Efficient Implementation of Cryptography on Points of an Elliptic Curve in Residue Number System

White-box attack context assumes that the running environments of algorithms are visible and modifiable. Algorithms that can resist the white-box attack context are called white-box cryptography. The elliptic curve digital signature algorithm (ECDSA) is one of the most widely used digital signature algorithms which can provide integrity, authenticity, and nonrepudiation. Since the private key in the classical ECDSA is plaintext, it is easy for attackers to obtain the private key. To increase the security of the private key under the white-box attack context, this article presents an algorithm for the white-box implementation of ECDSA. It uses the lookup table technology and the “cloud plus side” mode to protect the private key. The residue number system (RNS) theory is used to reduce the size of storage. Moreover, the article analyzes the security of the proposed algorithm against an exhaustive search attack, a random number attack, a code lifting attack, and so on. The efficiency of the proposed scheme is compared with that of the classical ECDSA through experiments.

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Neural network method for base extension in residue number system

10.47350/iccs-de.2020.01 ◽

2020 ◽

Author(s):

M. Babenko ◽

E. Shiriaev ◽

A. Tchernykh ◽

E. Golimblevskaia

Keyword(s):

Neural Network ◽

Elliptic Curve ◽

Chinese Remainder Theorem ◽

Homomorphic Encryption ◽

Computational Cost ◽

Number System ◽

Residue Number System ◽

Pseudorandom Sequence ◽

Base Extension ◽

Residue Number

Confidential data security is associated with the cryptographic primitives, asymmetric encryption, elliptic curve cryptography, homomorphic encryption, cryptographic pseudorandom sequence generators based on an elliptic curve, etc. For their efficient implementation is often used Residue Number System that allows executing additions and multiplications on parallel computing channels without bit carrying between channels. A critical operation in Residue Number System implementations of asymmetric cryptosystems is base extension. It refers to the computing a residue in the extended moduli without the application of the traditional Chinese Remainder Theorem algorithm. In this work, we propose a new way to perform base extensions using a Neural Network of a final ring. We show that it reduces 11.7% of the computational cost, compared with state-of-the-art approaches.

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EFFICIENT RNS-BASED DESIGN OF PROGRAMMABLE FIR FILTERS TARGETING FPL TECHNOLOGY

Journal of Circuits System and Computers ◽

10.1142/s0218126605002131 ◽

2005 ◽

Vol 14 (01) ◽

pp. 165-177 ◽

Cited By ~ 5

Author(s):

JAVIER RAMÍREZ ◽

UWE MEYER-BÄSE ◽

ANTONIO GARCÍA

Keyword(s):

High Performance ◽

Digital Signal ◽

Number System ◽

Low Complexity ◽

Residue Number System ◽

Quadratic Residue ◽

Fir Filter ◽

Efficient Implementation ◽

Fir Filters ◽

Residue Number

FIR filters are routinely used in the implementation of modern digital signal processing systems. Their efficient implementation using commercially available VLSI technology is a subject of continuous study and development. This paper presents the residue number system (RNS) implementation of reduced-complexity and high-performance FIR filters, using modern Altera APEX20K field-programmable logic (FPL) devices. Index arithmetic over Galois fields and the Quadratic Residue Number System (QRNS), along with a selection of a small wordwidth modulus set, are the keys for attaining low complexity and high throughput in real and complex FIR filters. RNS–FPL merged FIR filters demonstrated its superiority when compared to 2C (two's complement) filters, being about 65% faster and requiring fewer logic elements for most study cases. Special attention was paid to an efficient implementation of the multi-operand modulo adders. The replacement of a classical modulo adder tree by a binary adder with extended precision followed by a single modulo reduction stage reduced area requirements by 10% for a 32-tap FIR filter. On the other hand, an index arithmetic QRNS-based complex FIR filter yielded up to 60% performance improvement over a three-multiplier-per-tap 2C filter, while requiring fewer LEs for filters having more than eight taps. Particularly, a 32-tap filter needed 24% LEs less than the classical design.

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