Design of digital integrating machines and structures based on a certain redundant number system

Cybernetics ◽  
1976 ◽  
Vol 11 (6) ◽  
pp. 921-925
Author(s):  
A. I. Grechishnikov
Keyword(s):  
Number System ◽  
Redundant Number System

scholarly journals Digit Set Conversion from Redundant Number System into Complement Representation

1970 ◽  
Vol 3 (1) ◽  
pp. 39-44
Author(s):  
Veerasit Charoensiri ◽  
Athasit Surarerks
Keyword(s):  
Traditional Method ◽  
Number System ◽  
Propagation Problem ◽  
Number Representation ◽  
Generic Algorithm ◽  
Digit Set ◽  
Parallel Addition ◽  
Redundant Number System ◽  
Complement Number

Redundant number system was proposed in order to solve the carry-propagation problem. Although it provides a carry-free parallel addition, this representation requires a lot of space to store itself. Many conversions from the redundant number system into another number representation have been introduced to decrease the storage usage. This paper proposes a generic algorithm in order to convert the redundant number representation into the complement number representation. The proposed algorithm can perform the conversion of a number in any integer radix and eliminates the carry chain of the traditional method. The proofs of the proposed algorithm in term of correctness are also included in this paper.

SIKE in 32-bit ARM Processors Based on Redundant Number System for NIST Level-II

2021 ◽  
Vol 20 (3) ◽  
pp. 1-23
Author(s):  
Hwajeong Seo ◽  
Pakize Sanal ◽  
Reza Azarderakhsh
Keyword(s):  
Finite Field ◽  
High Performance ◽  
State Of The Art ◽  
Number System ◽  
Key Exchange ◽  
Finite Field Arithmetic ◽  
Level Ii ◽  
Previous State ◽  
Redundant Number System ◽  
Redundant Representation

We present an optimized implementation of the post-quantum Supersingular Isogeny Key Encapsulation (SIKE) for 32-bit ARMv7-A processors supporting NEON engine (i.e., SIMD instruction). Unlike previous SIKE implementations, finite field arithmetic is efficiently implemented in a redundant representation, which avoids carry propagation and pipeline stall. Furthermore, we adopted several state-of-the-art engineering techniques as well as hand-crafted assembly implementation for high performance. Optimized implementations are ported to Microsoft SIKE library written in “a non-redundant representation” and evaluated in high-end 32-bit ARMv7-A processors, such as ARM Cortex-A5, A7, and A15. A full key-exchange execution of SIKEp503 is performed in about 109 million cycles on ARM Cortex-A15 processors (i.e., 54.5 ms @2.0 GHz), which is about 1.58× faster than previous state-of-the-art work presented in CHES’18.

A Robust Watermarking Scheme Using Codes Based on the Redundant Residue Number System

2007 ◽  
pp. 271-305
Author(s):  
Vik Tor Goh ◽  
Mohammad Umar Siddiqi
Keyword(s):  
Digital Watermarking ◽  
Number System ◽  
Residue Number System ◽  
Literature Survey ◽  
Error Correction Codes ◽  
Robust Watermarking ◽  
Residue Number ◽  
Redundant Number System ◽  
Redundant Residue Number System ◽  
Watermarking Scheme

In this chapter, a watermarking scheme that utilizes error correction codes for added robustness is proposed. A literature survey covering various aspects of the watermarking scheme, such as the arithmetic redundant residue number system, and concepts related to digital watermarking is given. The requirements of a robust watermarking scheme are also described. In addition, descriptions and experimental results of the proposed watermarking scheme are provided to demonstrate the functionality of the scheme. The authors hope that with the completion of this chapter, the reader will have a better understanding of ideas related to digital watermarking as well as the arithmetic redundant number system.

scholarly journals Number systems in modular rings and their applications to "error-free" computations

2019 ◽  
Vol 43 (5) ◽  
pp. 901-911 ◽  
Author(s):  
V.M. Chernov
Keyword(s):  
Golden Ratio ◽  
Digital Signal ◽  
Number System ◽  
Parallel Machine ◽  
New Class ◽  
Number Systems ◽  
Residue Number ◽  
Discrete Orthogonal ◽  
Redundant Number System ◽  
Modular Reductions

The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations.

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