Một bộ xử lý ECC cho IoT sử dụng các đường cong Edwards và phép nhân modulo DFT

Springer Science and Business Media LLC - Tập 26 - Trang 1063-1075 - 2022
Osama Al-Khaleel1, Selcuk Baktir2, Alptekin Küpçü3
1Computer Engineering Department, Jordan University of Science and Technology, Irbid, Jordan
2College of Engineering and Technology, American University of the Middle East, Egaila, Kuwait
3Computer Science and Engineering, Koç University, Istanbul, Turkey

Tóm tắt

Trong công trình này, một bộ xử lý mã hóa đường ellip (ECC) được đề xuất để sử dụng trong các thiết bị Internet of Things (IoT). Bộ xử lý ECC được thiết kế dựa trên các đường cong Edwards xác định trên các trường số nguyên tố hữu hạn $$GF((2^{13}-1)^{13})$$, $$GF((2^{17}-1)^{17})$$, và $$GF((2^{19}-1)^{19})$$. Phép nhân modulo trong bộ xử lý ECC được thực hiện trong miền tần số bằng cách sử dụng bộ nhân modulo từ biến đổi Fourier rời rạc (DFT). Các bộ cộng và bộ nhân trong trường cơ sở khác nhau được thiết kế và sử dụng trong thiết kế của bộ nhân modulo DFT. Bộ xử lý ECC được mô tả và kiểm tra chức năng bằng ngôn ngữ VHDL và công cụ mô phỏng trong Xilinx ISE14.2. Hơn nữa, bộ xử lý ECC được tổng hợp bằng công cụ tổng hợp trong Xilinx ISE14.2, nhắm đến gia đình FPGA Virtex-5. Kết quả tổng hợp của chúng tôi cho thấy rằng bộ xử lý ECC được đề xuất đạt tốc độ cao hơn với mức hình thức diện tích nhỏ hơn so với các công trình tương tự trong tài liệu.

