Efficient algorithms for supersingular isogeny Diffie-Hellman

We propose a new suite of algorithms that significantly improve the performance of supersingular isogeny Diffie-Hellman (SIDH) key exchange. Subsequently, we present a full-fledged implementation of SIDH that is geared towards the 128-bit quantum and 192-bit classical security levels. Our library is the first constant-time SIDH implementation and is up to 2.9 times faster than the previous best (non-constant-time) SIDH software. The high speeds in this paper are driven by compact, inversion-free point and isogeny arithmetic and fast SIDH-tailored field arithmetic: on an Intel Haswell processor, generating ephemeral public keys takes 46 million cycles for Alice and 54 million cycles for Bob, while computing the shared secret takes 44 million and 52 million cycles, respectively. The size of public keys is only 564 bytes, which is significantly smaller than most of the popular post-quantum key exchange alternatives. Ultimately, the size and speed of our software illustrates the strong potential of SIDH as a post-quantum key exchange candidate and we hope that these results encourage a wider cryptanalytic effort

ОСОБЛИВОСТІ ВИКОРИСТАННЯ ІЗОГЕНІЙ ЕЛІПТИЧНИХ КРИВИХ В КРИПТОГРАФІЧНИХ ПРОТОКОЛАХ

В роботі досліджено особливості використання ізогеній суперсингулярних еліптичних кривих в криптографічних протоколах, зокрема в протоколі розділення ключа Діффі-Хеллмана. Виконано розрахунковий приклад проведення обчислень за загальною схемою алгоритму Вєлу в спеціалізованому математичному пакеті.Результати роботи можуть бути використані фахівцями з кібербезпеки для розробки криптографічних протоколів асиметричної криптографії, стійких до атак на квантовому комп'ютері

Post-Quantum Group Key Agreement Scheme

Progress in quantum technologies forces the development of new cryptographic primitives that are resistant to attacks of an adversary with a quantum computer. A large number of key establishment schemes have been proposed for two participants, but the area of group post-quantum key establishment schemes has not been studied a lot. Not so long ago, an isogeny-based key agreement scheme was proposed for three participants, based on a gradual increase in the degree of the key. We propose another principle for establishing a key for a group of participants using a tree-structure. The proposed key establishment scheme for four participants uses isogeny of elliptic curves as a mathematical tool

Fault attack on Supersingular Isogeny Cryptosystems

We present the first fault attack on cryptosystems based on supersingular isogenies. During the computation of the auxiliary points, the attack aims to change the base point to a random point on the curve via a fault injection. We will show that this would reveal the secret isogeny with one successful perturbation with high probability. We will exhibit the attack by placing it against signature schemes and key-exchange protocols with validations in place. Our paper therefore demonstrates the need to incorporate checks in implementations of the cryptosystem

Optimized Supersingular Isogeny Key Encapsulation on ARMv8 Processors

In this work, we present highly-optimized constant-time software libraries for Supersingular Isogeny Key Encapsulation (SIKE) protocol on ARMv8 processors. Our optimized hand-crafted assembly libraries provide the most efficient timing results on 64-bit ARM-powered devices. Moreover, the presented libraries can be integrated into any other cryptography primitives targeting the same finite field size. We design a new mixed implementation of field arithmetic on 64-bit ARM processors by exploiting the A64 and Advanced SIMD processing units working in parallel. Using these techniques, we are able to improve the performance of the entire protocol by the factor of 5 times compared to optimized C implementations on 64-bit ARM high-performance cores, providing 83-, 124-, and 159-bit quantum-security levels. Furthermore, we compare the performance of our proposed library with the previous highly-optimized ARMv8 assembly library available in the literature. The implementation results illustrate the overall 10% performance improvement in comparison with previous work, highlighting the benefit of using mixed implementation over relatively-large finite field size

Supersingular Isogeny Oblivious Transfer

We present an oblivious transfer (OT) protocol that combines the OT scheme of Chou and Orlandi together with thesupersingular isogeny Diffie-Hellman (SIDH) primitive of De Feo, Jao, and Pl\^ut. Our construction is a candidate for post-quantum secure OT and demonstrates that SIDH naturally supports OT functionality. We consider the protocol in the simplest configuration of $\binom{2}{1}$-OT and analyze the protocol to verify its security.Comment: 26 pages, 4 figures, Submitte

Towards Green Computing Oriented Security: A Lightweight Postquantum Signature for IoE

[EN] Postquantum cryptography for elevating security against attacks by quantum computers in the Internet of Everything (IoE) is still in its infancy. Most postquantum based cryptosystems have longer keys and signature sizes and require more computations that span several orders of magnitude in energy consumption and computation time, hence the sizes of the keys and signature are considered as another aspect of security by green design. To address these issues, the security solutions should migrate to the advanced and potent methods for protection against quantum attacks and offer energy efficient and faster cryptocomputations. In this context, a novel security framework Lightweight Postquantum ID-based Signature (LPQS) for secure communication in the IoE environment is presented. The proposed LPQS framework incorporates a supersingular isogeny curve to present a digital signature with small key sizes which is quantum-resistant. To reduce the size of the keys, compressed curves are used and the validation of the signature depends on the commutative property of the curves. The unforgeability of LPQS under an adaptively chosen message attack is proved. Security analysis and the experimental validation of LPQS are performed under a realistic software simulation environment to assess its lightweight performance considering embedded nodes. It is evident that the size of keys and the signature of LPQS is smaller than that of existing signature-based postquantum security techniques for IoE. It is robust in the postquantum environment and efficient in terms of energy and computations.This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University. Jeddah. under grant No. (DF-457-156-1441).Rani, R.; Kumar, S.; Kaiwartya, O.; Khasawneh, AM.; Lloret, J.; Al-Khasawneh, MA.; Mahmoud, M.... (2021). Towards Green Computing Oriented Security: A Lightweight Postquantum Signature for IoE. Sensors. 21(5):1-20. https://doi.org/10.3390/s2105188312021