Proxy Re-Encryption and Re-Signatures from Lattices

Proxy re-encryption (PRE) and Proxy re-signature (PRS) were introduced by Blaze, Bleumer and Strauss [Eurocrypt ’98]. Basically, PRE allows a semi-trusted proxy to transform a ciphertext encrypted under one key into an encryption of the same plaintext under another key, without revealing the underlying plaintext. Since then, many interesting applications have been explored, and many constructions in various settings have been proposed, while PRS allows a semi-trusted proxy to transform Alice’s signature on a message into Bob’s signature on the same message, but the proxy cannot produce new valid signature on new messages for either Alice or Bob. Recently, for PRE related progress, Cannetti and Honhenberger [CCS ’07] defined a stronger notion – CCA-security and construct a bi-directional PRE scheme. Later on, several work considered CCA-secure PRE based on bilinear group assumptions. Very recently, Kirshanova [PKC ’14] proposed the first single-hop CCA1-secure PRE scheme based on learning with errors (LWE) assumption. For PRS related progress, Ateniese and Hohenberger [CCS’05] formalized this primitive and provided efficient constructions in the random oracle model. At CCS 2008, Libert and Vergnaud presented the first multi-hop uni-directional proxy re-signature scheme in the standard model, using assumptions in bilinear groups. In this work, we first point out a subtle but serious mistake in the security proof of the work by Kirshanova. This reopens the direction of lattice-based CCA1-secure constructions, even in the single-hop setting. Then we construct a single-hop PRE scheme that is proven secure in our new tag-based CCA-PRE model. Next, we construct the first multi-hop PRE construction. Lastly, we also construct the first PRS scheme from lattices that is proved secure in our proposed unified security model.