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- Jacob Alperin-Sheriff, Chris Peikert
- CRYPTO
- 2014

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)

- Jacob Alperin-Sheriff, Chris Peikert
- Public Key Cryptography
- 2012

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)

- Jacob Alperin-Sheriff, Chris Peikert
- IACR Cryptology ePrint Archive
- 2013

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)

- Jacob Alperin-Sheriff
- Public Key Cryptography
- 2015

- Benjamin Woodbury, BENJAMIN WOODBURY FULLER, +38 authors Abhishek Jain
- 2015

- Jacob Alperin-Sheriff, Daniel Apon
- IACR Cryptology ePrint Archive
- 2016

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)

- Jacob Alperin-Sheriff, Jintai Ding, Albrecht Petzoldt, Daniel Smith-Tone
- IACR Cryptology ePrint Archive
- 2017

- Jacob Alperin-Sheriff
- IACR Cryptology ePrint Archive
- 2014

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)

Today we prove the " full version " of Coppersmith's Theorem, stated here. Theorem 1.1. Let N be a positive integer and f (x) ∈ Z[x] be a monic, degree-d polynomial. There is an algorithm that, given N and f , efficiently (i.e., in time polynomial in the bit length of the inputs) finds all integers x 0 such that f (x 0) = 0 mod N and |x 0 | ≤ B ≈ N 1/d. In… (More)