Side-channel attacks are a major issue for implementation of secure cryptographic schemes. Among these, key-leakage attacks describe a scenario in which an adversary is allowed to learn arbitrary information about the private key, the only constraint being the number of bits learned. In this work, we study key-leakage resilience according to the model presented by Akavia, Goldwasser and Vaikuntanathan at TCC ’09. As our main contribution, we present a code-based hash proof system; we obtain our construction by relaxing some of the requirements from the original definition of Cramer and Shoup. We then propose a leakage-resilient public-key encryption scheme that makes use of this hash proof system. To do so, we adapt a framework featured in a previous work by Alwen et al. regarding identity-based encryption (EUROCRYPT ’10). Our construction features error-correcting codes as a technical tool, and, as opposed to previous work, does not require the use of a randomness extractor.