Paper 2019/1070

Secure Delegation of Isogeny Computations and Cryptographic Applications

Robi Pedersen and Osmanbey Uzunkol

Abstract

We address the problem of speeding up isogeny computation for supersingular elliptic curves over finite fields using untrusted computational resources like third party servers or cloud service providers (CSPs). We first propose new, efficient and secure delegation schemes. This especially enables resource-constrained devices (e.g. smart cards, RFID tags, tiny sensor nodes) to effectively deploy post-quantum isogeny-based cryptographic protocols. To the best of our knowledge, these new schemes are the first attempt to generalize the classical secure delegation schemes for group exponentiations and pairing computation to an isogeny-based post-quantum setting. Then, we apply these secure delegation subroutines to improve the performance of supersingular isogeny-based zero-knowledge proofs of identity. Our experimental results show that, at the 128−bit quantum-security level, the proving party only needs about 3% of the original protocol cost, while the verifying party’s effort is fully reduced to comparison operations. Lastly, we also apply our delegation schemes to decrease the computational cost of the decryption step for the NIST postquantum standardization candidate SIKE.