323,302 research outputs found
Opposing average congruence class biases in the cyclicity and Koblitz conjectures for elliptic curves
No full textThe cyclicity and Koblitz conjectures ask about the distribution of primes of cyclic and prime-order reduction, respectively, for elliptic curves over Q. In 1976, Serre gave a conditional proof of the cyclicity conjecture, but the Koblitz conjecture (refined by Zywina in 2011) remains open. The conjectures are now known unconditionally “on average” due to work of Banks–Shparlinski and Balog–Cojocaru–David. Recently, there has been a growing interest in the cyclicity conjecture for primes in arithmetic progressions (AP), with relevant work by Akbal–Güloğlu and Wong. In this article, we adapt Zywina’s method to formulate the Koblitz conjecture for AP and refine a theorem of Jones to establish results on the moments of the constants in both the cyclicity and Koblitz conjectures for AP. In doing so, we uncover a somewhat counterintuitive phenomenon: On average, these two constants are oppositely biased over congruence classes. Finally, in an accompanying repository, we give Magma code for computing the constants discussed in this article
Faster Implementation of Scalar Multiplication on Koblitz Curves
No full textWe design a state-of-the-art software implementation of field and elliptic curve arithmetic in standard Koblitz curves at the 128-bit security level. Field arithmetic is carefully crafted by using the best formulae and implementation strategies available, and the increasingly common native support to binary field arithmetic in modern desktop computing platforms. The i-th power of the Frobenius automorphism on Koblitz curves is exploited to obtain new and faster interleaved versions of the well-known NAF scalar multiplication algorithm. The usage of the and
maps are employed to create analogues of the 3-and 4-dimensional GLV decompositions and in general, the -th power of the Frobenius automorphism is applied as an analogue of an -dimensional GLV decomposition. The effectiveness of these techniques is illustrated by timing the scalar multiplication operation for fixed, random and multiple points. To our knowledge, our library was the first to compute a random point scalar multiplication in less than 10^5 clock cycles among all curves with or without endomorphisms defined over binary or prime fields. The results of our optimized implementation suggest a trade-off between speed, compliance with the published standards and side-channel protection. Finally, we estimate the performance of curve-based cryptographic protocols instantiated using the proposed techniques and compare our results to related work
Arithmetic of tau-adic expansions for lightweight Koblitz curve cryptography
No full text© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Koblitz curves allow very efficient elliptic curve cryptography. The reason is that one can trade expensive point doublings to cheap Frobenius endomorphisms by representing the scalar as a τ-adic expansion. Typically elliptic curve cryptosystems, such as ECDSA, also require the scalar as an integer. This results in a need for conversions between integers and the τ-adic domain, which are costly and hinder the use of Koblitz curves on very constrained devices, such as RFID tags, wireless sensors, or certain applications of the Internet of things. We provide solutions to this problem by showing how complete cryptographic processes, such as ECDSA signing, can be completed in the τ-adic domain with very few resources. This allows outsourcing conversions to a more powerful party. We provide several algorithms for performing arithmetic operations in the τ-adic domain. In particular, we introduce a new representation allowing more efficient and secure computations compared to the algorithms available in the preliminary version of this work from CARDIS 2014. We also provide datapath extensions with different speed and side-channel resistance properties that require areas from less than one hundred to a few hundred gate equivalents on 0.13-μ m CMOS. These extensions are applicable for all Koblitz curves.sponsorship: This work was done when K. Jarvinen was an FWO Pegasus Marie Curie Fellow. S. Sinha Roy was supported by the Erasmus Mundus PhD Scholarship. The work was partly funded by KU Leuven under GOA TENSE (GOA/11/007) and the F+ fellowship (F+/13/039) and by the Hercules Foundation (AKUL/11/19). We thank one of the anonymous reviewers of a preliminary version of this paper for pointing out the option of Remark 5. (Erasmus Mundus PhD Scholarship, F+ fellowship|F+/13/039, Hercules Foundation|AKUL/11/19, KU Leuven under GOA TENSE|GOA/11/007)status: Publishe
Lightweight Coprocessor for Koblitz Curves: 283-bit ECC Including Scalar Conversion with only 4300 Gates
