Montgomery modular multiplication architecture for public key cryptosystems

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.

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Low latency modular multiplication for public-key cryptosystems using a scalable array of parallel processing elements

2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS) ◽

10.1109/mwscas.2013.6674830 ◽

2013 ◽

Cited By ~ 3

Author(s):

Yinan Kong ◽

Yufeng Lai

Keyword(s):

Parallel Processing ◽

Public Key ◽

Low Latency ◽

Modular Multiplication ◽

Processing Elements ◽

Public Key Cryptosystems

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

10.31237/osf.io/j6rxp ◽

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.

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Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

International Journal of Information Security and Privacy ◽

10.4018/ijisp.2017040102 ◽

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%.

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