Encyclopedia of Cryptography and Security

2011 Edition
| Editors: Henk C. A. van Tilborg, Sushil Jajodia

Lattice-Based Cryptography

  • Daniele Micciancio
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_417

Related Concepts


Lattice-based cryptography is a generic term used to encompass a wide range of cryptographic functions whose security is based on the conjectured intractability of Lattice problems, like (variants of) the  Shortest Vector Problem and the  Closest Vector Problems.

For applications of lattices in cryptanalysis,  Lattice Reduction.


The study of lattice-based cryptography was pioneered by Ajtai in 1996 [ 1], who proved that certain variants of the  knapsack cryptographic schemes are at least as hard to break on the average as approximating(the length estimation variant of) the  Shortest Vector Problem(GapSVP)within factors that grow only polynomially in the dimension n of thelattice. Two distinguishing features of Ajtai’s result, and lattice-basedcryptography in general, are that:
  • Breaking the cryptographic...

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Recommended Reading

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    Ajtai M (1996) Generating hard instances of lattice problems (extended abstract). In: Proceedings of the twenty-eighth annual ACM Symposium on the Theory of Computing (STOC’96), Philadelphia, 22–24 May 1996. ACM Press, New York, pp 99–108Google Scholar
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    Ajtai M, Dwork C (1997) A public-key cryptosystem with worstcase/average-case equivalence. In: Proceedings of the twenty-ninth annual ACM Symposium on Theory of Computing (STOC ’97), E1 Paso, 4–6 May 1997. ACM Press, New York, pp 284–293Google Scholar
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    Gentry C, Peikert C, Vaikuntanathan V (2008) Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of STOC ’08, Victoria, 17–20 May 2008. ACM Press, New York, pp 197–206Google Scholar
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    Lyubashevsky V, Micciancio D (2008) Asymptotically efficient lattice-based digital signatures. In: Proceedings of TCC ’08, New York, 19–21 March 2008. Lecture notes in computer science, vol 4948. Springer, Berlin, pp 37–54Google Scholar
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    Lyubashevsky V, Micciancio D (2009) On bounded distance decoding, unique shortest vectors, and the minimum distance problem. In: Proceedings of CRYPTO 2009, Santa Barbara, 16–20 August 2009. Lecture notes in computer science, vol 5677. Springer, Berlin, pp 577–594Google Scholar
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    Lyubashevsky V, Micciancio D, Peikert C, Rosen A (2008) Swifft: a modest proposal for FFT hashing. In: Proceedings of FSE ’08, Lausanne, 10–13 February 2008. Lecture notes in computer science, vol 5086. Springer, Berlin, pp 54–72Google Scholar
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    Micciancio D (2007) Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. Comput Complex 16(4):365–411zbMATHMathSciNetCrossRefGoogle Scholar
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    Micciancio D, Regev O (2007) Worst-case to average-case reductions based on Gaussian measure. SIAM J Comput 37(1):267–302zbMATHMathSciNetCrossRefGoogle Scholar
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    Micciancio D, Regev O (2008) Lattice-based cryptography. In: Bernstein DJ, Buchmann J, Dahmén E (eds) Post-quantum cryptography. Springer, BerlinGoogle Scholar
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    Peikert C, Vaikuntanathan V (2008) Noninteractive statistical zeroknowledge proofs for lattice problems. In: Proceedings of CRYPTO ’08, Santa Barbara, 17–21 August 2008. Lecture notes in computer science, vol 5157. Springer, Berlin, pp 536–553Google Scholar
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Daniele Micciancio
    • 1
  1. 1.Department of Computer Science & EngineeringUniversity of CaliforniaSan DiegoUSA