Paper 2026/544 Original: eprint.iacr.org/2026/544 ↗

HARE: Compact HQC via Distance-Informed Erasure Decoding

Abstract

We present HARE, a key encapsulation mechanism (KEM) scheme based on the Hamming Quasi-Cyclic (HQC) framework that achieves substantially reduced public key and ciphertext sizes. HARE focuses on two complementary techniques: a novel distance-informed erasure decoding method for the concatenated code and ciphertext compression based on covering codes. The distance-informed erasure decoding method uses distance information from the inner Reed-Muller decoder to identify unreliable local blocks and treats them as erasures for the outer Reed-Solomon decoder.This improves decoding performance and enables more compact code parameters. For ciphertext compression, HARE adopts a covering-code perspective and maps the ciphertext vector to a nearby codeword with a shorter representation. The use of the Kaikkonen-Rosendahl code provides a more favorable bandwidth trade-off than previously considered Hamming and Golay code constructions. Combining these techniques, HARE reduces the combined size of the public key and ciphertext by 15.4%, 14.8%, and 15.3% at NIST security categories 1, 3, and 5, respectively, compared with HQC.