A Multi-factor RSA-like Scheme with Fast Decryption Based on Rédei Rational Functions over the Pell Hyperbola

  • Emanuele Bellini
  • Nadir MurruEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11973)


We propose a generalization of an RSA-like scheme based on Rédei rational functions over the Pell hyperbola. Instead of a modulus which is a product of two primes, we define the scheme on a multi-factor modulus, i.e. on a product of more than two primes. This results in a scheme with a decryption which is quadratically faster, in the number of primes factoring the modulus, than the original RSA, while preserving a better security. The scheme reaches its best efficiency advantage over RSA for high security levels, since in these cases the modulus can contain more primes. Compared to the analog schemes based on elliptic curves, as the KMOV cryptosystem, the proposed scheme is more efficient. Furthermore a variation of the scheme with larger ciphertext size does not suffer of impossible group operation attacks, as it happens for schemes based on elliptic curves.


Cryptography Pell conic Rédei rational functions RSA 


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Authors and Affiliations

  1. 1.Technology Innovation InstituteAbu DhabiUAE
  2. 2.Department of MathematicsUniversity of TurinTurinItaly

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