From Newsgroup: sci.crypt


In this article we have created the table that classifies all primitive triples, shown some properties of basic triples and discussed about the
use of primitive Pythagorean triples in cryptography.

I have pondered about whether we can find a practical use for the
classified primitive triple table. One possible use could be in
cryptography. We have shown that the Z component of a primitive triple can
be easily generated from two parameters, b and j. But we cannot easily
work out the original value of b and j from a given Z because we have two unknowns, b and j, for only one equation, Z=(b+j)^2+b^2. For example, what
are the values of b and j that generate the primitive Pythagorean triple (X=14719726793rCa, Y=518663627978rCa, Z=518872459612805)?

The heart of the RSA cryptosystem is to find two prime integers p and q so large that the factoring of the product p-+q is very hard. With large primitive Pythagorean triples, it is also very hard to work out the
original b and j from a given Z. So, I think that the three integers b, j
and Z could work at the place of p, q and p-+q for an alternate
cryptosystem similar to RSA. In addition, large prime integers are
difficult to find while b and i, with j=2i-1, can be any integers, which
would make the alternate cryptosystem simpler and cheaper than the RSA cryptosystem. The fact that the integers X, Y and Z are coprime could be useful for cryptography too.

But I am not a cryptographer and cannot evaluate the validity of this
idea. Would any cryptographer be interested?

For more detail, please read -2 Classification of primitive Pythagorean triples -+ https://pengkuanonmaths.blogspot.com/2025/09/classification-of-primitive-pythagorean.html

https://www.academia.edu/143986307/Classification_of_primitive_Pythagorean_triples


--- Synchronet 3.21a-Linux NewsLink 1.2