Paper 2023/589

$\texttt{CryptographicEstimators}$: a Software Library for Cryptographic Hardness Estimation

Abstract

The estimation of the computational complexity of hard problems is essential for determining secure parameters for cryptographic systems. To date, those estimations are often performed in an ad-hoc manner. This led to a scattered landscape of available estimation scripts, with multiple scripts for the same problem with varying outputs. Overall, this complicates the task of reaching consensus on the hardness of cryptographic problems. Furthermore, for designers it makes it difficult to gather precise information on the concrete difficulty of the underlying problems. Especially in the light of the still ongoing NIST PQC standardization effort and the upcoming call for post-quantum secure digital signature schemes there is a pressing need for a reliable point of access for concrete security estimates. In this work we present the first open-source software library entirely dedicated to cryptographic hardness estimation, the $\texttt{CryptographicEstimators}$ library. In contrast to most previous estimators, this library follows a modern object-oriented software architecture, which provides a wide variety of features. Overall the design is optimized to ease extending existing estimators by new algorithms and makes it simple to integrate completely new estimators. In this work we further specify the algorithmic cost model underlying the estimators. In order to provide a starting point for the project, we gathered and integrated estimators for six different hardness assumptions, including the syndrome decoding problem, the multivariate quadratic problem, the code equivalence problem, the permuted kernel problem and different flavors thereof. In our effort of gathering those estimation scripts, we also normalized those estimates to fit into the cost model and to measure the same unit operations.