scholarly journals Efficient Fixed-base exponentiation and scalar multiplication based on a multiplicative splitting exponent recoding

2018 ◽  
Vol 9 (2) ◽  
pp. 115-136
Author(s):  
Jean-Marc Robert ◽  
Christophe Negre ◽  
Thomas Plantard
Keyword(s):  
Scalar Multiplication ◽  
Fixed Base

scholarly journals Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication

Sensors ◽  
2013 ◽  
Vol 13 (7) ◽  
pp. 9483-9512
Author(s):  
Hwajeong Seo ◽  
Hyunjin Kim ◽  
Taehwan Park ◽  
Yeoncheol Lee ◽  
Zhe Liu ◽  
...  
Keyword(s):  
Scalar Multiplication ◽  
Fixed Base

Improved Fixed-Base Comb Method for Fast Scalar Multiplication

2012 ◽  
pp. 342-359 ◽  
Author(s):  
Nashwa A. F. Mohamed ◽  
Mohsin H. A. Hashim ◽  
Michael Hutter
Keyword(s):  
Scalar Multiplication ◽  
Fixed Base ◽  
Comb Method

scholarly journals Hyper-and-elliptic-curve cryptography

2014 ◽  
Vol 17 (A) ◽  
pp. 181-202 ◽  
Author(s):  
Daniel J. Bernstein ◽  
Tanja Lange
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Base Point ◽  
Scalar Multiplication ◽  
Key Generation ◽  
Diffie Hellman ◽  
Fixed Base ◽  
Shared Secret ◽  
Genus 2 ◽  
Point Scalar Multiplication

AbstractThis paper introduces ‘hyper-and-elliptic-curve cryptography’, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (for example, Diffie–Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point scalar multiplication (for example, key generation) and multi-scalar multiplication (for example, signature verification).

scholarly journals Novel Key Recovery Attack on Secure ECDSA Implementation by Exploiting Collisions between Unknown Entries

2021 ◽  
pp. 1-26
Author(s):  
Sunghyun Jin ◽  
Sangyub Lee ◽  
Sung Min Cho ◽  
HeeSeok Kim ◽  
Seokhie Hong
Keyword(s):  
Power Consumption ◽  
Digital Signatures ◽  
Scalar Multiplication ◽  
Side Channel ◽  
Validation Process ◽  
Key Recovery ◽  
Private Key ◽  
Signature Generation ◽  
Fixed Base ◽  
Key Recovery Attack

In this paper, we propose a novel key recovery attack against secure ECDSA signature generation employing regular table-based scalar multiplication. Our attack exploits novel leakage, denoted by collision information, which can be constructed by iteratively determining whether two entries loaded from the table are the same or not through side-channel collision analysis. Without knowing the actual value of the table entries, an adversary can recover the private key of ECDSA by finding the condition for which several nonces are linearly dependent by exploiting only the collision information. We show that this condition can be satisfied practically with a reasonable number of digital signatures and corresponding traces. Furthermore, we also show that all entries in the pre-computation table can be recovered using the recovered private key and a sufficient number of digital signatures based on the collision information. As case studies, we find that fixed-base comb and T_SM scalar multiplication are vulnerable to our attack. Finally, we verify that our attack is a real threat by conducting an experiment with power consumption traces acquired during T_SM scalar multiplication operations on an ARM Cortex-M based microcontroller. We also provide the details for validation process.

scholarly journals Concrete quantum cryptanalysis of binary elliptic curves

2020 ◽  
pp. 451-472
Author(s):  
Gustavo Banegas ◽  
Daniel J. Bernstein ◽  
Iggy Van Hoof ◽  
Tanja Lange
Keyword(s):  
Elliptic Curves ◽  
Quantum Computer ◽  
Discrete Logarithm ◽  
Base Point ◽  
Scalar Multiplication ◽  
Logarithmic Factor ◽  
Fixed Base ◽  
Logical Qubits ◽  
Toffoli Gates ◽  
Point Scalar Multiplication

This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines. The main optimization target is the size of the quantum computer, i.e., the number of logical qubits required, as this appears to be the main obstacle to implementing Shor’s polynomial-time discrete-logarithm algorithm. The secondary optimization target is the number of logical Toffoli gates. For an elliptic curve over a field of 2n elements, this paper reduces the number of qubits to 7n + ⌊log2(n)⌋ + 9. At the same time this paper reduces the number of Toffoli gates to 48n3 + 8nlog2(3)+1 + 352n2 log2(n) + 512n2 + O(nlog2(3)) with double-and-add scalar multiplication, and a logarithmic factor smaller with fixed-window scalar multiplication. The number of CNOT gates is also O(n3). Exact gate counts are given for various sizes of elliptic curves currently used for cryptography.

Representation of information in SEM by equal signal lines

1978 ◽  
Vol 36 (1) ◽  
pp. 144-145
Author(s):  
E. Rau ◽  
N. Karelin ◽  
V. Dukov ◽  
M. Kolomeytsev ◽  
S. Gavrikov ◽  
...  
Keyword(s):  
Electronic System ◽  
Space Distribution ◽  
Specimen Surface ◽  
Universal Method ◽  
Base Level ◽  
Signal Value ◽  
Information Signal ◽  
Fixed Base ◽  
Scanning Line ◽  
Amplitude Analyzer

There are different methods and devices for the increase of the videosignal information in SEM. For example, with the help of special pure electronic [1] and opto-electronic [2] systems equipotential areas on the specimen surface in SEM were obtained. This report generalizes quantitative universal method for space distribution representation of research specimen parameter by contour equal signal lines. The method is based on principle of comparison of information signal value with the fixed levels.Transformation image system for obtaining equal signal lines maps was developed in two versions:1)In pure electronic system [3] it is necessary to compare signal U (see Fig.1-a), which gives potential distribution on specimen surface along each scanning line with fixed base level signals εifor obtaining quantitative equipotential information on solid state surface. The amplitude analyzer-comparator gives flare sport videopulses at any fixed coordinate and any instant time when initial signal U is equal to one of the base level signals ε.

A solution to the rear-vision problem in a fixed-base driving simulator

2004 ◽  
Author(s):  
Guihua Yang ◽  
Farnaz Baniahmad ◽  
Beverly K. Jaeger ◽  
Ronald R. Mourant
Keyword(s):  
Driving Simulator ◽  
Fixed Base

Implementation of an Elliptic Curve Scalar Multiplication Method Using Division Polynomials

2014 ◽  
Vol E97.A (1) ◽  
pp. 300-302 ◽  
Author(s):  
Naoki KANAYAMA ◽  
Yang LIU ◽  
Eiji OKAMOTO ◽  
Kazutaka SAITO ◽  
Tadanori TERUYA ◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Scalar Multiplication ◽  
Division Polynomials ◽  
Elliptic Curve Scalar Multiplication
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