Sung-Hak Kwon

Using the self duality of an optimal normal basis (ONB) of type II, we present a bit parallel systolic multiplier over GF(2/sup m/), which has a low hardware complexity and a low latency. We show that our multiplier has a latency m+1 and the basic cell of our circuit design needs 5 latches (flip-flops). On the other hand, most of other multipliers of the same type have latency 3m and the basic cell of each multiplier needs 7 latches. Comparing the gates areas in each basic cell, we find that the

After Miller's original algorithm for the Tate pairing computation, many improved algorithms have been suggested, to name just a few, by Galbraith et al. and Barreto et al., especially for the fields with characteristic three. Also Duursma and Lee found a closed formula of the Tate pairing computation for the fields with characteristic three. In this paper, we show that a similar argument is also possible for the finite fields with characteristic two. That is, we present a closed formul

In this paper, we review existing clinical research data on post-endovascular repair (EVAR) intrasac pressure and relation with abdominal aortic aneurysm (AAA) size changes. Based on the review, we hypothesize that intrasac pressure has a significant impact on post-EVAR AAA size changes, and post-EVAR remodeling depends also on how the pressure has changed over a period of time. The previously developed model of an AAA based on a constrained mixture approach is extended to include vascular adapt

LetEbe an elliptic curve over Q. Observing certain relations between the torsion subgroups ofEandED, theD-quadratic twist ofE, we prove that the torsion subgroups ofEis stable for all but finitely many quadratic extensions. Moreover, using the result ofK. Ono, we classify the torsion subgroup ofEover all quadratic extensions whenEis of the formE:y2=x(x+M)(x+N), whereMandNare integers. In the special case when torsion subgroup ofEover Q is isomorphic to Z/2Z⊕Z/8Z, we prove that the torsion subgro

Recently, a new concept called the c-differential uniformity was proposed by Ellingsen et al. (2020), which generalizes the notion of differential uniformity measuring the resistance against differential cryptanalysis. Since then, finding functions having low c-differential uniformity has attracted the attention of many researchers. However it seems that, at this moment, there are not many non-monomial permutations having low c-differential uniformity. In this paper, we present new classes of (a

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand

Finding permutation polynomials with low differential and boomerang uniformity is an important topic in S-box designs of many block ciphers. For example, AES chooses the inverse function as its S-box, which is differentially 4-uniform and boomerang 6-uniform. Also there has been considerable research on many non-quadratic permutations which are modifications of the inverse function. In this paper, we give a novel approach which shows that plenty of existing modifications of the inverse function

Presented is a square root algorithm in 𝔽 q which generalises Atkins's square root algorithm [see reference 6] for q ≡ 5 (mod 8) and Müller's algorithm [see reference 7] for q ≡ 9 (mod 16). The presented algorithm precomputes a primitive 2 s ‐th root of unity ξ where s is the largest positive integer satisfying 2 s | q −1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favourably compared with the algorithms