یک طرح تسهیم راز آستانه ای مقاوم در برابر حملات کوانتومی

دلیری حسنجانی, پریسا; دقیق, حسن

یک طرح تسهیم راز آستانه ای مقاوم در برابر حملات کوانتومی

نوع مقاله : مقاله پژوهشی

نویسندگان

¹ دانشجوی دکتری، دانشکده علوم، دانشگاه کاشان، کاشان، ایران

² دانشیار، دانشکده علوم، دانشگاه کاشان، کاشان، ایران

چکیده

یکی از مسائل مهم ‏رمزنگاری، آسیب‌پذیری طرح‌های تسهیم راز در برابر حملات کوانتومی است. این مقاله، یک طرح تسهیم راز تأییدپذیر با استفاده از سامانه رمزنگاری پساکوانتومی لیندنر-پایکرت را معرفی کرده است. امنیت این طرح به دلیل استفاده از سامانه رمزنگاری پساکوانتومی لیندنر-پایکرت در برابر حملات کوانتومی تأیید شده است. این طرح بر اساس مسئله یادگیری با خطا در حلقه استوار است که نسخه جبری مسئله یادگیری با خطا است. به‌طوری‌که پارامترها از یک حلقه چندجمله‌ای با استفاده از توزیع گاوسی انتخاب شده‌اند. از آنجا که تمامی پارامترهای کلید عمومی و سهام‌ها در برابر حملات کوانتومی مقاوم هستند، در این طرح به کانال امن نیازی نیست.

کلیدواژه‌ها

20.1001.1.23224347.1404.13.2.4.1

موضوعات

امنیت اطلاعات، رمزنگاری، پنهان نگاری، پروتکل ها و استانداردها

عنوان مقاله [English]

A threshold secret sharing scheme resistant to quantum attacks

نویسندگان [English]

parisa daliri hasanjani ¹
hassan Daghigh ²

¹ PhD student, Faculty of Science, Kashan University, Kashan, Iran

² Associate Professor, Faculty of Science, Kashan University, Kashan, Iran

چکیده [English]

In this paper, a new verifiable secret sharing scheme is presented. This scheme uses the idea used by Lindner-Peikert in his well-known cryptosystem. The security is based on the Ring Learning With Error (RLWE) problem, which is an algebraic variant of the Learning With Error (LWE) problem, and is believed to be quantum resistant. Our new scheme does not require any secure channel.

کلیدواژه‌ها [English]

Secret sharing scheme Lattice with errors Ring learning cryptosystem Lindner
Peikert Hash function

مراجع

[1] A di. Shamir, "How to share a secret," Communications of the ACM 2.11. 612-613, 1979.‏ https://doi.org/10.1145/359168.359176

[2] G. Blakley, ''Safeguarding Cryptographic Keys,'' In Proc. AFIPS 1979 National Computer Conf, pp. 313–317, June 1979. https://doi.org /10.1109 /MARK .1979 .88 1 7296.

[3] C. S. Chum, X. Zhang, ''Hash function-based secret sharing scheme designs,'' Security and Communication Networks, 6(5). pp. 584-592, 2013. https://doi.org /10.1002/sec.576.

[4] A. Das, A. Adhikari, ''An efficient multi-use multi-secret sharing scheme based on hash function,'' Applied mathematics letters, 23(9), pp. 993-996, 2010. https:// doi.org/10.1016/j.aml.2010.04.024.

[5] J. Shao, ''Efficient verifiable multi-secret sharing scheme based on hash function,'' Information Sciences, 278. pp. 104-109, 2014. https://doi.org/10.1016/j.ins.2014.03.025.

[6] M. Farhadi, H. Bypour, and R. Mortazavi, “A Hash-Based Multi-Use Multi-Stage Secret Sharing Scheme with General Access Structure,” JOURNAL OF ELECTRONIC AND CYBER DEFENCE, vol. 6, no. 3 (23) , pp. 107–115, 2018, (in Persian), Dor: 20.1001.1.23224347.1397.6.3.9.9.

[7] P. W. Shor, ''Algorithms for Quantum Computation: Discrete Logarithms and Factoring,'' Proc. of the 35th Annual Symposium on Foundations of Computer Science , Washington , DC , USA: IEEE Computer Society, pp . 124-134, 1994. https://doi.org /10.1109 /SFCS.1994. 365700.

[8] R . J . McEliece, ''A Public-Key Cryptosystem Based on Algebraic Coding Theory,'' DSN Progress Report, vol . 42, no . 44 , pp. 114-116 , 1978 .

[9] M. Ajtai, ''Generating Hard Instances Of Lattice Problems (Extended Abstract),'' Proc. of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, New York, NY, USA: ACM, pp. 99-108, 1996.

[10] Georgescu, ''A Lwe-Based Secret Sharing Scheme,'' IJCA Special Issue on Network Security and Cryptography , no . 3 , pp . 27-29 , December , published by Foundation of Computer Science, New York, USA, 2011. https://doi.org/10.2478/v10127-012-0042-8.

