Design of high-speed residue-to-binary number system converter based on Chinese Remainder Theorem

2002 ◽  
Author(s):  
S.J. Piestrak
Keyword(s):  
High Speed ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Binary Number

HIGH-SPEED AND SECURE ENCRYPTION SCHEMES BASED ON CHINESE REMAINDER THEOREM FOR STORAGE AND TRANSMISSION OF MEDICAL INFORMATION

2010 ◽  
Vol 10 (01) ◽  
pp. 167-190 ◽  
Author(s):  
GANESH AITHAL ◽  
K. N. HARI BHAT ◽  
U. SRIPATI ACHARYA
Keyword(s):  
High Speed ◽  
Stream Cipher ◽  
Medical Information ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Side Channel ◽  
Direct Sum ◽  
Number Systems ◽  
System Representation ◽  
Cryptographic Scheme

Medical records generated in hospitals often contain private and sensitive information. This privileged information must be prevented from falling into wrong hands. Thus, there is a strong need for developing a secure cryptographic scheme that can be adapted to use in conjunction with transmission and storage of medical information. Previous approaches have proposed the use of the advanced encryption standard (AES) algorithm for this purpose. In this article, we are proposing a new robust, high-speed, and secure cryptographic scheme that has the added advantage of being immune to side-channel attacks. In our article, we have shown that the performance of this scheme is superior in certain aspects to that of the A5/1 system used in global system for mobile (GSM) systems. The parallel architecture employed in this scheme makes it suitable to use in systems where the data-processing operations have to be carried out in real time. Residue number systems (RNS) based on Chinese remainder theorem (CRT) permits the representation of large integers in terms of combinations of smaller ones. The set of all CRT number system representation of an integer from 0 to M-1 with component wise modular addition and multiplication constitutes a direct sum of smaller commutative rings. An encryption and decryption algorithm based on the properties of direct sum of smaller rings offers distinct advantages over decimal or fixed radix arithmetic. We have utilized the representation of integers using CRT to successfully design additive, multiplicative, and affine stream cipher systems. The use of number system based on CRT allows speeding up the encryption/decryption algorithms, reduces the time complexity, and provides immunity to side-channel, algebraic, and known plain text attacks. In this article, the characteristics of additive, multiplicative, and affine stream cipher systems based on CRT number system representation have been studied and analyzed.

scholarly journals A High-Speed Division Algorithm for Modular Numbers Based on the Chinese Remainder Theorem with Fractions and Its Hardware Implementation

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 261 ◽  
Author(s):  
Nikolai Chervyakov ◽  
Pavel Lyakhov ◽  
Mikhail Babenko ◽  
Anton Nazarov ◽  
Maxim Deryabin ◽  
...  
Keyword(s):  
High Speed ◽  
Chinese Remainder Theorem ◽  
Main Idea ◽  
Number System ◽  
Residue Number System ◽  
Division Algorithm ◽  
Number Of Zeros ◽  
Number Systems ◽  
Higher Power ◽  
Computational Resources

In this paper, a new simplified iterative division algorithm for modular numbers that is optimized on the basis of the Chinese remainder theorem (CRT) with fractions is developed. It requires less computational resources than the CRT with integers and mixed radix number systems (MRNS). The main idea of the algorithm is (a) to transform the residual representation of the dividend and divisor into a weighted fixed-point code and (b) to find the higher power of 2 in the divisor written in a residue number system (RNS). This information is acquired using the CRT with fractions: higher power is defined by the number of zeros standing before the first significant digit. All intermediate calculations of the algorithm involve the operations of right shift and subtraction, which explains its good performance. Due to the abovementioned techniques, the algorithm has higher speed and consumes less computational resources, thereby being more appropriate for the multidigit division of modular numbers than the algorithms described earlier. The new algorithm suggested in this paper has O (log2 Q) iterations, where Q is the quotient. For multidigit numbers, its modular division complexity is Q(N), where N denotes the number of bits in a certain fraction required to restore the number by remainders. Since the number N is written in a weighed system, the subtraction-based comparison runs very fast. Hence, this algorithm might be the best currently available.

LARGE DYNAMIC RANGE RNS SYSTEMS AND THEIR RESIDUE TO BINARY CONVERTERS

2007 ◽  
Vol 16 (02) ◽  
pp. 267-286 ◽  
Author(s):  
ALEXANDER SKAVANTZOS ◽  
MOHAMMAD ABDALLAH ◽  
THANOS STOURAITIS
Keyword(s):  
High Speed ◽  
Dynamic Range ◽  
Chinese Remainder Theorem ◽  
Digital Signal ◽  
Number System ◽  
Residue Number System ◽  
New Class ◽  
Mixed Radix Conversion ◽  
Residue Number ◽  
Signal Processors

