On the maximal weight of (p,q)(p,q)-ary chain partitions with bounded parts

A $(p,q)$-ary chain is a special type of chain partition of integers with parts of the form $p^aq^b$ for some fixed integers $p$ and $q$. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound $m$. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of $m$, asymptotically independent of $\max(p,q)$, and we provide an efficient algorithm to compute it.Comment: 17 page

Radix-10 BKM Algorithm for Computing Transcendentals on Pocket Computers

We present a radix-10 variant of the BKM algorithm. It is a shift-and-add, CORDIC-like algorithm that allows fast computation of complex exponentials and logarithms. This radix-10 version is suitable for implementation in a pocket computer.Nous proposons une variante de l'algorithme BKM adaptée au calcul en base de 10. C'est un algorithme à additions et décalages, qui permet d'évaluer rapidement des exponentielles et logarithmes complexes. cette version adaptée à l base de 10 est destinée à l'implantation des calculatrices de poch

An Alternative Approach for SIDH Arithmetic

In this paper, we present new algorithms for the field arithmetic of supersingular isogeny Diffie-Hellman; one of the fifteen remaining candidates in the NIST post-quantum standardization process. Our approach uses a polynomial representation of the field elements together with mechanisms to keep the coefficients within bounds during the arithmetic operations. We present timings and comparisons for SIKEp503 and suggest a novel 736-bit prime that offers a $1.17\times$ speedup compared to SIKEp751 for a similar level of security

Faster cofactorization with ECM using mixed representations

This paper introduces a novel implementation of the elliptic curve factoring method specifically designed for medium-size integers such as those arising by billions in the cofactorization step of the number field sieve. In this context, our algorithm requires fewer modular multiplications than any other publicly available implementation. The main ingredients are: the use of batches of primes, fast point tripling, optimal double-base decompositions and Lucas chains, and a good mix of Edwards and Montgomery representations

Hybrid Binary-Ternary Joint Sparse Form and its Application in Elliptic Curve Cryptography

Multi-exponentiation is a common and time consuming operation in public-key cryptography. Its elliptic curve counterpart, called multi-scalar multiplication is extensively used for digital signature verification. Several algorithms have been proposed to speed-up those critical computations. They are based on simultaneously recoding a set of integers in order to minimize the number of general multiplications or point additions. When signed-digit recoding techniques can be used, as in the world of elliptic curves, Joint Sparse Form (JSF) and interleaving $w$-NAF are the most efficient algorithms. In this paper, a novel recoding algorithm for a pair of integers is proposed, based on a decomposition that mixes powers of 2 and powers of 3. The so-called Hybrid Binary-Ternary Joint Sparse Form require fewer digits and is sparser than the JSF and the interleaving $w$-NAF. Its advantages are illustrated for elliptic curve double-scalar multiplication; the operation counts show a gain of up to 18\%

Randomized Mixed-Radix Scalar Multiplication

A covering system of congruences can be defined as a set of congruence relations of the form: $\{r_1 \pmod{m_1}, r_2 \pmod{m_2}, \dots, r_t \pmod{m_t}\}$ for $m_1, \dots, m_t \in \mathbb{N}$ satisfying the property that for every integer $k$ in $\mathbb{Z}$, there exists at least an index $i \in \{1, \dots, t\}$ such that $k \equiv r_i \pmod{m_i}$. First, we show that most existing scalar multiplication algorithms can be formulated in terms of covering systems of congruences. Then, using a special form of covering systems called exact \mbox{$n$-covers}, we present a novel uniformly randomized scalar multiplication algorithm with built-in protections against various types of side-channel attacks. This algorithm can be an alternative to Coron\u27s scalar blinding technique for elliptic curves, in particular when the choice of a particular finite field tailored for speed compels to use a large random factor

Improving Goldschmidt Division, Square Root and Square Root Reciprocal

The aim of this paper is to accelerate division, square root and square root reciprocal computations, when Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm assuming 4-cycle pipelined multiplier and discuss obtained number of cycles and error achieved. Extensions to other than 4-cycle multipliers are given.Le but de cet article est l'accélération de la division, et du calcul de racines carrées et d'inverses de racines carrées lorsque la méthode de Goldschmidt est utilisée sur un multiplieur pipe-line. Nous faisons ceci en remplaçant la dernière itération par l'addition d'un terme de correction qui peut être déduit d'une lecture de table effectuée lors des premières itérations. Nous décrivons plusieurs variantes de l'algorithme obtenu en supposant un multiplieur à 4 étages de pipe-line, et donnons pour chaque variante l'erreur obtenue et le nombre de cycles de calcul. Des extensions de ce travail à des multiplieurs dont le nombre d'étages est différent sont présentées

