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From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.

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Public-key cryptosystems based on composite degree residuosity classes

Distance-Regular Graphs

Stream ciphers.- The BAA attacks on several classes of stream ciphers.- Measure indexes on the security of stream ciphers.- The stability of linear complexity of sequences.- The period stability of sequences.- Summary and open problems.

The stability theory of stream ciphers

Introduction and philosophy Chinese remainder algorithm in modular computations in algorithmics in bridging computations in coding theory in cryptography tutorial in information theory tutorial in algebra list of mathematical symbols.

Chinese remainder theorem: applications in computing, coding, cryptography

In this paper, error-correcting codes from perfect nonlinear mappings are constructed, and then employed to construct secret sharing schemes. The error-correcting codes obtained in this paper are very good in general, and many of them are optimal or almost optimal. The secret sharing schemes obtained in this paper have two types of access structures. The first type is democratic in the sense that every participant is involved in the same number of minimal-access sets. In the second type of access structures, there are a few dictators who are in every minimal access set, while each of the remaining participants is in the same number of minimal-access sets.

Linear codes from perfect nonlinear mappings and their secret sharing schemes

Preface. Introduction. Applications of number theory. An outline of this book. Stream Ciphers. Stream cipher systems. Additive synchronous stream ciphers. Nonadditive synchronous stream ciphers. Stream ciphering with block ciphers. Cooperative distributed ciphering. Some keystream generators. Generators based on counters. Some number-theoretic generators. Cryptographic aspects of sequences. Minimal polynominal and linear complexity. Pattern distribution of key streams. Correlation functions. Sphere complexity and linear cryptanalysis. Higher order complexities. Harmony on binary NSGs. Security attacks. Primes, Primitive Roots and Sequences. Cyclotomic polynominals. Two basic problems from stream ciphers. A basic theorem and main bridge. Primes, primitive roots and binary sequences. Primes, primitive roots and ternary sequences. Primes, negord and sequences. Prime powers, primitive roots and sequences. Prime products and sequences. Binary sequences and primes. Ternary sequences and primes. On cryptographic primitive roots. Linear complexity of sequences over Z m . Period and its cryptographic importance. Cyclotomy and Cryptographic Functions. Cyclotomic numbers. Cyclotomy and cryptography. Cyclotomy and difference parameters. Cyclotomy and the differential cryptanalysis. Cryptographic cyclotomic numbers. Cryptographic functions from Z p to Z d . The case d = 2. The case d = 3. The case d = 4. The case d = 5. The case d = 6. The case d = 8. The case d = 10. The case d = 12. Cryptographic functions from Z pq to Z d . Whiteman's generalized cyclotomy and cryptography. Cryptographic functions from Z pq to Z 2 . Cryptographic functions from Z pq to Z 4 . Cryptographic functions from Z p2 to Z 2 . Cryptographic functions defined on GF(p m ) . The origin of cyclotomic numbers. Special Primes and Sequences. Sophie Germain primes and sequences. Their importance in stream ciphers. Their relations with other number-theoretic problems. The existence problem. A search for cryptographic Sophie Germain primes. Tchebychef primes and sequences. Their cryptographic significance. Existence and search problem. Other primes of form k x 2 n + 1 and sequences. Primes of form ( a n - 1)/( a - 1) and sequences. Mersenne primes and sequences. Cryptographic primes of form ((4 u ) n - 1)/(4 u - 1). Prime repunits and their cryptographic values. n ! +/- 1 and p# +/- 1 Primes and sequences. Twin primes and sequences over GF (2). The significance of twins and their sexes. Cryptographic twins and the sex distribution. Twin primes and sequences over GF (3). Other special primes and sequences. Prime distribution and their significance. Primes for stream ciphers and for RSA. Difference Sets and Cryptographic Functions. Rudiments of difference sets. Difference sets and autocorrelation functions. Differece sets and nonlinearity. Difference sets and information stability. Difference sets and linear approximation. Almost difference sets.

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Stream Ciphers and Number Theory

Secret sharing has been a subject of study for over 20 years, and has had a number of real-world applications. There are several approaches to the construction of secret sharing schemes. One of them is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code, which is a difficult problem in general. In this paper, a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums. Some linear codes whose covering structure can be determined are constructed, and then used to construct secret sharing schemes with nice access structures.

Cunsheng Ding

Papers

The stability theory of stream ciphers

Chinese remainder theorem: applications in computing, coding, cryptography

Linear codes from perfect nonlinear mappings and their secret sharing schemes

Stream Ciphers and Number Theory

Secret sharing schemes from three classes of linear codes