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Bootstrapping is a technique, originally due to Gentry (STOC 2009), for " refreshing " ciphertexts of a somewhat homomorphic encryption scheme so that they can support further homomorphic operations. To date, bootstrapping remains the only known way of obtaining fully homomorphic encryption for arbitrary unbounded computations. Over the past few years,… (More)

Gentry's " bootstrapping " technique (STOC 2009) constructs a fully homomorphic encryption (FHE) scheme from a " somewhat homomorphic " one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Unfortunately, bootstrap-ping is computationally very expensive, despite the great deal… (More)

We initiate the study of security for key-dependent messages (KDM), sometimes also known as " circular " or " clique " security, in the setting of identity-based encryption (IBE). Circular/KDM security requires that ciphertexts preserve secrecy even when they encrypt messages that may depend on the secret keys, and arises in natural usage scenarios for IBE.… (More)

The Learning with Rounding (LWR) problem was first introduced by Banerjee, Peikert, and Rosen (Eurocrypt 2012) as a de-randomized form of the standard Learning with Errors (LWE) problem. The original motivation of LWR was as a building block for constructing efficient, low-depth pseudorandom functions on lattices. It has since been used to construct… (More)

We present a lattice-based stateless signature scheme provably secure in the standard model. Our scheme has a constant number of matrices in the public key and a single lattice vector (plus a tag) in the signatures. The best previous lattice-based encryption schemes were the scheme of Ducas and Micciancio (CRYPTO 2014), which required a logarithmic number… (More)

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