Faster side-channel resistant elliptic curve scalar multiplication

2010 ◽  
pp. 29-40 ◽  
Author(s):  
Alexandre Venelli ◽  
François Dassance
Keyword(s):  
Elliptic Curve ◽  
Scalar Multiplication ◽  
Side Channel ◽  
Elliptic Curve Scalar Multiplication

scholarly journals Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xingran Li ◽  
Wei Yu ◽  
Bao Li
Keyword(s):  
Elliptic Curve ◽  
Efficient Algorithm ◽  
Multicore Processors ◽  
Scalar Multiplication ◽  
Side Channel ◽  
Elliptic Curve Cryptosystem ◽  
Side Channel Attacks ◽  
Binary Fields ◽  
Speed Up ◽  
Elliptic Curve Scalar Multiplication

Accelerating scalar multiplication has always been a significant topic when people talk about the elliptic curve cryptosystem. Many approaches have been come up with to achieve this aim. An interesting perspective is that computers nowadays usually have multicore processors which could be used to do cryptographic computations in parallel style. Inspired by this idea, we present a new parallel and efficient algorithm to speed up scalar multiplication. First, we introduce a new regular halve-and-add method which is very efficient by utilizing λ projective coordinate. Then, we compare many different algorithms calculating double-and-add and halve-and-add. Finally, we combine the best double-and-add and halve-and-add methods to get a new faster parallel algorithm which costs around 12.0% less than the previous best. Furthermore, our algorithm is regular without any dummy operations, so it naturally provides protection against simple side-channel attacks.

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

MicroBlaze-Based Multiprocessor Embedded Cryptosystem on FPGA for Elliptic Curve Scalar Multiplication Over Fp

2019 ◽  
Vol 28 (03) ◽  
pp. 1950037 ◽  
Author(s):  
A. Bellemou ◽  
N. Benblidia ◽  
M. Anane ◽  
M. Issad
Keyword(s):  
Elliptic Curve ◽  
Scalar Multiplication ◽  
Security Level ◽  
Prime Field ◽  
Montgomery Modular Multiplication ◽  
Parallel Implementations ◽  
High Radix ◽  
System On Programmable Chip ◽  
Xilinx Fpga ◽  
Elliptic Curve Scalar Multiplication

In this paper, we present Microblaze-based parallel architectures of Elliptic Curve Scalar Multiplication (ECSM) computation for embedded Elliptic Curve Cryptosystem (ECC) on Xilinx FPGA. The proposed implementations support arbitrary Elliptic Curve (EC) forms defined over large prime field ([Formula: see text]) with different security-level sizes. ECSM is performed using Montgomery Power Ladder (MPL) algorithm in Chudnovsky projective coordinates system. At the low abstraction level, Montgomery Modular Multiplication (MMM) is considered as the critical operation. It is implemented within a hardware Accelerator MMM (AccMMM) core based on the modified high radix, [Formula: see text] MMM algorithm. The efficiency of our parallel implementations is achieved by the combination of the mixed SW/HW approach with Multi Processor System on Programmable Chip (MPSoPC) design. The integration of multi MicroBlaze processor in single architecture allows not only the flexibility of the overall system but also the exploitation of the parallelism in ECSM computation with several degrees. The Virtex-5 parallel implementations of 256-bit and 521-bis ECSM computations run at 100[Formula: see text]MHZ frequency and consume between 2,739 and 6,533 slices, 22 and 72 RAMs and between 16 and 48 DSP48E cores. For the considered security-level sizes, the delays to perform single ECSM are between 115[Formula: see text]ms and 14.72[Formula: see text]ms.

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