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IEEE International Conference on Mobile Ad-Hoc and Sensor Systems (MASS)

A Quantum Diffie-Hellman Protocol

Pranav Subramaniam, Abhishek Parakh

Published Oct 1, 2014• 5 citations
Publisher

Abstract

In this paper, a quantum version of Diffie-Hellman key agreement protocol is developed using the commutative rotation transformations.
DOI
10.1109/mass.2014.89

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•Aug 19, 2020•0 citations
In this paper, a quantum version of Diffie-Hellman key agreement protocol is developed using the commutative rotation transformations. Qubits rotated by secret rotation angles and exchanged over a quantum channel are appropriately measured to form a secret shared key. Additional "slack" rotations are used to ensure that measurement of the commutative transformations always result in the same bit value, for legitimate party, in the absence of an eavesdropper. The performance of the quantum protocol is evaluated in terms of the number of exchanges needed for a given key size and the probability of detecting an eavesdropper.
In this paper, a quantum version of Diffie-Hellman key agreement protocol is developed using the commutative rotation transformations. Qubits rotated by secret rotation angles and exchanged over a quantum channel are appropriately measured to form a secret shared key. Additional 'slack' rotations are used to ensure that measurement of the commutative transformations always result in the same bit value, for legitimate party, in the absence of an eavesdropper. The performance of the quantum protocol is evaluated in terms of the number of exchanges needed for a given key size and the probability of detecting an eavesdropper. We also compare the proposed protocol with BB84.
We analyze the Commutative Supersingular Isogeny Diffie-Hellman protocol (CSIDH), a novel supersingular isogeny-based key establishment protocol. Our analysis is from three perspectives: \n \nQuantum Cryptanalysis. Building upon quantum attacks on ordinary isogeny-based cryptography, we propose a subexponential-time quantum algorithm for inverting the complex multiplication group action for supersingular elliptic curves, which uses only polynomial quantum space. This improves upon previously-known algorithms which required subexponential quantum space. \n \nOptimization. We develop more efficient algorithms for evaluating the class group action in the context of CSIDH. We consider "strategies"—formerly only considered for Supersingular Isogeny Diffie-Hellman (SIDH)—in the context of CSIDH, and develop systematic methods for optimizing "permutations" of the small primes used in CSIDH, which previously had been treated only in an ad hoc fashion. We also develop a systematic technique to optimize the CSIDH keyspace. These optimizations are complementary to prior work on optimizing CSIDH, including improved field arithmetic, Splitting Isogenies into Multiple Batches (SIMBA), and the two-point method. We apply our optimizations to the CSIDH-512 parameter set and give experimental results. \n \nFault Attacks. We consider physical attacks on static/ephemeral CSIDH in which limited information about which isogenies are "real" and which are "dummy" is revealed. We determine bounds on the number of fault injections required to recover the static secret key, and show that simply reordering the real and dummy isogenies from the ubiquitous "real-then-dummy" ordering to a dynamic random ordering dramatically increases the number of faults required, with negligible impact on the running time of the key exchange protocol (in contrast with prior fault attack countermeasures, which prevent fault attacks entirely at the cost of doubling the running time for key exchange).