Fast scalable radix-4 Montgomery modular multiplier

Wang, Shenghong; Lin, Wen-Ching; Ye, Jheng-Hao; Shieh, Ming-Der

doi:10.1109/iscas.2012.6271962

Cited by 22 publications

(22 citation statements)

References 10 publications

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“…With k = 2, it can be shown that the modified Booth coding [13] can be applied to both q i and b i in Algorithm 1, which is firstly proposed in [12] and then applied in [8]. The problem can be considered in two separate cases: (1) the Booth coding with q i is valid; (2) the Booth coding with b i is valid.…”

Section: Precomputation and Double Booth-encodings With Radix-4 Mmentioning

confidence: 99%

“…The designs with [8] and [6] are employing similar algorithms, while the latter is radix-2 design. The clock cycles in their work are computed from the time and frequency in [6], [8].…”

Section: Equations (1) and (2) Then Yields The Returned Valuementioning

confidence: 99%

“…The clock cycles in their work are computed from the time and frequency in [6], [8]. While the result in [8] is a little faster than this work, its time for a 1024-bit Montgomery modular multiplication may increase to some extent for full postprocessing. Meanwhile, the improved feedforward scalable architecture consumes fewer LUTs than that in [8].…”

Section: Equations (1) and (2) Then Yields The Returned Valuementioning

confidence: 99%

“…Among these low-latency scalable Montgomery modular multipliers, a left-shifting mechanism is used in [5], [9], while other work employs right-shifting architectures, where the highest performance is obtained by Shieh et al's in [6], [8], [10]. However, the architecture with their algorithm is a little hard to follow because of complex reorganization of partial products.…”

Section: Introductionmentioning

confidence: 99%

“…Although it is of good performance, a radix-4 feedforward scalable Montgomery modular multiplier is suffering from the long critical path to determine quotient digits. In this work, a technique of precomputation [2] and double Booth encodings [8], [12] is used to ease quotient determination in radix-4 feedforward scalable Montgomery modular multiplier. The results of hardware implementation shows an improvement of 44.4% in performance.…”

Section: Introductionmentioning

confidence: 99%

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Improving radix-4 feedforward scalable montgomery modular multiplier by precomputation and double booth-encodings

2013

Proceedings of 2013 3rd International Conference on Computer Science and Network Technology

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Hardware implementation of multiprecision modular multiplications in public-key cryptography has led to various developments of scalable Montgomery modular multipliers, which are fast enough constrained from limited hardware resources. Among the candidates, the feedforward scalable Montgomery modular multiplier achieves low latency with simple logics and little change in the algorithm. However, the performance of high-radix feedforward scalable Montgomery modular multiplier is deteriorated by quotient determination. In this work, the method of double Booth-encodings and precomputation, which is firstly proposed for a traditional scalable Montgomery modular multiplier by Pinckney et al., is applied to radix-4 feedforward scalable Montgomery modular multiplier. FPGA implementation shows that the critical path is reduced by about 31% while the cost of hardware resources also decreases.

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Section: Precomputation and Double Booth-encodings With Radix-4 Mmentioning

confidence: 99%

“…The designs with [8] and [6] are employing similar algorithms, while the latter is radix-2 design. The clock cycles in their work are computed from the time and frequency in [6], [8].…”

Section: Equations (1) and (2) Then Yields The Returned Valuementioning

confidence: 99%

Section: Equations (1) and (2) Then Yields The Returned Valuementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improving radix-4 feedforward scalable montgomery modular multiplier by precomputation and double booth-encodings

2013

Proceedings of 2013 3rd International Conference on Computer Science and Network Technology

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High Radix Montgomery Multiplication

Vollala¹,

Ramasubramanian

Tiwari³

2021

Energy-Efficient Modular Exponential Techniques for Public-Key Cryptography

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Fast RSA decryption through high-radix scalable Montgomery modular multipliers

Liu

2015

Sci. China Inf. Sci.

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This paper improves the quotient-pipelined high radix scalable Montgomery modular multiplier by processing w-bit and k-bit words in carry save form instead of some (w + k)-bit length operands. It directly reduces both the critical path and the area overhead of the original processing elements. Then based on this improved high-radix scalable Montgomery modular multiplier, we propose an efficient hardware architecture for RSA decryption with Chinese Remainder Theorem. With simple configuration logics, the hardware unit works in three modes: (1) scalable modular reduction for precomputation, (2) scalable Montgomery modular multiplication for modular exponentiation, where an approximation method is developed to reduce the expanded result below the modulus, and (3) scalable multiplication for post-processing. Hardware implementation shows that the proposed architecture is optimal with reference to the literature in terms of speed, area, and frequency. A 4096-bit RSA decryption in XC2V6000-6 FPGA can be completed in 11.05 ms with 14041 slices/17409 LUTs, 128 16 × 16 multipliers, and 70 kbits of block RAMs. Finally, by the use of Montogmery powering ladder the modular exponentiation unit based on the improved high radix scalable Montgomery modular multiplier can be built resistant to fault and simple power attacks. A 1024-bit modular exponentiation unit with such resistances costs about 255K NAND2 gates in .18 µm CMOS process, and one full modular exponentiation takes about 1.44 ms at 250 MHz.

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Fast scalable radix-4 Montgomery modular multiplier

Cited by 22 publications

References 10 publications

Improving radix-4 feedforward scalable montgomery modular multiplier by precomputation and double booth-encodings

Improving radix-4 feedforward scalable montgomery modular multiplier by precomputation and double booth-encodings

High Radix Montgomery Multiplication

Fast RSA decryption through high-radix scalable Montgomery modular multipliers

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