Abstract
The Peregrine signature scheme is one of the candidates in the ongoing Korean post-quantum cryptography competition. It is proposed as a high-speed variant of Falcon, which is a hash-and-sign signature scheme over NTRU lattices and one of the schemes selected by NIST for standardization. To this end, Peregrine replaces the lattice Gaussian sampler in the Falcon signing procedure with a new sampler based on the centered binomial distribution. While this modification offers significant advantages in terms of efficiency and implementation, it does not come with a provable guarantee that signatures do not leak information about the signing key. Unfortunately, lattice based signature schemes in the hash-and-sign paradigm that lack such a guarantee (such as GGH, NTRUSign or DRS) have generally proved insecure.
In this paper, we show that Peregrine is no exception, by demonstrating a practical key recovery attack against it. We observe that the distribution of Peregrine signatures is a hidden transformation of some public distribution and still leaks information about the signing key. By adapting the parallelepiped-learning technique of Nguyen and Regev (Eurocrypt 2006), we show that the signing key can be recovered from a relatively small number of signatures. The learning technique alone yields an approximate version of the key, from which we can recover the exact key using a decoding technique due to Thomas Prest (PKC 2023).
For the reference implementation (resp. the official specification version) of Peregrine-512, we fully recover the secret key with good probability in a few hours given around 25,000 (resp. 11 million) signature samples.
