Mathematical problems in cryptology
type: Item
instance of: scholarly article
title: Mathematical problems in cryptology
zbMATH Open document ID: 0851.94017
DOI: 10.1007/BF01096271
author: Yanyan Li
published in: Journal of Soviet Mathematics
publication date: 1996-04-23T00:00:00Z
review text: The paper contains a wide ranging survey of the problems of interest in modern cryptography. Beginning with some historical background and terminology, it gives a brief description of data encryption standard (DES) and public key cryptography, including systems based on knapsacks, the linear code system of McEliece and systems based on formal language theory and on partially linear transformations. The RSA system is also described. The wide variety of cryptographic protocols available, including threshold schemes, resiliency, contract signing, identification and many others, are noted. The role of complexity theory in cryptography is discussed with particular attention to the characteristics of one-way functions. The existence of secure pseudorandom generators is considered. Sections on the notions of probabilistic encryption, cryptographic security and NP-completeness and zero-knowledge proofs conclude the paper. One hundred and sixty references are included. 169 Refs.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 94-02
Mathematics Subject Classification ID: 68P25
zbMATH DE Number: 859195
zbMATH Keywords: bibliography
zbMATH Keywords: survey
zbMATH Keywords: cryptography
zbMATH Keywords: data encryption standard
zbMATH Keywords: public key cryptography
zbMATH Keywords: RSA system
zbMATH Keywords: cryptographic protocols
zbMATH Keywords: one-way functions
zbMATH Keywords: pseudorandom generators
zbMATH Keywords: zero-knowledge proofs
zbMATH Keywords: DES
reviewed by: Ian Blake
describes a project that uses: McEliece
MaRDI profile type: Publication
cites work: RSA and Rabin Functions: Certain Parts are as Hard as the Whole
cites work: Factoring with Cyclotomic Polynomials
cites work: Q3210139
cites work: Q3734302
cites work: Algebraic coding theory
cites work: Factoring Polynomials Over Large Finite Fields
cites work: How to Generate Cryptographically Strong Sequences of Pseudorandom Bits
cites work: Subquadratic zero-knowledge
cites work: Cryptanalysis: a survey of recent results
cites work: Universal classes of hash functions
cites work: A Zero-One Law for Boolean Privacy
cites work: Fast evaluation of logarithms in fields of characteristic two
cites work: Discrete logarithms in \(\mathrm{GF}(p)\)
cites work: New directions in cryptography
cites work: Perfectly secure message transmission
cites work: Flipping Persuasively in Constant Time
cites work: Q3325625
cites work: The complexity of promise problems with applications to public-key cryptography
cites work: Cryptocomplexity and NP-completeness
cites work: Q4037491
cites work: Q4198056
cites work: A uniform-complexity treatment of encryption and zero-knowledge
cites work: Q3729902
cites work: Q4038698
cites work: Q3777937
cites work: Probabilistic encryption
cites work: The knowledge complexity of interactive proof-systems
cites work: A New Trapdoor Knapsack Public Key Cryptosystem
cites work: Q3798593
cites work: Solving Simultaneous Modular Equations of Low Degree
cites work: A cryptanalytic time-memory trade-off
cites work: Q3327698
cites work: Absolute results concerning one-way functions and their applications
cites work: Security, veriflability, and universality in distributed computing
cites work: Some remarks on witness functions for nonpolynomial and noncomplete sets in NP
cites work: A cryptanalytic observation concerning systems based on language theory
cites work: Observations concerning a public-key cryptosystem based on iterated morphisms
cites work: On one-way functions and polynomial-time isomorphisms
cites work: M mod 3 security of RSA
cites work: Q3826477
cites work: Q3822227
cites work: Q4273679
cites work: One way functions and pseudorandom generators
cites work: The Discrete Logarithm Hides $O(\log n)$ Bits
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cites work: Q3752293
cites work: Q3726006
cites work: Q4739657
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