The kth-order nonhomomorphicity of S-boxes

Nonhomomorphicity is a new nonlinearity criterion of a mapping or S-box used in a private key encryption algorithm. An important advantage of nonhomomorphicity over other nonlinearity criteria is that the value of nonhomomorphicity is easy to estimate by the use of a fast statistical method. Due to the Law of Large Numbers, such a statistical method is highly reliable. Major contributions of this paper are (1) to explicitly express the nonhomomorphicity by other nonlinear characteristics, (2) to identify tight upper and lower bounds on nonhomomorphicity, and (3) to find the mean of nonhomomorphicity over all the S-boxes with the same size. It is hoped that these results on nonhomomorphicity facilitate the analysis and design of S-boxes

Nonlinearity and propagation characteristics of balanced boolean functions

Three of the most important criteria for cryptographically strong Boolean functions are the balancedness, the nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balancedness and nonlinearity, and to study systematic methods for constructing Boolean functions satisfying some or all of the three criteria. We show that concatenating, splitting, modifying and multiplying (in the sense of Kronecker) sequences can yield balanced Boolean functions with a very high nonlinearity. In particular, we show that balanced Boolean functions obtained by modifying and multiplying sequences achieve a nonlinearity higher than that attainable by any previously known construction method. We also present methods for constructing balanced Boolean functions that are highly nonlinear and satisfy the strict avalanche criterion (SAC). Furthermore we present methods for constructing highly nonlinear balanced Boolean functions satisfying the propagation criterion with respect to all but one or three vectors. A technique is developed to transform the vectors where the propagation criterion is not satisfied in such a way that the functions constructed satisfy the propagation criterion of high degree while preserving the balancedness and nonlinearity of the functions. The algebraic degrees of functions constructed are also discussed, together with examples illustrating the various constructions

Engineering DNA polymerases for application in DNB-based sequencing technology

DNA polymerases serve as the core engine to afford sequence information in sequencing technologies that have revolutionized modern biological research. For application in the DNB-based sequencing platform, an assemblage of DNA polymerases was engineered to catalyze the requisite biochemical reaction. In the process, naturally occurring polymerases were tapped into through deep-learning algorithms for constraints between individual protein residues to narrow down the protein sequence space and to annotate protein sequences in light of their catalytic properties. And the constraints were subsequently applied in designing potential polymerase candidates with the guidance of the sequence annotations. Additionally, ancestral protein sequences were estimated to expand the candidate repertoire. Furthermore, the candidates were subjected to in silico screening before examined by an HTS methodology based on fluorescence signal. Finally, the resulting proteins were expressed and purified for testing in the DNB-based sequencing platform. Our sequencing data suggested that these proteins behave better than their existing counterparts

An ID-Based Signcryption Scheme with Compartmented Secret Sharing for Unsigncryption

In this paper the ID-based signcryption scheme of Li, Xin, and Hu is extended to a compartmented scheme. If an organization is partitioned into different compartments, this scheme allows any member of a specific compartment to participate in the unsigncryption; moreover, each member of a compartment has information unique to that individual. This construction is the first (to the authors’ knowledge) to combine identity-based encryption, Shamir’s threshold scheme, and signcryption into an implementable compartmented sharing scheme

Brother Joseph N. Streiff, S.M. 1918-1985

News release announces Brother Joseph M. Streiff, S.M., died at age 67 after suffering from leukemia

The Generalized XOR Lemma

Abstract The XOR Lemma states that a mapping is regular or balanced if and only if all the linear combinations of the component functions of the mapping are balanced Boolean functions. The main contribution of this paper is to extend the XOR Lemma to more general cases where a mapping may not be necessarily regular. The extended XOR Lemma has applications in the design of substitution boxes or S-boxes used in secret key ciphers. It also has applications in the design of stream ciphers as well as one-way hash functions. Of independent interest is a new concept introduced in this paper that relates the regularity of a mapping to subspaces

3D characterization of ultrasonic melt processing on the microstructural refinement of Al-Cu alloys by synchrotron X-ray tomography

The effect of ultrasonic melting processing on three-dimensional architecture of intermetallic phases and pores in two multicomponent cast Al-5.0Cu-0.6Mn-0.5 Fe alloys is characterized using conventional microscopy and synchrotron X-ray microtomography. The two alloys are found to contain intermetallic phases such as Al15(FeMn)3Cu2, Al7Cu2Fe, Al3(FeMn), Al6(FeMn), and Al2Cu that have complex networked morphology in 3D. The application of USP in alloys can obtained refined and equiaxed microstructures. The grain size of 0.5Fe and 1.0 Fe alloys is greatly decreased from 16.9 m, 15.8 m without USP to 13.3 m, 12.2 m with USP, respectively. The results show that USP significantly reduce the volume fraction, grain size, interconnectivity, and equivalent diameter of the intermetallic phases in both alloys. The volume fraction of pores in both alloys is reduced due to the USP degassing effect. The refinement mechanism of USP induced fragmentation of primary and secondary dendrites via acoustic bubbles and acoustic streaming flow were discussed.Comment: 28 pages, 16 figures

Skew-Frobenius map on twisted Edwards curve

In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skew-Frobenius map defined on the quadratic twist of an twisted Edwards curve. Our results show that the Frobenius endomorphism on twisted Edwards curve and the skew-Frobenius endomorphism on quadratic twist of an twisted Edwards curve can be exploited to devise fast point multiplication algorithm that do not use any point doubling. As an application, the GLV method can be used for speeding up point multiplication on twisted Edwards curve