[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ? isclosely approximated by C - ?(V/n) Q-1(?) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.

/pdf/channel-coding-rate-in-the-finite-blocklength-regime-35xxh8quud.pdf

Channel Coding Rate in the Finite Blocklength Regime

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on an eavesdropper's power. This article provides a concise up-to-date review of QKD, biased toward the practical side. Essential theoretical tools that have been developed to assess the security of the main experimental platforms are presented (discrete-variable, continuous-variable, and distributed-phase-reference protocols).

/pdf/the-security-of-practical-quantum-key-distribution-1qnjoq3c7p.pdf

The security of practical quantum key distribution

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

Spectra of graphs

There has been much interest in quantum key distribution. Experimentally, quantum key distribution over 150 km of commercial Telecom fibers has been successfully performed. The crucial issue in quantum key distribution is its security. Unfortunately, all recent experiments are, in principle, insecure due to real-life imperfections. Here, we propose a method that can for the first time make most of those experiments secure by using essentially the same hardware. Our method is to use decoy states to detect eavesdropping attacks. As a consequence, we have the best of both worlds--enjoying unconditional security guaranteed by the fundamental laws of physics and yet dramatically surpassing even some of the best experimental performances reported in the literature.

https://arxiv.org/pdf/quant-ph/0411004.pdf

Decoy State Quantum Key Distribution

In this paper we show an explicit relation between authentication codes and codes correcting independent errors. This relation gives rise to several upper bounds on A-codes. We also show how to construct A-codes starting from error correcting codes. The latter is used to show that if Ps exceeds PI by an arbitrarily small positive amount, then the number of source states grows exponentially with the number of keys but if PS = PI it will grow only linearly.

Advances in Cryptology-Eurocrypt '93

Some results about the cross-correlation function between two maximal linear sequences

Considered are p-ary bent functions having the form f(x)=Tr/sub n/(/spl sigma//sub i=0//sup s/a/sub i/x/sup di/). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. The (weak) regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given. Finally, some criteria for an arbitrary quadratic function to be bent are proven.

/pdf/monomial-and-quadratic-bent-functions-over-the-finite-fields-26asp6ow66.pdf

Monomial and quadratic bent functions over the finite fields of odd characteristic

The weight distribution of irreducible cyclic codes with block lengths n1((q1−1)N)

Almost difference sets have interesting applications in cryptography and coding theory. We give a well-rounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost difference sets, and four classes of binary sequences of period n/spl equiv/0 (mod 4) with optimal autocorrelation. We have also obtained two classes of relative difference sets and four classes of divisible difference sets (DDSs). We also point out that a result due to Jungnickel (1982) can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation.

/pdf/almost-difference-sets-and-their-sequences-with-optimal-36qpbcv42g.pdf

Tor Helleseth

Papers

Advances in Cryptology-Eurocrypt '93

Some results about the cross-correlation function between two maximal linear sequences

Monomial and quadratic bent functions over the finite fields of odd characteristic

The weight distribution of irreducible cyclic codes with block lengths n1((q1−1)N)

Almost difference sets and their sequences with optimal autocorrelation