RNS Approach in Lattice-Based Cryptography

  • Jean-Claude BajardEmail author
  • Julien Eynard


Lattice-based cryptography (LBC) is a main branch of modern cryptography. Growing up and evolving mainly since 1996 [1], it is known to be a viable post-quantum alternative to all cryptosystems based on the factorization and discrete logarithm problems [30], such as the widely used Diffie-Hellman [8] key-exchange protocol and RSA [26]. Beyond a post-quantum security, many other important properties make LBC interesting. Nowadays, primitives based on q-ary ideal lattices arouse interest since they are related to special properties, such as security proofs based on worst-case of computationally hard problems in lattices like Learning-with-Error [21, 24, 25], or homomorphic encryption [6, 7, 10], which is constantly evolving since its appearance in 2009.


Residue number systems Lattice-based cryptography Montgomery reduction Closest vector problem Rounding-off Base extension 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Sorbonne UniversitésUPMC, CNRS, LIP6ParisFrance
  2. 2.Department of Electrical and Computer EngineeringUniversity of WaterlooWaterlooCanada

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