Mixed-radix Naccache–Stern encryption

  • Rémi Géraud
  • David Naccache
Regular Paper


In this work, we explore a combinatorial optimization problem stemming from the Naccache–Stern cryptosystem. We show that solving this problem results in bandwidth improvements, and suggest a polynomial-time approximation algorithm to find an optimal solution. Our work suggests that using optimal radix encoding results in an asymptotic 50% increase in bandwidth.


Non-linear optimization Public-key encryption Geometric algorithm Naccache–Stern cryptosystem Numeration systems 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Information Security Group, Département d’informatique de l’ÉNS, École Normale Supérieure, CNRSPSL Research UniversityParisFrance

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