A SCALAR OPERATION BASED ENDOMORPHISM SPARSE METHOD FOR SOLVING HYPERSINGULAR ELLIPTIC CURVE LADDER FOR INTERNET OF THINGS DEVICE SECURITY AUTHENTICATION
Keywords:
Internet of Things, SIKE, Safety Certification, Supersingular elliptic curves.Abstract
At present, RSA, ECC and other asymmetric encryption algorithms are mainly used in the authentication of the Internet of Things gateway, but due to the limited amount of computation of embedded devices and the inability to resist quantum attacks, the traditional encryption algorithms are difficult to meet the security needs of the existing Internet of Things authentication, so it is urgent to develop a lightweight encryption algorithm that can resist quantum attacks. In this paper, we propose a lightweight SIKE encryption algorithm for security authentication of Internet of Things devices based on the latest release of NIST's key exchange algorithm based on hypersingular endomorphisms (SIKE algorithm), which is optimized by solving the ladder of hypersingular elliptic curves with sparse hSomomorphisms and double-channel exchange of random prime numbers. The simulation results show that the computational overhead of the algorithm can be reduced by 40% in the prime number solving stage, by 32% in the key exchange stage, and by more than 28% in ASIC implementation circuit area (taking logic gate as an example), and the final FOM value can be more than 300.References
[1] Koziel Brian et al. Post-Quantum Cryptography on FPGA Based on Isogenies on Elliptic Curves[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2017, 64(1) : 86-99.
[2] Pessl P , Bruinderink L G , Yarom Y . To BLISS-B or not to be: Attacking strongSwan's Implementation of Post-Quantum Signatures[C]// the 2017 ACM SIGSAC Conference. ACM, 2017.
[3] Majot A , Yampolskiy R . Global catastrophic risk and security implications of quantum computers[J]. Futures, 2015, 72:S0016328715000294.
[4] Anton Stolbunov. Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Advances in Mathematics of Communications, 4(2):215–235, 2010
[5] Andrew Childs, David Jao, and Vladimir Soukharev. Constructing elliptic curve isogenies in quantum subexponential time. Journal of Mathematical Cryptology, 8(1):1–29, 2014
[6] David Jao and Luca De Feo. Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In International Workshop on Post-Quantum Cryptography, pages 19–34. Springer, 2011
[7] Cheng C , Lu R , Petzoldt A , et al. Securing the Internet of Things in a Quantum World[J]. IEEE Communications Magazine, 2017, 55(2):116-120.
[8] Joye M , Yen S M . Optimal left-to-right binary signed-digit recoding[J]. IEEE Transactions on Computers, 2000, 49(7):740-748.
[9] Saarinen M J O . Ring-LWE Ciphertext Compression and Error Correction: Tools for Lightweight Post-Quantum Cryptography[C]// Acm International Workshop on Iot Privacy. ACM, 2017.
[10] Basu Roy D , Mukhopadhyay D . [IEEE 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI) - Hong Kong (2018.7.8-2018.7.11)] 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI) - Minimalistic Perspective to Public Key Implementations on FPGA[C]// 2018:381-386.
[11] Fan J , Hsieh M H , Chen H , et al. Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors[J]. 2018.
[12] Roetteler M , Naehrig M , Svore K M , et al. Quantum resource estimates for computing elliptic curve discrete logarithms[J]. 2017.
[13] Oliveira B D , Fábio. On Privacy-Pres