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

Since 1974, several algorithms have been developed that attempt to factor a large number N by doing extensive computations module N and occasionally taking GCDs with N. These began with Pollard's p 1 and Monte Carlo methods. More recently, Williams published a p + 1 method, and Lenstra discovered an elliptic curve method (ECM). We present ways to speed all of these. One improvement uses two tables during the second phases of p ? 1 and ECM, looking for a match. Polynomial preconditioning lets us search a fixed table of size n with n/2 + o(n) multiplications. A parametrization of elliptic curves lets Step 1 of ECM compute the x-coordinate of nP from that of P in about 9.3 1og2 n multiplications for arbitrary P.

/pdf/speeding-the-pollard-and-elliptic-curve-methods-of-5bfndnc50y.pdf

Speeding the Pollard and elliptic curve methods of factorization

ertification mechanism for verifying the secure flow of information through a program. Because it exploits the properties of a lattice structure among security classes, the procedure is sufficiently simple that it can easily be included in the analysis phase of most existing compilers. Appropriate semantics are presented and proved correct. An important application is the confinement problem: The mechanism can prove that a program cannot cause supposedly nonconfidential results to depend on confidential input data.

/pdf/certification-of-programs-for-secure-information-flow-3kbmz311vw.pdf

Certification of programs for secure information flow

Abstruct- Elliptic cuwe cryptosystems have the potential to provide relatively small block size, high-security public key schemes that can be efficiently implemented. As with other known public key schemes, such as RSA and discrete exponentiation in a finite field, some care must be exercised when selecting the parameters involved, in this case the elliptic curve and the underlying field. Specific classes of cuwes that give little or no advantage over previously known schemes are discussed. The main result of the paper is to demonstrate the reduction of the elliptic curve logarithm problem to the logarithm problem in the multiplicative group of an extension of the underlying finite field. For the class of supersingular elliptic curves, the reduction takes probabilistic polynomial time, thus providing a probabilistic subexponential time algorithm for the former problem. Index Tem- Discrete logarithms, elliptic curves, public key CryPtOSraPhY.

Reducing elliptic curve logarithms to logarithms in a finite field

We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the so-called strong RSA assumption. Moreover, a hash function can be incorporated into the scheme in such a way that it is also secure in the random oracle model under the standard RSA assumption.

Signature schemes based on the strong RSA assumption

Factorizations of b[n]±1, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers

/pdf/new-primality-criteria-and-factorizations-of-2-1-2qx5k7wzb4.pdf

New primality criteria and factorizations of 2^{}±1

Let {a(n)} be the Rudin-Shapiro sequence, and let s(n) = ∑a(k) and t(n) = ∑(-1)k a(k). In this paper we show that the sequences {s(n)/√n} and {t(n)/√n} do not have cumulative distribution functions, but do have logarithmic distribution functions (given by a specific Lebesgue integral) at each point of the respective intervals [√3/5, √6] and [0, √3]. The functions a(x) and s(x) are also defined for real x ≥ 0, and the function [s(x) – a(x)]/√x is shown to have a Fourier expansion whose coefficients are related to the poles of the Dirichlet series ∑a(n)/n, where Re τ > ½.

/pdf/on-sums-of-rudin-shapiro-coefficients-ii-1mus5dpoeb.pdf

On sums of Rudin-Shapiro coefficients II

where n > 0 and Po(x) = Qo(x) = 1. (See [4] also. Note in this reference that Po(x) =Qo(x) =x.) These polynomials have been used by Kahane and Salem in their book [1 ] to prove several theorems about trigonometric series. Rider [2] used a generalization of these polynomials to complete the solution of a problem partially solved in [4]. In a more recent paper Rider [3] employed the polynomials to exhibit certain subalgebras of the group algebra of the unit circle. In particular, in this paper Rider obtained a special case of Theorem 4 below. The first few polynomials are

/pdf/note-on-the-shapiro-polynomials-8cpolal00u.pdf

Note on the Shapiro polynomials

In this paper we derive the power series expansions of four infinite products of the form 1I (1Xn) 7 (1 + Xn), nES1 nES2 where the index sets Si and S2 are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.

/pdf/some-infinite-product-identities-xco16ydvx0.pdf

Some infinite product identities

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