Từ khóa

#Bộ xử lý ECC #Internet of Things #đường cong Edwards #nhân modulo DFT

Tài liệu tham khảo

Morales-Sandoval, M., Flores, L.A.R., Cumplido, R., Garcia-Hernandez, J.J., Feregrino, C., Algredo, I.: A compact fpga-based accelerator for curve-based cryptography in wireless sensor networks. J. Sens. 2021, 8860413 (2021). https://doi.org/10.1155/2021/8860413 Mosenia, A., Jha, N.K.: A comprehensive study of security of internet-of-things. IEEE Trans. Emerg. Topics Comput. 5(4), 586–602 (2017). https://doi.org/10.1109/TETC.2016.2606384 Joglekar, J., Bhutani, S., Patel, N., Soman, P.: Lightweight elliptical curve cryptography (ecc) for data integrity and user authentication in smart transportation iot system. In: Karrupusamy, P. (ed.) Sustainable Communication Networks and Application, pp. 270–278. Springer, Berlin (2020) Hammi, B., Fayad, A., Khatoun, R., Zeadally, S., Begriche, Y.: A lightweight ecc-based authentication scheme for internet of things (iot). IEEE Syst. J. 14(3), 3440–3450 (2020). https://doi.org/10.1109/JSYST.2020.2970167 Di Matteo, S., Baldanzi, L., Crocetti, L., Nannipieri, P., Fanucci, L., Saponara, S.: Secure elliptic curve crypto-processor for real-time iot applications. Energies (2021). https://doi.org/10.3390/en14154676 Dhillon, P.K., Kalra, S.: Elliptic curve cryptography for real time embedded systems in iot networks. In: 2016 5th International conference on wireless networks and embedded systems (WECON), pp. 1–6 (2016). https://doi.org/10.1109/WECON.2016.7993462 Liu, Z., Seo, H.: Iot-nums: evaluating nums elliptic curve cryptography for iot platforms. IEEE Trans. Inf. Forensics Sec. 14(3), 720–729 (2019). https://doi.org/10.1109/TIFS.2018.2856123 Manifavas, C., Hatzivasilis, G., Fysarakis, K., Rantos, K.: Lightweight cryptography for embedded systems—a comparative analysis. In: Data Privacy Management and Autonomous Spontaneous Security, pp. 333–349 (2014) Meiklejohn, S., Erway, C.C., Küpçü, A., Hinkle, T., Lysyanskaya, A.: \(\{\)ZKPDL\(\}\): A \(\{\)Language-Based\(\}\) system for efficient \(\{\)Zero-Knowledge\(\}\) proofs and electronic cash. In: USENIX Security Symposium (2010) Yeh, L.-Y., Chen, P.-J., Pai, C.-C., Liu, T.-T.: An energy-efficient dual-field elliptic curve cryptography processor for internet of things applications. IEEE Trans. Circuits Syst. II 67(9), 1614–1618 (2020). https://doi.org/10.1109/TCSII.2020.3012448 Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) Advances in Cryptology—CRYPTO ’85 Proceedings, pp. 417–426. Springer, Berlin, Heidelberg (1986) Koblitz, N.: Elliptic curve cryptosystems. Math. Comput. 48(177), 203–209 (1987) Bos, J.W., Costello, C., Longa, P., Naehrig, M.: Selecting elliptic curves for cryptography: an efficiency and security analysis. J. Cryptograph. Eng. 6(4), 259–286 (2016). https://doi.org/10.1007/s13389-015-0097-y Baktir, S., Kumar, S.S., Paar, C., Sunar, B.: A state-of-the-art elliptic curve cryptographic processor operating in the frequency domain. MONET 12(4), 259–270 (2007). https://doi.org/10.1007/s11036-007-0022-4 Bos, J., Kaihara, M., Kleinjung, T., Lenstra, A.K., Montgomery, P.L.: On the security of 1024-bit rsa and 160-bit elliptic curve cryptography. Cryptology ePrint Archive, Report 2009/389 (2009) Kocaogullar, C., Yıldırım, K., Sakaogulları, M.A., Küpçü, A.: Basgit: A secure digital epassport alternative. In: ISCTURKEY (2021) Taheri-Boshrooyeh, S., Küpçü, A., Özkasap, Ö.: Security and privacy of distributed online social networks. In: 2015 IEEE 35th international conference on distributed computing systems workshops, pp. 112–119 (2015). IEEE Yüksel, B., Küpçü, A., Özkasap, Ö.: Research issues for privacy and security of electronic health services. Future Gener. Comput. Syst. 68, 1–13 (2017) Edwards, H.: A normal form for elliptic curves. Bull. Am. Math. Soc. 44, 393–423 (2007). https://doi.org/10.1090/S0273-0979-07-01153-6 Abarzúa, R., Martínez, S., Mendoza, V., Thériault, N.: Same value analysis on Edwards curves. J. Cryptograph. Eng. 10(1), 27–48 (2020). https://doi.org/10.1007/s13389-019-00206-6 Bernstein, D.J.: Curve25519: New diffie-hellman speed records. In: PKC, pp. 207–228 (2006) Bernstein, D.J., Hamburg, M., Krasnova, A., Lange, T.: Elligator: Elliptic-curve points indistinguishable from uniform random strings. In: ACM CCS, pp. 967–980 (2013) Hamburg, M.: Ed448-goldilocks, a new elliptic curve. IACR Cryptol. ePrint Arch. 2015, 625 (2015) Renes, J., Costello, C., Batina, L.: Complete addition formulas for prime order elliptic curves. In: EUROCRYPT, pp. 403–428 (2016) Martínez, S., Sadornil, D., Tena, J., Tomàs, R., Valls, M.: On edwards curves and zvp-attacks. Appl. Algebra Eng. Commun. Comput. 