Fast Montgomery Modular Multiplier Using FPGAs

Pajuelo-Holguera, Francisco; Granado-Criado, José M.; Gómez–Pulido, Juan A.

doi:10.1109/les.2021.3090029

Cited by 11 publications

(3 citation statements)

References 24 publications

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“…Designs reported in [19], [20], [24], [28], and [29] are based on IM, [17], [18] is based on SP, and the rest of the listed designs are based on the MM method. In terms of computational time, [13], [14], [15], [21], [22], [23], [26], [27] are 2.93×, 4.5×, 1.72 ×, 1.02×, 1.74×, 4.58×, 1.3×, 4.3× times better but consumes 2.6×, 9.17×, 22×, 3.9×, 5.77×, 23×, 9.5×, and 24.6× more NLUTs, respectively.…”

Section: A Ffm Implementation Resultsmentioning

confidence: 99%

“…Several useful modifications and related architectures have been proposed for all these three approaches [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]. Designs reported in [14], [15], [16], [21], [22], [23], [25], [26], and [27] are based on MM, [19], [20], [24], [28], [29], [30] are based on IM and [17], [18] are using NIST recommended SP primes. Most of these designs are then further utilized in the development of several ECPM architectures [17], [19], [20], [21], [30], [31], [32], [33], [34], [35], [36], [37], [38].…”

Section: Introductionmentioning

confidence: 99%

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EC-Crypto: Highly Efficient Area-Delay Optimized Elliptic Curve Cryptography Processor

2023

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Elliptic Curve Cryptography (ECC) based security protocols require much shorter key space which makes ECC the most suitable option for resource-limited devices as compared to the other public key cryptography (PKC) schemes. This paper presents a highly efficient area-delay optimized ECC crypto processor over the general prime field (F p ). It is structured on a new novel finite field multiplier (FFM) where several optimization techniques have been incorporated to shorten the latency and hardware resource consumption. The proposed FFM architecture is embedded with a finite field adder/subtractor (FFAS) unit which is utilized to perform FFAS operations instead of deploying a dedicated unit. The Common Z (Co-Z) coordinates with the Montgomery ladder method are used to compute point multiplication, a core operation in all ECC-based crypto protocols. The work also proposes an efficient scheduling strategy to execute low-level finite field arithmetic primitives with minimum latency on the employed finite field arithmetic units. Due to these techniques, the proposed ECC processor is optimized for hardware resources, latency, and throughput. It is captured in Verilog-HDL, synthesized, and implemented on Virtex-7, Kintex-7, and Virtex-6 FPGA platforms using Xilinx Vivado and ISE Design Suite tools. On the Virtex-7 FPGA platform, it computes a single 256-bit scalar multiplication primitive in 0.7 ms, consumes just 6.2K slices, and delivers a throughput of 1428 operations per second. The implementation results show that it is a highly efficient design outperforming the state-of-the-art by providing a better area-delay product and higher efficiency. Therefore, it has the potential to be deployed in many applications where both latency and resource requirements are critical.INDEX TERMS Elliptic curve cryptography (ECC), finite field multiplication, field programmable gate array (FPGA), hardware acceleration, finite field arithmetic.

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Section: A Ffm Implementation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

EC-Crypto: Highly Efficient Area-Delay Optimized Elliptic Curve Cryptography Processor

2023

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“…Several MM and IM-based bitserial and digit-serial modular multipliers along with their FPGA implementations have been reported. In previous works, modular multipliers are based on MM 27,[43][44][45][46][47] while others are developed using the IM method. 25,29,31,33,[48][49][50][51][52] In these designs, several modifications have been introduced to reduce computational delay and hardware area occupation such as carry-save addition, residue number system (RNS), redundant sign digit (RSD) system, and even some designs utilizing built-in components of the modern FPGAs.…”

Section: Introductionmentioning

confidence: 99%

Area‐time efficient point multiplication architecture on twisted Edwards curve over general prime field GF(p)

Javeed

El-Moursy

2023

Circuit Theory & Apps

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Elliptic curve point multiplication is the main primitive required in almost all security schemes using elliptic curve cryptography (ECC). It is the leading computationally intensive operation that sets the overall performance of the associated cryptosystem. This work presents a highly novel area–time efficient elliptic curve point multiplier over a general prime field . It is based on an efficient radix‐23 parallel multiplier, which performs a ‐bit multiplication in clock cycles. On the system level, the twisted Edwards curves with unified point addition using projective coordinates are adopted, where an efficient scheduling technique is presented to schedule several operations on deployed modular arithmetic units. Due to the introduced optimization at different stages of the design, latency, hardware resource requirement, and total clock cycle count are reduced significantly. Synthesis, and implementation of the proposed design over different Xilinx FPGA platforms are completed using the Xilinx ISE Design Suite tool for key sizes of 192, 224, and 256 bits. The 256‐bit Xilinx Virtex‐7 FPGA implementation reveals that it completes a single point multiplication operation in 0.8 ms and occupies 6.7K FPGA slices in a clock cycle count of 132.2K. It produces significantly better area–time product and throughput per slice than the contemporary designs. The proposed design also has the potential to counter simple power analysis and timing attacks. Thus, it is an elegant solution to develop ECC‐based cryptosystems for applications, where both speed and hardware resource consumption are important.

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GMC-crypto: Low latency implementation of ECC point multiplication for generic Montgomery curves over GF(p)

Javeed,

Shah,

Gregg

2024

Journal of Parallel and Distributed Computing

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Fast Montgomery Modular Multiplier Using FPGAs

Cited by 11 publications

References 24 publications

EC-Crypto: Highly Efficient Area-Delay Optimized Elliptic Curve Cryptography Processor

EC-Crypto: Highly Efficient Area-Delay Optimized Elliptic Curve Cryptography Processor

Area‐time efficient point multiplication architecture on twisted Edwards curve over general prime field GF(p)

GMC-crypto: Low latency implementation of ECC point multiplication for generic Montgomery curves over GF(p)

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