**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.

**Category / Keywords: **public-key cryptography / RSA, Pseudoprimes in base 2, Carmichael numbers

**Date: **received 27 May 2020

**Contact author: **mwojt at ukw edu pl

**Available format(s): **PDF | BibTeX Citation

**Version: **20200603:092947 (All versions of this report)

**Short URL: **ia.cr/2020/624

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