Meta-analyses of FibroTest diagnostic value in chronic liver disease

<p>Abstract</p> <p>Background</p> <p>FibroTest (FT) is a biomarker of liver fibrosis initially validated in patients with chronic hepatitis C (CHC).</p> <p>The aim was to test two hypotheses, one, that the FT diagnostic value was similar in the three other frequent fibrotic diseases: chronic hepatitis B (CHB), alcoholic liver disease (ALD) and non-alcoholic fatty liver disease (NAFLD); and the other, that the FT diagnostic value was similar for intermediate and extreme fibrosis stages.</p> <p>Methods</p> <p>The main end points were the FT area under the ROC curves (AUROCs) for the diagnosis of bridging fibrosis (F2F3F4 vs. F0F1), standardized for the spectrum of fibrosis stages, and the comparison of FT AUROCs between adjacent stages. Two meta-analyses were performed: one combining all the published studies (random model), and one of an integrated data base combining individual data. Sensitivity analysis integrated the independency of authors, lenght of biopsy, prospective design, respect of procedures, comorbidities, and duration between biopsy and serum sampling.</p> <p>Results</p> <p>A total of 30 studies were included which pooled 6,378 subjects with both FT and biopsy (3,501 HCV, 1,457 HBV, 267 NAFLD, 429 ALD, and 724 mixed). Individual data were analyzed in 3,282 patients. The mean standardized AUROC was 0.84 (95% CI, 0.83–0.86), without differences between causes of liver disease: HCV 0.85 (0.82–0.87), HBV 0.80 (0.77–0.84), NAFLD 0.84 (0.76–0.92), ALD 0.86 (0.80–0.92), mixed 0.85 (0.80–0.93). The AUROC for the diagnosis of the intermediate adjacent stages F2 vs. F1 (0.66; 0.63–0.68, n = 2,055) did not differ from that of the extreme stages F3 vs. F4 (0.69; 0.65–0.72, n = 817) or F1 vs. F0 (0.62; 0.59–0.65, n = 1788).</p> <p>Conclusion</p> <p>FibroTest is an effective alternative to biopsy in patients with chronic hepatitis C and B, ALD and NAFLD. The FT diagnostic value is similar for the diagnosis of intermediate and extreme fibrosis stages.</p

Interest of Fluvoxamine as an Add-On to Clozapine in Children With Severe Psychiatric Disorder According to CYP Polymorphisms: Experience From a Case Series

Despite its drastic efficacy in resistant psychiatric disorders, clozapine remains rarely used in youth due to its side effects. Clozapine plasma level is determined through its metabolism involving several isoforms of cytochromes 450 (CYP450) family. Isoform CYP1A2 appears as a limiting enzyme involved in the metabolism of clozapine, while isoforms 2C19, 2D6, 3A4, and 3A5 also contribute in a minor way. Clozapine efficacy is limited by a significant inter-patient variability in exposure according to CYP's polymorphisms. Clozapine plasma levels may be increased with CYP inhibitors such as fluvoxamine. This drug is a potent enzymatic inhibitor of CYP1A2 and, to a lesser extent, of CYP3A4 and CYP2D6. Hence, in case of CYP's polymorphisms in youth, the use of fluvoxamine as add-on to clozapine could help in reaching clinical and biological efficacy and allowing lower clozapine dosage and a better tolerance profile as it has already been described in adults. We report four pediatric cases with severe psychiatric disorders underlying our experience with CYP polymorphism explorations and the use of fluvoxamine as add-on to clozapine. Our four patients clinically improved after the introduction of fluvoxamine, enhancing clozapine metabolism and therefore the clozapine plasma level within therapeutic range. Despite the interesting results of fluvoxamine, we report a severe issue of tolerance for one patient, emphasizing the need for caution regarding possible drug interactions when fluvoxamine is considered. Hence, we propose a detailed step-by-step multidisciplinary protocol