24(6), 507–517 (2013) Bos, J.W., Halderman, J.A., Heninger, N., Moore, J., Naehrig, M., Wustrow, E.: Elliptic curve cryptography in practice. In: Financial Cryptography and Data Security, pp. 157–175 (2014) Faugère, J.-C., Perret, L., Petit, C., Renault, G.: Improving the complexity of index calculus algorithms in elliptic curves over binary fields. In: EUROCRYPT, pp. 27–44 (2012) Gandolfi, K., Mourtel, C., Olivier, F.: Electromagnetic analysis: concrete results. In: CHES, pp. 251–261 (2001) Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19(90), 297–301 (1965) Schönhage, A., Strassen, V.: Schnelle multiplikation großer zahlen. Computing 7(3), 281–292 (1971) Fürer, M.: Faster integer multiplication. SIAM J. Comput. 39(3), 979–1005 (2009) Baktır, S., Sunar, B.: Finite field polynomial multiplication in the frequency domain with application to elliptic curve cryptography. In: ISCIS, pp. 991–1001 (2006) Chen, J., Liu, P., Zhao, H., Zhang, C., Zhang, J.: Analytical studying the axial performance of fully encapsulated rock bolts. Eng. Failure Anal. 128, 105580 (2021). https://doi.org/10.1016/j.engfailanal.2021.105580 Wu, S.-L., Al-Khaleel, M.D.: Optimized waveform relaxation methods for rc circuits: discrete case. ESAIM M2AN 51(1), 209–223 (2017). https://doi.org/10.1051/m2an/2016061 Chen, J., Li, D.: Numerical simulation of fully encapsulated rock bolts with a tri-linear constitutive relation. Tunn. Undergr. Space Technol. 120, 104265 (2022). https://doi.org/10.1016/j.tust.2021.104265 Wu, S.-L., Al-Khaleel, M.D.: Semi-discrete Schwarz waveform relaxation algorithms for reaction diffusion equations. BIT Numer. Math. 54(3), 831–866 (2014). https://doi.org/10.1007/s10543-014-0475-3 Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: Kurosawa, K. (ed.) ASIACRYPT, pp. 29–50 (2007) Mentens, N., Batina, L., Baktir, S.: An elliptic curve cryptographic processor using edwards curves and the number theoretic transform. In: BalkanCryptSec, pp. 94–102 (2014). https://doi.org/10.1007/978-3-319-21356-9_7 Verri Lucca, A., Mariano Sborz, G.A., Leithardt, V.R.Q., Beko, M., Albenes Zeferino, C., Parreira, W.D.: A review of techniques for implementing elliptic curve point multiplication on hardware. J. Sens. Actuator Netw. 10(1), 3 (2021) Absar, S., Hossain, M., Kong, Y.: Efficient hardware implementation of modular arithmetic and group operation over prime field. Internet Things Cloud Comput. 7(1), 31–38 (2019). https://doi.org/10.11648/j.iotcc.20190701.15 Ding, J., Li, S., Gu, Z.: High-speed ecc processor over nist prime fields applied with toom-cook multiplication. IEEE Trans. Circuits Syst. I 66(3), 1003–1016 (2019). https://doi.org/10.1109/TCSI.2018.2878598 Hossain, M.R., Hossain, M.S.: Efficient fpga implementation of modular arithmetic for elliptic curve cryptography. In: 2019 International conference on electrical, computer and communication engineering (ECCE), pp. 1–6 (2019). https://doi.org/10.1109/ECACE.2019.8679419 Javeed, K., Wang, X.: Low latency flexible fpga implementation of point multiplication on elliptic curves over gf(p). I. J. Circuit Theory Appl. 45(2), 214–228 (2017) Kudithi, T., Sakthivel, R.: An efficient hardware implementation of the elliptic curve cryptographic processor over prime field. Int. J. Circuit Theory Appl. 48(8), 1256–1273 (2020) Hu, X., Zheng, X., Zhang, S., Li, W., Cai, S., Xiong, X.: A high-performance elliptic curve cryptographic processor of sm2 over gf(p). Electronics 8, 431 (2019). https://doi.org/10.3390/electronics8040431 Bailey, D.V., Paar, C.: Optimal extension fields for fast arithmetic in public-key algorithms. In: CRYPTO, pp. 472–485 (1998) Bailey, D.V., Paar, C.: Efficient arithmetic in finite field extensions with application in elliptic curve cryptography. J. Cryptol. 14(3), 153–176 (2001) Awaludin, A.M., Larasati, H.T., Kim, H.: High-speed and unified ecc processor for generic weierstrass curves over gf(p) on fpga. Sensors 21(4), 1251 (2021) Al-Khaleel, O., Baktır, S., Küpçü, A.: Fpga implementation of an ecc processor using edwards curves and dft modular multiplication. In: 2021 12th International conference on information and communication systems (ICICS), pp. 344–351 (2021). https://doi.org/10.1109/ICICS52457.2021.9464611 Esiner, E., Küpçü, A., Özkasap, Ö.: Analysis and optimization on flexdpdp: A practical solution for dynamic provable data possession. In: International conference on intelligent cloud computing, pp. 65–83 (2014). Springer Esiner, E., Kachkeev, A., Braunfeld, S., Küpçü, A., Özkasap, Ö.: Flexdpdp: flexlist-based optimized dynamic provable data possession. ACM Trans. Storage (TOS) 12(4), 1–44 (2016) Etemad, M., Küpçü, A.: Generic dynamic data outsourcing framework for integrity verification. ACM Comput. Surv. (CSUR) 53(1), 1–32 (2020)