Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

2017 ◽  
Vol 11 (2) ◽  
pp. 11-24
Author(s):  
Satyanarayana Vollala ◽  
B. Shameedha Begum ◽  
Amit D. Joshi ◽  
N. Ramasubramanian
Keyword(s):  
Power Consumption ◽  
Arithmetic Operation ◽  
Efficient Implementation ◽  
Public Key ◽  
Modular Exponentiation ◽  
Modular Multiplication ◽  
The Public ◽  
Public Key Cryptosystems ◽  
Security Services ◽  
The Cost

It is widely recognized that the public-key cryptosystems are playing tremendously an important role for providing the security services. In majority of the cryptosystems the crucial arithmetic operation is modular exponentiation. It is composed of a series of modular multiplications. Hence, the performance of any cryptosystem is strongly depends on the efficient implementation of these operations. This paper presents the Bit Forwarding 3-bits(BFW3) technique for efficient implementation of modular exponentiation. The modular multiplication involved in BFW3 is evaluated with the help of Montgomery method. These techniques improves the performance by reducing the frequency of modular multiplications. Results shows that the BFW3 technique is able to reduce the frequency of multiplications by 18.20% for 1024-bit exponent. This reduction resulted in increased throughput of 18.11% in comparison with MME42_C2 at the cost of 1.09% extra area. The power consumption reduced by 8.53% thereby saving the energy up to 10.10%.

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).

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.

Key Authentication Scheme-based on Discrete Logarithms and Chinese Remainder Theorem

2016 ◽  
Vol 66 (6) ◽  
pp. 590
Author(s):  
P. Kumaraswamy ◽  
C.V. Guru Rao ◽  
V. Janaki ◽  
K.V.T.K.N. Prashanth
Keyword(s):  
Chinese Remainder Theorem ◽  
Authentication Scheme ◽  
Third Party ◽  
Public Key ◽  
Online Services ◽  
Trusted Third Party ◽  
Discrete Logarithms ◽  
The Public ◽  
Public Key Cryptosystems

<p>Public key cryptosystems are secure only when the authenticity of the public key is assured. Shao proposed<br />a new scheme to overcome the problems of the existing schemes, which suffers from two major drawbacks. The<br />first drawback is the availability of users’ passwords in plaintext format in key server which are prone to attacks<br />by ill-minded users. The second one is depending on the key server blindly for certificate generation, without<br />further verification by the user. To overcome these severe drawbacks, we proposed an improved key authentication<br />scheme based on Chinese remainder theorem and discrete logarithms. Our scheme allows the user to generate his/<br />her certificate without the help of any trusted third party. This scheme is intended for online services, military and<br />defense applications to exchange keys securely.<br /> </p>

scholarly journals Identity-Based Signature Schemes for Multivariate Public Key Cryptosystems

2019 ◽  
Vol 62 (8) ◽  
pp. 1132-1147 ◽  
Author(s):  
Jiahui Chen ◽  
Jie Ling ◽  
Jianting Ning ◽  
Jintai Ding
Keyword(s):  
General Scheme ◽  
Security Analysis ◽  
Distribution Center ◽  
Public Key ◽  
Signature Schemes ◽  
The Public ◽  
Public Key Cryptosystems ◽  
Unique Identity ◽  
Identity Based ◽  
Multivariate Public Key

Abstract In this paper, we proposed an idea to construct a general multivariate public key cryptographic (MPKC) scheme based on a user’s identity. In our construction, each user is distributed a unique identity by the key distribution center (KDC) and we use this key to generate user’s private keys. Thereafter, we use these private keys to produce the corresponding public key. This method can make key generating process easier so that the public key will reduce from dozens of Kilobyte to several bits. We then use our general scheme to construct practical identity-based signature schemes named ID-UOV and ID-Rainbow based on two well-known and promising MPKC signature schemes, respectively. Finally, we present the security analysis and give experiments for all of our proposed schemes and the baseline schemes. Comparison shows that our schemes are both efficient and practical.

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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