Iterative modular multiplication algorithmwithout magnitude comparison

Chiou, Che Wun; Yang, Ted C.

doi:10.1049/el:19941383

Cited by 16 publications

(2 citation statements)

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“…It avoids magnitude comparison, which is the critical operation in traditional modular multiplications. The magnitude comparison slows down for longer operands, because its computation time is linearly proportional to the word length of the operands [9].…”

Section: Modular Exponential Algorithm -Smme(abn)mentioning

confidence: 99%

<title>Modular exponential accelerator chip based on precomputations for RSA cryptography application</title>

1999

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A new algorithm, Square-and-Multiply for Modular Exponentiation (SMME), is proposed to calculate a modular exponentiation that is the core arithmetic function in RSA cryptography. The SMME scans the exponent from its MSB and pre-computes a set of exponents to the maximum bit length of 1. These pre-computed exponents are stored in a look-up table. By using the look-up table, the number of multiplications required for modular exponentiation can be reduced. Modular multiplications are performed using a modified Montgomery's algorithm. The SMME takes in the order of n2(1+ 1/(21)) cycles to execute one n-bit modular exponentiation. The memory size to accommodate the pre-computed exponents is a 2'' (n+1)-bit RAM.The SMME, with its regularity and local connections in a systolic array, makes it suitable for VLSI implementation.A 64-bit modular exponentiation chip is being designed using a 0.8 m CMOS standard cell library from AMS. The simulation results show that at 25 MHz, the throughput is approximately 236 KBps; and an estimation of 40 KBps for a 512-bit exponent.

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Section: Modular Exponential Algorithm -Smme(abn)mentioning

confidence: 99%

<title>Modular exponential accelerator chip based on precomputations for RSA cryptography application</title>

1999

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“…None of these surveys cover sum of residues papers. Other publications, [4,29,30], have made note of the sum of residues technique but categorize it along with other classical algorithms. At first sight, this may look like a classical algorithm as the quotient digit q is selected from the most significant bits of the partial result.…”

Section: The Relationship Between Division and Modular Multiplicationmentioning

confidence: 99%

Revisiting Sum of Residues Modular Multiplication

Kong

Phillips

2010

Journal of Electrical and Computer Engineering

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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).

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