The Residue Number System (RNS) is an integer system appropriate for implementing fast digital signal processors. It can be used for supporting high-speed arithmetic by operating in parallel channels without need for exchanging information among the channels. In this paper, two novel RNS are proposed. First, a new RNS system based on the modulus set {2n+1, 2n - 1, 2n + 1, 2n + 2(n+1)/2 + 1, 2n - 2(n+1)/2 + 1}, n odd, is developed, along with an efficient implementation of its residue-to-weighted converter. The new RNS is a balanced five-modulus system, appropriate for large dynamic ranges. The proposed residue-to-binary converter is fast and hardware efficient and is based on a one's complement multi-operand adder that adds operands of size only 80% of the size dictated by the system's dynamic range. Second, a new class of multi-modulus RNS systems is proposed. These systems are based on sets consisting of two groups of moduli with the modulus product within one group being of the form 2a(2b - 1), while the modulus product within the other group is of the form 2c - 1. Their RNS-to-weighted converters are based on efficient combinations of the Chinese Remainder Theorem and Mixed Radix Conversion decoding techniques. Systems based on four, five, and seven moduli are constructed and analyzed. The new systems allow efficient implementations for their RNS-to-weighted decoders, imply fast and balanced RNS arithmetic, and may achieve large dynamic ranges. The presented residue-to-weighted converters for these systems rely on simple mod (2x - 1) hardware, which can be easily implemented as one's complement hardware.

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

scholarly journals Computationally Efficient Approach to Implementation of the Chinese Remainder Theorem Algorithm in Minimally Redundant Residue Number System

2021 ◽  
Author(s):  
Mikhail Selianinau
Keyword(s):  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Computer Applications ◽  
Efficient Approach ◽  
Residue Modulo ◽  
Modern Computer ◽  
New Variant ◽  
Residue Number ◽  
Residue Code

AbstractIn this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue code, is investigated. It is shown that the rank of a number can be represented by a sum of an inexact rank and a two-valued correction to it. We propose a new variant of minimally redundant RNS, which provides low computational complexity for the rank calculation, and its effectiveness analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the excess residue modulo 2, the complexity of the rank calculation goes down from $O\left (k^{2}\right )$ O k 2 to $O\left (k\right )$ O k with respect to required modular addition operations and lookup tables, where k equals the number of non-redundant RNS moduli.

scholarly journals Constant-coefficient FIR filters based on residue number system arithmetic

2012 ◽  
Vol 9 (3) ◽  
pp. 325-342 ◽  
Author(s):  
Negovan Stamenkovic ◽  
Vladica Stojanovic
Keyword(s):  
Power Dissipation ◽  
High Speed ◽  
Finite Impulse Response ◽  
Number System ◽  
Residue Number System ◽  
Fir Filter ◽  
Fir Filters ◽  
Residue Number ◽  
Low Power Dissipation ◽  
Residue Arithmetic

In this paper, the design of a Finite Impulse Response (FIR) filter based on the residue number system (RNS) is presented. We chose to implement it in the (RNS), because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC) unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.

scholarly journals Improved Modular Division Implementation with the Akushsky Core Function

Computation ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Mikhail Babenko ◽  
Andrei Tchernykh ◽  
Viktor Kuchukov
Keyword(s):  
Approximate Method ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Division Algorithm ◽  
Incorrect Result ◽  
Core Function ◽  
Residue Number ◽  
Division Operation

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

scholarly journals Application of the neural network computing technology for calculating the interval-index characteristics of a minimally redundant modular code

2019 ◽  
Vol 62 (6) ◽  
pp. 652-660
Author(s):  
A. F. Chernyavsky ◽  
A. A. Kolyada ◽  
S. Yu. Protasenya
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
High Speed ◽  
Theoretical Estimate ◽  
Structural Complexity ◽  
Fold Increase ◽  
Number System ◽  
Parallel Structure ◽  
Network Computing ◽  
Time Expenditures

The article is devoted to the problem of creation of high-speed neural networks (NN) for calculation of interval-index characteristics of a minimally redundant modular code. The functional base of the proposed solution is an advanced class of neural networks of a final ring. These neural networks perform position-modular code transformations of scalable numbers using a modified reduction technology. A developed neural network has a uniform parallel structure, easy to implement and requires the time expenditures of the order (3[log2b]+ [log2k]+6tsum  close to the lower theoretical estimate. Here b and k is the average bit capacity and the number of modules respectively; t sum is the duration of the two-place operation of adding integers. The refusal from a normalization of the numbers of the modular code leads to a reduction of the required set of NN of the finite ring on the (k – 1) component. At the same time, the abnormal configuration of minimally redundant modular coding requires an average k-fold increase in the interval index module (relative to the rest of the bases of the modular number system). It leads to an adequate increase in hardware expenses on this module. Besides, the transition from normalized to unregulated coding reduces the level of homogeneity of the structure of the NN for calculating intervalindex characteristics. The possibility of reducing the structural complexity of the proposed NN by using abnormal intervalindex characteristics is investigated.

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