Cold Boot Attacks on LUOV

Abstract

This research article assesses the feasibility of cold boot attacks on the lifted unbalanced oil and Vinegar (LUOV) scheme, a variant of the UOV signature scheme. This scheme is a member of the family of asymmetric cryptographic primitives based on multivariable polynomials over a finite field K and has been submitted as candidate to the ongoing National Institute of Standards and Technology (NIST) standardisation process of post-quantum signature schemes. To the best of our knowledge, this is the first time that this scheme is evaluated in this setting. To perform our assessment of the scheme in this setting, we review two implementations of this scheme, the reference implementation and the libpqcrypto implementation, to learn the most common in-memory private key formats and next develop a key recovery algorithm exploiting the structure of this scheme. Since the LUOV’s key generation algorithm generates its private components and public components from a 256-bit seed, the key recovery algorithm works for all the parameter sets recommended for this scheme. Additionally, we tested the effectiveness and performance of the key recovery algorithm through simulations and found the key recovery algorithm may retrieve the private seed when α = 0.001 (probability that a 0 bit of the original secret key will flip to a 1 bit) and β (probability that a 1 bit of the original private key will flip to a 0 bit) in the range { 0.001 , 0.01 , 0.02 , … , 0.15 } by enumerating approximately 2 40 candidates.