Exponential sums and lattice reduction: Applications to cryptography

IE Shparlinski*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

We describe a rather surprising, yet powerful, combination of two famous number theoretic techniques: bounds of exponential sums and lattice reduction algorithms. This combination has led to a number of cryptographic applications, helping to make rigorous several heuristic approaches and provides a two edge sword to defend and attack. It can be used prove important security results arid also to create powerful attacks. The examples of the first group include results about the bit security of the Diffie-Hellman key exchange system, of the Shamir message passing scheme and of the XTR and LUC cryptosystems. The examples of the second group include attacks on the Digital Signature Scheme and its modifications which are provably insecure under certain conditions.

Original languageEnglish
Title of host publicationFinite fields with applications to coding theory, cryptography and related areas
EditorsGary L Mullen, Henning Stichtenoth, Horacio TapiaRecillas
Place of PublicationBerlin; New York
PublisherSpringer, Springer Nature
Pages286-298
Number of pages13
ISBN (Print)3540439617
Publication statusPublished - 2002
Event6th International Conference on Finite Fields and Applications (Fq6) - OAXACA, Mexico
Duration: 21 May 200126 May 2001

Conference

Conference6th International Conference on Finite Fields and Applications (Fq6)
CountryMexico
CityOAXACA
Period21/05/0126/05/01

Keywords

  • SECURITY
  • SYSTEM

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