Paper 2020/624

RSA for poor men: a cryptosystem based on probable primes to base 2 numbers

Marek Wójtowicz

Abstract

We show it is possible to build an RSA-type cryptosystem by utilizing probable primes to base 2 numbers. Our modulus N is the product nm of such numbers (so here both prime and some composite, e.g. Carmichael or Fermat, numbers are acceptable) instead of prime numbers. Moreover, we require for n and m to be distinct only, not necessarily coprime, and so we don't have to worry about whether any of the numbers n,m is composite or not. The encryption and decryption processes are similar as those in the RSA. Hence, in this cryptosystem we may apply the above kind of numbers of arbitrary length being still sure that the system works well. The price for that is the size of words permitted by the new system: any message M, as a number, must be smaller than log (in base 2) of nm.