Article

Abstract models of computation in cryptography

Author:

Ueli MaurerAuthors Info & Claims

IMA'05: Proceedings of the 10th international conference on Cryptography and Coding

Pages 1 - 12

https://doi.org/10.1007/11586821_1

Published: 19 December 2005 Publication History

Abstract

Computational security proofs in cryptography, without unproven intractability assumptions, exist today only if one restricts the computational model. For example, one can prove a lower bound on the complexity of computing discrete logarithms in a cyclic group if one considers only generic algorithms which can not exploit the properties of the representation of the group elements.

We propose an abstract model of computation which allows to capture such reasonable restrictions on the power of algorithms. The algorithm interacts with a black-box with hidden internal state variables which allows to perform a certain set of operations on the internal state variables, and which provides output only by allowing to check whether some state variables satisfy certain relations. For example, generic algorithms correspond to the special case where only the equality relation, and possibly also an abstract total order relation, can be tested.

We consider several instantiation of the model and different types of computational problems and prove a few known and new lower bounds for computational problems of interest in cryptography, for example that computing discrete logarithms is generically hard even if an oracle for the decisional Diffie-Hellman problem and/or other low degree relations were available.

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Cited By

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Hhan MYamakawa TYun A(2024)Quantum Complexity for Discrete Logarithms and Related ProblemsAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68391-6_1(3-36)Online publication date: 18-Aug-2024
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Index Terms

Abstract models of computation in cryptography
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

IMA'05: Proceedings of the 10th international conference on Cryptography and Coding

December 2005

459 pages

ISBN:354030276X

Editor:
Nigel P. Smart
Dept. Computer Science, University of Bristol, Woodland Road, Bristol, United Kingdom

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 December 2005

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Garg SKolonelos DPolicharla GWang M(2024)Threshold Encryption with Silent SetupAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68394-7_12(352-386)Online publication date: 18-Aug-2024
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Identity-Based signcryption from identity-based cryptography

A Provably Secure Proxy Signature Scheme in Certificateless Cryptography

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