelation function. These sequences can be used specifically in a variety of key generation and distribution problems and, more generally, as pseudorandom sequences.