No full text© International Association for Cryptologic Research 2015. We propose a lightweight coprocessor for 16-bit microcontrollers that implements high security elliptic curve cryptography. It uses a 283-bit Koblitz curve and offers 140-bit security. Koblitz curves offer fast point multiplications if the scalars are given as specific τ-adic expansions, which results in a need for conversions between integers and τ-adic expansions. We propose the first lightweight variant of the conversion algorithm and, by using it, introduce the first lightweight implementation of Koblitz curves that includes the scalar conversion. We also include countermeasures against side-channel attacks making the coprocessor the first lightweight coprocessor for Koblitz curves that includes a set of countermeasures against timing attacks, SPA, DPA and safe-error fault attacks. When the coprocessor is synthesized for 130nm CMOS, it has an area of only 4, 323 GE. When clocked at 16 MHz, it computes one 283-bit point multiplication in 98ms with a power consumption of 97. 70 μW, thus, consuming 9. 56 μJ of energy.sponsorship: S. Sinha Roy was supported by the Erasmus Mundus PhD Scholarship and K. Jarvinen was funded by FWO Pegasus Marie Curie Fellowship. This work was supported by the Research Council KU Leuven: TENSE (GOA/11/007), by iMinds, by the Flemish Government, FWO G.0550.12N, G.00130.13N and FWO G.0876.14N, and by the Hercules Foundation AKUL/11/19. We thank Bohan Yang for his help with ASIC synthesis and simulations. (Erasmus Mundus PhD Scholarship, FWO Pegasus Marie Curie Fellowship, Research Council KU Leuven: TENSE|GOA/11/007, iMinds, Flemish Government|FWO G.0550.12N, Flemish Government|G.00130.13N, Flemish Government|FWO G.0876.14N, Hercules Foundation|AKUL/11/19, EPSRC|EP/L001802/1)status: Publishe
Speeding up the arithmetic on hyperelliptic Koblitz curves of genus two
No full textKoblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations.In this paper, we generalize their ideas to hyperelliptic curves of genus 2.We consider the following two hyperelliptic curves C a : v 2 + uv = u 5 + au 2 + 1 defined over F2 with a = 0, 1, and show how to speed up the arithmetic in the Jacobian JCa(F2n) by making use of the Frobenius automorphism.With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian.If we allow 6 precomputations, we are even able to speed up by a factor of 7
Provably Sublinear Point Multiplication on Koblitz Curves and its Hardware Implementation
No full textAbstract. We describe algorithms for point multiplication on Koblitz curves using multiple-base expansions of the form k = P ±τ a (τ − 1) b and k = P ±τ a (τ − 1) b (τ 2 − τ − 1) c. We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first provably sublinear point multiplication algorithm on Koblitz curves. For the first type, we conjecture that the number of terms is sublinear and provide numerical evidence demonstrating that the number of terms is significantly less than that of τ-adic non-adjacent form expansions. We present details of an innovative FPGA implementation of our algorithm and performance data demonstrating the efficiency of our method.
Diffusive author(s), cohesive author: Analysis of S/N (1994)
No full textThis study indicates the ways in which various aspects of the author(s) are brought forth in Dumb type’s performance art, the S/N production. Previous research has suggested a non-hierarchical organization of Dumb type and the absence of a “privileged author” in Dumb type’s collaborative work, S/N. However, the results that I have investigated from member’s interviews on the creative process of S/N along with my analysis of the recorded images of S/N, indicate a different aspect of the author(s). First, S/N was created through, so to speak, the collective ideas of the members of Dumb type. Further, S/N has at least nine quotations from previous performances, installations, and printed writings, besides the work-in-progress technique. Explicating one of the “author functions” as given by Michel Foucault, each text has plural subjects of the author. However, it has been revealed from members’ interviews that Teiji Furuhashi had a decision-making role in selecting the members’ ideas within the performance. Since then, S/N has had plural subjects of creation; however, Furuhashi is one of the subjects of creation along with the “privileged author.” S/N has plural authors (diffusive authors) yet at the same time, it has a “privileged author,” Teiji Furuhashi (cohesive author)
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Provably Sublinear Point Multiplication on Koblitz Curves and its Hardware Implementation
No full textWe describe algorithms for point multiplication on Koblitz curves
using multiple-base expansions of the form and
We prove that the number of terms in the second type is sublinear in
the bit length of k, which leads to the first provably sublinear point
multiplication algorithm on Koblitz curves. For the first type, we
conjecture that the number of terms is sublinear and provide
numerical evidence demonstrating that the number of terms is
significantly less than that of -adic non-adjacent form
expansions. We present details of an innovative FPGA
implementation of our algorithm and performance data demonstrating the
efficiency of our method
- …