[11] R. El Bansarkhani and M. Meziani, ''An Efficient Lattice-Based Secret Sharing Construction,'' Information Security Theory and Practice. Security, Privacy and Trust in Computing Systems and Ambient Intelligent Ecosystems, ser. Lecture Notes in Computer Science, I. Askoxylakis, H. Phls, and J. Posegga, Eds. Springer Berlin Heidelberg, vol. 7322, pp. 160-168, 2012. https://doi.org/10.1007/978-3-642-30955-7_14.

[12] S. Asaad, H. A. Khorasgani, T. Eghlidos, and M. Aref, "Sharing secret using lattice construction," In Telecommunications (IST), 2014 7th International Symposium on, pp. 901-906. IEEE, 2014. https://doi.org/10.1109/ISTEL.2014.7000831.

[13] [13] Khorasgani, Hamidreza Amini, Saba Asaad, Taraneh Eghlidos, and Mohammadreza Aref. "A lattice-based threshold secret sharing scheme." In Information Security and Cryptology (ISCISC), 2014 11th International ISC Conference on, pp. 173-179. IEEE, 2014. https://doi.org/10.1109/ISCISC.2014.6994043.

[14] F. Li, J. Yan, S. Zhu, H. Hu, ''A verifiable multi-secret sharing scheme based on short integer solution,'' Chinese Journal of Electronics, 32(3), 1-8, 2023. https://doi.org/10.23919/cje.2021.00.062.

[15] [15] N. Kiamari, M. Hadian, S. Mashhadi, ''Non-interactive verifiable LWE-based multi secret sharing scheme,'' Multimedia Tools and Applications, 82(14), 22175-22187, 2023. https://doi.org/10.1007/s11042-022-13347-4

[16] M. Hadian Dehkordi, S. Mashhadi, and N. Kiamari, ''Two Verifiable Multi-Secret Sharing Schemes: A Linear Scheme with Standard Security and A Lattice-Based Scheme,'' JOURNAL OF ELECTRONIC AND CYBER DEFENCE, vol. 8, no. 3 (31) , pp. 101–115, 2020, (in Persian), Dor: 20.1001.1.23224347.1399.8.3.8.2.

[17] J. Hoffstein, P. Jill, and H. Silverman. "NTRU: A ring-based public key cryptosystem," International algorithmic number theory symposium. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998.‏

[18] A. Amroudi, Nakhaei, A. Zaghain, and M. Sajadieh. "A verifiable (k, n, m)-threshold multi-secret sharing schem e based on ntru cryptosystem," Wireless Personal Comm unications 96, 1393-1405, 2017.‏

[19] A. I. Hussein, A. T. MaoLood, E. K. Gbashi, ''NTRU- SSS: Anew Method Signcryption Post Quantum Cryp tography Based on Shamir’s Secret Sharing, '' Computers, Materials & Continua, 76(1), 2023. https://doi.org/10.32604/cmc.2023.039804.

[20] J. Sharafi, H. Daghigh. "A Ring-LWE-based digital sign ature inspired by Lindner–Peikert scheme." Journal of Mathematical Cryptology 16, no. 1 205-214, 2022. https://doi.org/10.1515/jmc-2021-0013.

[21] D. Micciancio, O. Regev, ''Lattice-based cryptography,'' In Post-quantum cryptography (pp. 147-191). Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. https://doi.org/10.1007/978-3-540-88702-7-5.

[22] O.Regev, ''New lattice-based cryptographic constructio ns,'' Journal of the ACM (JACM), 51(6), 899-942, 2004. https://doi.org/10.1145/1039488.1039490.

[23] R. Lindner, C. Peikert, ''Better key sizes (and attacks) for LWE-based encryption,"Cryptographers Track at the RSA Conference. Springer, Berlin, Heidelberg, 2011. https://doi.org/10.1007/978-3-642-19074-2-21.

[24] V. Lyubashevsky, C. Peikert, and O. Regev, ''On ideal lattices and learning with errors over rings,'' in Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 1-2, Springer 2010. https://doi.org/10.1007/978-3-642-13190-5_1.

[25] B. Rajabi and Z. Eslami, ''A Verifiable Threshold Secret Sharing Scheme Based on Lattices,'' Information Science , vol. 501 pp. 655–661, 2019. https://doi.org /10 .101 6 /j.ins.2018.11.004.

[26] [O. Regev, ''On Lattices , Learning with Errors , Random Linear Codes , and Cryptography,'' J .ACM, 56(6): 34: 134:40, September 2009. https://doi.org/10.1145/1568318.1568324.

[27] D . Micciancio and S . Goldwasser , ''Complexity of Lattice Problems : A Cryptographic Perspective,'' Ser . Milken Institute Series on Financial Inno vation and Economic Growth . Springer US, 2002. https://doi.org/10.1007/978-1-4615-0897-7

[28] D . Bernstein , J . Buchmann , and E . Dahmen , ''Post-Quantum Cryptography,'' Springer , 2009. https://doi.org/10.1038/nature23461.

[29] C. Peikert, ''Public-key cryptosystems from the worst-case shortest vector problem,'' InProceedings of the forty-first annual ACM symposium on Theory of computing May 31 (pp. 333-342), 2009.

[30] V. Lyubashevsky, C. Peikert, O. Regev, ''On ideal lattic es and learning with errors over rings,'' Journal of the ACM (JACM), Vol. 6, 1–35, 2013.