An efficient signed digit montgomery multiplication for RSA

Lim, Daesung; Chang, Nam Su; Ji, Sung; Kim, Chang Han; Lee, Sang-Jin; Park, Young-Ho

doi:10.1016/j.sysarc.2009.04.001

Cited by 7 publications

(4 citation statements)

References 13 publications

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“…Alan Daly et al (Daly & Marnane, 2002) presented a pipeline architecture for implementing modular multiplications and modular exponentiation used in RSA cryptographic process to exploit the carry chain length extensively meant for reconfigurable architecture. Daesung Lim et al devised an efficient multiplier in (Lim et al, 2009) to perform Montgomery multiplication using signed digit representation as demanded by modular exponentiation approach. The proposed multiplier is suitable for any public-key cryptography that deals with integer arithmetic namely DSA, RSA, and Elliptic curve cryptography.…”

Section: Montgomery Multiplicationmentioning

confidence: 99%

Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

Vollala

Begum

Joshi

et al. 2017

International Journal of Information Security and Privacy

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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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Section: Montgomery Multiplicationmentioning

confidence: 99%

Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

Vollala

Begum

Joshi

et al. 2017

International Journal of Information Security and Privacy

View full text Add to dashboard Cite

show abstract

“…Alan Daly et al presented a pipeline architecture for implementing modular multiplications and modular exponentiation used in RSA cryptographic process to exploit the carry chain length extensively meant for reconfigurable architecture. Daesung Lim et al devised an efficient multiplier in to perform Montgomery multiplication using signed digit representation as demanded by modular exponentiation approach. The proposed multiplier is suitable for any public‐key cryptography that deals with integer arithmetic, namely, DSA, RSA, and elliptic curve cryptography (ECC).…”

Section: Related Workmentioning

confidence: 99%

Efficient modular exponential algorithms compatible with hardware implementation of public-key cryptography

Vollala

Geetha²,

Ramasubramanian

2016

Security Comm. Networks

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It is widely recognized that the public‐key cryptosystem is playing a pivotal role to provide the security services not only in electronic world but also for secured key exchanges in military applications. Modular exponentiation is the crucial, but expensive, operation in several public‐key cryptostyems, which makes use of repeated modular multiplications. So, the performance of public‐key cryptography is highly influenced by the competent implementation of modular exponentiation. In order to speed up the entire process, it is essential to develop the modular exponential algorithms, which reduces the frequency of modular multiplications, and the time required to implement each modular multiplication. In this paper, we present the bit forwarding (BFW) techniques to reduce the count of modular multiplications for hardware implementation of modular exponentiation. Montgomery multiplication method is customized according to the needs of BFW techniques and implemented with radix‐2, named as adaptable Montgomery multiplication, and also implemented with high radix and named as adaptable high‐radix Montgomery multiplication. It has been computed that it is possible to reduce 11.16%, 15.14% and 18.20% of modular multiplications by BFW1, BFW2, and BFW3 algorithms, respectively, for 1024‐bit exponent in comparison with prevailing techniques. This reduction will result in increased throughput and decreased power consumption. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Because the modulus is at least 1024 bits in size, high throughput is difficult to achieve without the use of hardware acceleration. The majority of the contributions are based on the Montgomery's modular multiplication (MMM), which replaces trial division by the modulus with a series of additions and divisions by a power of two [1,2,3,4,5,6,7,8,9]. Thus, it is well suited to hardware implementation.…”

Section: Introductionmentioning

confidence: 99%

“…If addition is computationally costly, all other related operations will be affected accordingly. If a redundant number system or systolic array system is employed, then the carry-propagation chain can be eliminated [3,4,5,7]. Recently, Manochehri et al presented MMM with a new recording method in which one step of the main loop is removed [8].…”

Section: Introductionmentioning

confidence: 99%

Enhancement of a modified radix-2 Montgomery modular multiplication

Choi

Lee

2014

IEICE Electron. Express

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Recently, Manochehri et al. proposed a modified radix-2 Montgomery modular multiplication with a new recording method. In this letter, we present an improvement to their scheme that makes it simpler and faster. Manochehri et al.'s algorithm requires n + 2 iterations, whereas the proposed (non-pipelined) algorithm requires n + 2 iterations. Moreover, there is no need for post-processing to obtain the correct output, nor for a non-standard operation such as bitwise subtraction. The area/time complexity of our pipelined multiplier is reduced by approximately 24.36% compared to Manochehri et al.'s multiplier. The proposed architecture is simple, modular, and regular. Moreover, it exhibits low complexity and propagation delay. Accordingly, it is well suited for VLSI implementation.

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An efficient signed digit montgomery multiplication for RSA

Cited by 7 publications

References 13 publications

Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

Efficient modular exponential algorithms compatible with hardware implementation of public-key cryptography

Enhancement of a modified radix-2 Montgomery modular multiplication

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