scholarly journals Improved Sum of Residues Modular Multiplication Algorithm

Cryptography ◽  
2019 ◽  
Vol 3 (2) ◽  
pp. 14 ◽  
Author(s):  
Mohamad Ali Mehrabi
Keyword(s):  
Parallel Implementation ◽  
Critical Issue ◽  
Public Key ◽  
Practical Implementation ◽  
Modular Multiplication ◽  
Public Key Cryptosystems ◽  
Multiplication Algorithm ◽  
Number Systems ◽  
Residue Number ◽  
Hardware Architectures

Modular reduction of large values is a core operation in most common public-key cryptosystems that involves intensive computations in finite fields. Within such schemes, efficiency is a critical issue for the effectiveness of practical implementation of modular reduction. Recently, Residue Number Systems have drawn attention in cryptography application as they provide a good means for extreme long integer arithmetic and their carry-free operations make parallel implementation feasible. In this paper, we present an algorithm to calculate the precise value of “ X mod p ” directly in the RNS representation of an integer. The pipe-lined, non-pipe-lined, and parallel hardware architectures are proposed and implemented on XILINX FPGAs.

scholarly journals Design of a Modular Multiplier for Public-Key Cryptography Applications Using Residue Number System and Signed-Digit Representation

2020 ◽  
Author(s):  
Mohammad Hizzani
Keyword(s):  
Public Key Cryptography ◽  
Number System ◽  
Residue Number System ◽  
Public Key ◽  
Modular Multiplication ◽  
Secret Key ◽  
Public Key Cryptosystems ◽  
Number Systems ◽  
Wide Range ◽  
Residue Number

Public-Key Cryptosystems are prone to wide range of cryptanalyses due to its property of having key pairs one of them is public. Therefore, the recommended length of these keys is extremely large (e.g. in RSA and D-H the key is at least 2048 bits long) and this leads the computation of such cryptosystems to be slower than the secret-key cryptosystems (i.e. AES and AES-family). Since, the key operation in such systems is the modular multiplication; in this research a novel design for the modular multiplication based on the Montgomery Multiplication, the Residue Number Systems for moduli of any form, and the Signed-Digit Representation is proposed. The proposed design outperforms the current designs in the literature in terms of delay with at least 28% faster for the key of 2048 bits long. Up to our knowledge, this design is the first design that utilizes Signed-Digit Representation with the Residue Number System for moduli of any form.

scholarly journals Revisiting Sum of Residues Modular Multiplication

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Yinan Kong ◽  
Braden Phillips
Keyword(s):  
Public Key Cryptography ◽  
Number System ◽  
Residue Number System ◽  
The Other ◽  
Public Key ◽  
Modular Multiplication ◽  
Residue Number ◽  
The Cost

In the 1980s, when the introduction of public key cryptography spurred interest in modular multiplication, many implementations performed modular multiplication using a sum of residues. As the field matured, sum of residues modular multiplication lost favor to the extent that all recent surveys have either overlooked it or incorporated it within a larger class of reduction algorithms. In this paper, we present a new taxonomy of modular multiplication algorithms. We include sum of residues as one of four classes and argue why it should be considered different to the other, now more common, algorithms. We then apply techniques developed for other algorithms to reinvigorate sum of residues modular multiplication. We compare FPGA implementations of modular multiplication up to 24 bits wide. The sum of residues multipliers demonstrate reduced latency at nearly 50% compared to Montgomery architectures at the cost of nearly doubled circuit area. The new multipliers are useful for systems based on the Residue Number System (RNS).

Parallel implementation of public key cryptosystems using Web workers

2014 ◽  
Author(s):  
Takuya Sumi ◽  
Tsukasa Ishiguro ◽  
Shinsaku Kiyomoto ◽  
Yutaka Miyake ◽  
Toru Kobayashi ◽  
...  
Keyword(s):  
Parallel Implementation ◽  
Public Key ◽  
Public Key Cryptosystems

A Scalable and Systolic Architectures of Montgomery Modular Multiplication for Public Key Cryptosystems Based on DSPs

2017 ◽  
Vol 1 (3) ◽  
pp. 219-236 ◽  
Author(s):  
Amine Mrabet ◽  
Nadia El-Mrabet ◽  
Ronan Lashermes ◽  
Jean-Baptiste Rigaud ◽  
Belgacem Bouallegue ◽  
...  
Keyword(s):  
Public Key ◽  
Modular Multiplication ◽  
Public Key Cryptosystems ◽  
Montgomery Modular Multiplication
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