70,530 research outputs found
Chasing diagrams in cryptography
Cryptography is a theory of secret functions. Category theory is a general
theory of functions. Cryptography has reached a stage where its structures
often take several pages to define, and its formulas sometimes run from page to
page. Category theory has some complicated definitions as well, but one of its
specialties is taming the flood of structure. Cryptography seems to be in need
of high level methods, whereas category theory always needs concrete
applications. So why is there no categorical cryptography? One reason may be
that the foundations of modern cryptography are built from probabilistic
polynomial-time Turing machines, and category theory does not have a good
handle on such things. On the other hand, such foundational problems might be
the very reason why cryptographic constructions often resemble low level
machine programming. I present some preliminary explorations towards
categorical cryptography. It turns out that some of the main security concepts
are easily characterized through the categorical technique of *diagram
chasing*, which was first used Lambek's seminal `Lecture Notes on Rings and
Modules'.Comment: 17 pages, 4 figures; to appear in: 'Categories in Logic, Language and
Physics. Festschrift on the occasion of Jim Lambek's 90th birthday', Claudia
Casadio, Bob Coecke, Michael Moortgat, and Philip Scott (editors); this
version: fixed typos found by kind reader
Applications of finite geometry in coding theory and cryptography
We present in this article the basic properties of projective geometry, coding theory, and cryptography, and show how
finite geometry can contribute to coding theory and cryptography. In this way, we show links between three research areas, and in particular, show that finite geometry is not only interesting from a pure mathematical point of view, but also of interest for applications. We concentrate on introducing the basic concepts of these three research areas and give standard references for all these three research areas. We also mention particular results involving ideas from finite geometry, and particular results in cryptography involving ideas from coding theory
Quantum Cryptography
Quantum cryptography is a new method for secret communications offering the
ultimate security assurance of the inviolability of a Law of Nature. In this
paper we shall describe the theory of quantum cryptography, its potential
relevance and the development of a prototype system at Los Alamos, which
utilises the phenomenon of single-photon interference to perform quantum
cryptography over an optical fiber communications link.Comment: 36 pages in compressed PostScript format, 10 PostScript figures
compressed tar fil
Learning with Errors is easy with quantum samples
Learning with Errors is one of the fundamental problems in computational
learning theory and has in the last years become the cornerstone of
post-quantum cryptography. In this work, we study the quantum sample complexity
of Learning with Errors and show that there exists an efficient quantum
learning algorithm (with polynomial sample and time complexity) for the
Learning with Errors problem where the error distribution is the one used in
cryptography. While our quantum learning algorithm does not break the LWE-based
encryption schemes proposed in the cryptography literature, it does have some
interesting implications for cryptography: first, when building an LWE-based
scheme, one needs to be careful about the access to the public-key generation
algorithm that is given to the adversary; second, our algorithm shows a
possible way for attacking LWE-based encryption by using classical samples to
approximate the quantum sample state, since then using our quantum learning
algorithm would solve LWE
Modern Cryptography Volume 1
This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas
A Talk on Quantum Cryptography, or How Alice Outwits Eve
Alice and Bob wish to communicate without the archvillainess Eve
eavesdropping on their conversation. Alice, decides to take two college
courses, one in cryptography, the other in quantum mechanics. During the
courses, she discovers she can use what she has just learned to devise a
cryptographic communication system that automatically detects whether or not
Eve is up to her villainous eavesdropping. Some of the topics discussed are
Heisenberg's Uncertainty Principle, the Vernam cipher, the BB84 and B92
cryptographic protocols. The talk ends with a discussion of some of Eve's
possible eavesdropping strategies, opaque eavesdropping, translucent
eavesdropping, and translucent eavesdropping with entanglement.Comment: 31 pages, 8 figures. Revised version of a paper published in "Coding
Theory, and Cryptography: From Geheimscheimschreiber and Enigma to Quantum
Theory," (edited by David Joyner), Springer-Verlag, 1999 (pp. 144-174). To be
published with the permission of Springer-Verlag in an AMS PSAPM Short Course
volume entitled "Quantum Computation.
07381 Executive Summary - Cryptography
The topics covered in the seminar spanned most areas of cryptography,
in one way or another, both in terms of the types of schemes
(public-key cryptography, symmetric cryptography, hash functions and
other cryptographic functions, multi-party protocols, etc.) and in terms of the
mathematical methods and techniques used (algebra, number theory,
elliptic curves, probability theory, information theory,
combinatorics, quantum theory, etc.). The range of applications
addressed in the various talks was broad, ranging from secure
communication, key management, authentication, digital signatures and
payment systems to e-voting and Internet security.
While the initial plan had been to focus more exclusively on public-key
cryptography, it turned out that this sub-topic branches out into
many other areas of cryptography and therefore the organizers
decided to expand the scope, emphasizing quality rather than
close adherence to public-key cryptography. This decision turned
out to be a wise one.
What was common to almost all the talks is that rigorous mathematical
proofs for the security of the presented schemes were given. In fact,
a central topic of many of the talks were proof methodologies for
various contexts
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