R-LWE-Based distributed key generation and threshold decryption

Ever since the appearance of quantum computers, prime factoring and discrete logarithm based cryptography has been put in question, giving birth to the so called post-quantum cryptography. The most prominent field in post-quantum cryptography is lattice-based cryptography, protocols that are proved to be as difficult to break as certain difficult lattice problems like Learning With Errors (LWE) or Ring Learning With Errors (RLWE). Furthermore, the application of cryptographic techniques to different areas, like electronic voting, has also seen to a great interest in distributed cryptography. In this work we will give two original threshold protocols based in the lattice problem RLWE: one for key generation and one for decryption. We will prove them both correct and secure under the assumption of hardness of some well-known lattice problems and we will give a rough implementation of the protocols in C to give some tentative results about their viability.Peer ReviewedPostprint (published version

Revisiting Proxy Re-Encryption: Forward Secrecy, Improved Security, and Applications

We revisit the notion of proxy re-encryption (PRE), an enhanced public-key encryption primitive envisioned by Blaze et al. (Eurocrypt\u2798) and formalized by Ateniese et al. (NDSS\u2705) for delegating decryption rights from a delegator to a delegatee using a semi-trusted proxy. PRE notably allows to craft re-encryption keys in order to equip the proxy with the power of transforming ciphertexts under a delegator\u27s public key to ciphertexts under a delegatee\u27s public key, while not learning anything about the underlying plaintexts. We study an attractive cryptographic property for PRE, namely that of forward secrecy. In our forward-secret PRE (fs-PRE) definition, the proxy periodically evolves the re-encryption keys and permanently erases old versions while the delegator\u27s public key is kept constant. As a consequence, ciphertexts for old periods are no longer re-encryptable and, in particular, cannot be decrypted anymore at the delegatee\u27s end. Moreover, delegators evolve their secret keys too, and, thus, not even they can decrypt old ciphertexts once their key material from past periods has been deleted. This, as we will discuss, directly has application in short-term data/message-sharing scenarios. Technically, we formalize fs-PRE. Thereby, we identify a subtle but significant gap in the well-established security model for conventional PRE and close it with our formalization (which we dub fs-PRE^+). We present the first provably secure and efficient constructions of fs-PRE as well as PRE (implied by the former) satisfying the strong fs-PRE^+ and PRE^+ notions, respectively. All our constructions are instantiable in the standard model under standard assumptions and our central building block are hierarchical identity-based encryption (HIBE) schemes that only need to be selectively secure