New Algorithm for Classical Modular Inverse

The concept of autonomous wireless sensor networks involves energy harvesting, as well as effective management of system resources. Public-key cryptography (PKC) offers the advantage of elegant key agreement schemes with which a secret key can be securely established over unsecure channels. In addition to solving the key management problem, the other major application of PKC is digital signatures, with which non-repudiation of messages exchanges can be achieved. The motivation for studying low-power and area efficient modular arithmetic algorithms comes from enabling public-key security for low-power devices that can perform under constrained environment like autonomous wireless sensor networks. This paper presents a cryptographic coprocessor tailored to the autonomous wireless sensor networks constraints. Such hardware circuit is aimed to support the implementation of different public-key cryptosystems based on modular arithmetic in GF(p) and GF(2 m ). Key components of the coprocessor are described as GEZEL models and can be easily transformed to VHDL and implemented in hardware.

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“…More effective algorithms are based on extended Euclid algorithm, as binary extended Euclid algorithm (EEI) 14 .…”

Section: Modular Inversementioning

confidence: 99%

Low-power cryptographic coprocessor for autonomous wireless sensor networks

Olszyna

Winiecki

2013

Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2013

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“…For computing the modular inverse in the INV unit, the left-shift modular inverse algorithm [22] is used.…”

Section: Design Of Modular Systemmentioning

confidence: 99%

Design of a Residue Number System Based Linear System Solver in Hardware

BuăźEk

Kubalik

Lórencz

et al. 2016

J Sign Process Syst

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This paper is focused on error-free solution of dense linear systems using residual arithmetic in hardware. The designed Modular System uses hardware identical Residual Processors (RP)s for solving independent systems of linear congruences and combines their solutions into the solution of the given linear system. This approach uses the residue number system which is based on the Chinese remainder theorem. In order to efficiently exploit parallel processing and cooperation of the individual components, a hardware architecture of the Modular System with several RPs is designed. In order to verify the proposed architecture, a Xilinx FPGA with a MicroBlaze processor was used. Experimental results are obtained for an evaluation FPGA board with Virtex 6. Results from implementation serve for subsequent theoretical analysis of the system performance for various linear system sizes and further improvement of the system. The proposed system can be useful as a special hardware peripheral or a part of an embedded system for solving large nonsingular systems of linear equations with integer, rational or floating-point coefficients with arbitrary precision.

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“…The regular inverse a −1 is obtained by computing the Montgomery product of x and 1 (see [23] for variants, see also [16]). If one has an algorithm for a −1 , then one can get x = (a2 −k ) −1 by inverting the Montgomery product of x and 1.…”

Section: Appendix a Pseudo-codementioning

confidence: 99%

Trading Inversions for Multiplications in Elliptic Curve Cryptography

et al. 2006

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Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S = (2P + Q) from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication.

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New Algorithm for Classical Modular Inverse

Cited by 22 publications

References 12 publications

Low-power cryptographic coprocessor for autonomous wireless sensor networks

Low-power cryptographic coprocessor for autonomous wireless sensor networks

Design of a Residue Number System Based Linear System Solver in Hardware

Trading Inversions for Multiplications in Elliptic Curve Cryptography

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