Area-Efficient Realization of Binary Elliptic Curve Point Multiplication Processor for Cryptographic Applications
Abstract
:1. Introduction
1.1. Low-Area Hardware Implementations with Limitations
1.2. Novelty and Contributions
1.3. Main Findings and Significance
2. Background
2.1. ECC over
Algorithm 1 Montgomery PM algorithm [12] | |
1 | Input: with , |
2 | Output: |
3 | Set, , and |
4 | for (i from m−2 down to 0) do |
39 | , |
40 |
2.2. Design Rationales
3. Proposed Crypto Processor Design
3.1. Data Memory
3.2. Arithmetic Unit
Algorithm 2 Polynomial reduction over (algorithm 2.42 of [9]) | |
1 | Input: Polynomial, with bit length |
2 | Output: Polynomial, with m bit length |
|
3.3. Control Unit and Clock Cycles Calculation
4. Results and Comparison
4.1. Results
4.2. Comparisons
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Device | Area Results | Timing Results | Power (mW) | |||
---|---|---|---|---|---|---|
Slices | LUTs | Clock Cycles | Freq (MHz) | Latency (ms) | ||
Virtex-6 | 407 | 2442 | 7, 16, 459 | 100 | 7.16 | 73 |
50 | 14.32 | 39 | ||||
10 | 71.64 | 7 | ||||
Virtex-7 | 391 | 2346 | 7, 16, 459 | 100 | 7.16 | 51 |
50 | 14.32 | 28 | ||||
10 | 71.64 | 4 |
Ref. # | Algorithm (or) PM Method | Device | Slices | LUTs | Clock Cycles | Freq MHz | Latency (s) | Power (mW) | Details |
---|---|---|---|---|---|---|---|---|---|
[12] | Montgomery | Virtex-7 | 2207 | 9965 | 3960 | 369 | 10 | - | 163 bit binary field |
[12] | Montgomery | Virtex-7 | 5120 | 18,953 | 5634 | 357 | 15 | - | 233 bit binary field |
[13] | Montgomery | Virtex-7 | 1529 | 4162 | 3798 | 383 | 9 | - | 163 bit binary field |
[13] | Montgomery | Virtex-7 | 2048 | 6407 | 5402 | 379 | 14 | - | 233 bit binary field |
[14] | Double and Add | Virtex-7 | - | 50,789 | 65,783 | 91 | 722 | - | 256 bit prime field |
[15] | Montgomery | Virtex-5 | 473 | - | - | 359 | 110 | - | 163 bit binary field |
[15] | Binary | Virtex-5 | 420 | - | - | 362 | 830 | - | 163 bit binary field |
[15] | Frobenius Map | Virtex-5 | 710 | - | - | 165 | 300 | - | 163 bit binary field |
[16] | Lopez Dahab | Virtex-7 | 3657 | 10,128 | 3426 | 135 | 25 | - | 163 bit binary field |
[17] | Montgomery | Artix-7 | 442 | - | 1,553,782 | 190 | 8177 | - | 233 bit binary field |
[18] | Frobenius Map | Artix-7 | - | 8577 | 55,068 | 150 | 367 | 379 | 163 bit binary field |
TW | Montgomery | Virtex-5 | 411 | 1758 | 716,459 | 139 | 5154 | 84 | 233 bit binary field |
TW | Montgomery | Virtex-7 | 391 | 2346 | 716,459 | 161 | 4450 | 77 | 233 bit binary field |
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Aljaedi, A.; Jamal, S.S.; Rashid, M.; Alharbi, A.R.; Alotaibi, M.; Alanazi, D.J. Area-Efficient Realization of Binary Elliptic Curve Point Multiplication Processor for Cryptographic Applications. Appl. Sci. 2023, 13, 7018. https://doi.org/10.3390/app13127018
Aljaedi A, Jamal SS, Rashid M, Alharbi AR, Alotaibi M, Alanazi DJ. Area-Efficient Realization of Binary Elliptic Curve Point Multiplication Processor for Cryptographic Applications. Applied Sciences. 2023; 13(12):7018. https://doi.org/10.3390/app13127018
Chicago/Turabian StyleAljaedi, Amer, Sajjad Shaukat Jamal, Muhammad Rashid, Adel R. Alharbi, Mohammed Alotaibi, and Dalal J. Alanazi. 2023. "Area-Efficient Realization of Binary Elliptic Curve Point Multiplication Processor for Cryptographic Applications" Applied Sciences 13, no. 12: 7018. https://doi.org/10.3390/app13127018
APA StyleAljaedi, A., Jamal, S. S., Rashid, M., Alharbi, A. R., Alotaibi, M., & Alanazi, D. J. (2023). Area-Efficient Realization of Binary Elliptic Curve Point Multiplication Processor for Cryptographic Applications. Applied Sciences, 13(12), 7018. https://doi.org/10.3390/app13127018