Fully Homomorphic Encryption with Polylog Overhead

Gentry, Craig; Halevi, Shai; Smart, Nigel P.

doi:10.1007/978-3-642-29011-4_28

Cited by 308 publications

(268 citation statements)

References 16 publications

(42 reference statements)

Supporting

Mentioning

263

Contrasting

Unclassified

Order By: Relevance

“…An implementation is described in [GHS12b] with an efficient (given the current state of knowledge) homomorphic evaluation of the full AES encryption circuit. The authors use the batch RLWE-based scheme proposed in [BGV12,GHS12a], that allows one to encrypt vectors of plaintexts in a single ciphertext and to perform any permutation on the underlying plaintext vector while manipulating only the ciphertext [SV11].…”

Section: Brakerski and Vaikuntanathan's Scheme Based On The Learning mentioning

confidence: 99%

“…As opposed to [BGV12,GHS12a], we cannot use an underlying algebraic structure to perform rotations over plaintext bits (clearly, the automorphisms of Z do not provide any useful action on ciphertexts). Instead we show how to perform arbitrary permutations on the plaintext vector during the ciphertext refresh operation at no additional cost (but with a slight increase of the public key size).…”

Section: Brakerski and Vaikuntanathan's Scheme Based On The Learning mentioning

confidence: 99%

See 1 more Smart Citation

Batch Fully Homomorphic Encryption over the Integers

Cheon

Coron²,

Kim

et al. 2013

Advances in Cryptology – EUROCRYPT 2013

221

137

View full text Add to dashboard Cite

Abstract. We extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) to batch fully homomorphic encryption, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintext bits as a single ciphertext. Our variant remains semantically secure under the (error-free) approximate-GCD problem. We also show how to perform arbitrary permutations on the underlying plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance: we describe an implementation of the fully homomorphic evaluation of AES encryption, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by Gentry et al. at Crypto 2012 for their implementation of a Ring-LWE based fully homomorphic encryption scheme.

show abstract

Section: Brakerski and Vaikuntanathan's Scheme Based On The Learning mentioning

confidence: 99%

Section: Brakerski and Vaikuntanathan's Scheme Based On The Learning mentioning

confidence: 99%

Batch Fully Homomorphic Encryption over the Integers

Cheon

Coron²,

Kim

et al. 2013

Advances in Cryptology – EUROCRYPT 2013

221

137

View full text Add to dashboard Cite

show abstract

“…HElib is built to provide an effective use of ciphertext-packing techniques [10], and in particular it provides the ability to view the multiple plaintext elements encrypted in a single ciphertext as an array and arbitrarily permute that array. However, it does not (yet) provide an interface to group several ciphertexts into a single larger array and permute that larger array.…”

Section: Methodsmentioning

confidence: 99%

Private Database Access with HE-over-ORAM Architecture

Gentry

Halevi

Jutla

et al. 2015

Applied Cryptography and Network Security

Self Cite

View full text Add to dashboard Cite

Enabling private database queries is an important and challenging research problem with many real-world applications. The goal is for the client to obtain the results of its queries without learning anything else about the database, while the outsourced server learns nothing about the queries or data, including access patterns. The secure-computation-over-ORAM architecture offers a promising approach to this problem, permitting sub-linear time processing of the queries (after pre-processing) without compromising security.In this work we examine the feasibility of this approach, focusing specifically on securecomputation protocols based on somewhat-homomorphic encryption (SWHE). We devised and implemented secure two-party protocols in the semi-honest model for the path-ORAM protocol of Stefanov et al. This provides access by index or keyword, which we extend (via pre-processing) to limited conjunction queries and range queries. Some of our sub-protocols may be interesting in their own right, such as our new protocols for encrypted comparisons and blinded permutations.We implemented our protocols on top of the HElib homomorphic encryption library. Our basic single-threaded implementation takes about 30 minutes to process a query on a database with 2 22 records and 120-bit long keywords, providing a cause for optimism about the viability of this direction, and we expect a better optimized implementation to be much faster.

show abstract

“…(3) The third category starts with Brakerski and Vaikuntanathan [BV11b,BV11a]. More variants appear in [NLV11,BGV12,GHS12b,Bra12,GSW13]. The security of these schemes are based on the learning with errors (LWE) and on the ring-learning with errors (RLWE) problems.…”

Section: Related Workmentioning

confidence: 99%

On Key Recovery Attacks Against Existing Somewhat Homomorphic Encryption Schemes

Chenal

Tang

2015

Progress in Cryptology - LATINCRYPT 2014

View full text Add to dashboard Cite

In this paper, we continue this line of research and show that most existing somewhat homomorphic encryption schemes are not IND-CCA1 secure. In fact, we show that these schemes suffer from key recovery attacks (stronger than a typical IND-CCA1 attack), which allow an adversary to recover the private keys through a number of decryption oracle queries. The schemes, that we study in detail, include those by Brakerski and Vaikuntanathan at Crypto 2011 and FOCS 2011, and that by Gentry, Sahai and Waters at Crypto 2013. We also develop a key recovery attack that applies to the somewhat homomorphic encryption scheme by van Dijk et al., and our attack is more efficient and conceptually simpler than the one developed by Zhang et al.. Our key recovery attacks also apply to the scheme by Brakerski, Gentry and Vaikuntanathan at ITCS 2012, and we also describe a key recovery attack for the scheme developed by Brakerski at Crypto 2012.

show abstract

Fully Homomorphic Encryption with Polylog Overhead

Cited by 308 publications

References 16 publications

Batch Fully Homomorphic Encryption over the Integers

Batch Fully Homomorphic Encryption over the Integers

Private Database Access with HE-over-ORAM Architecture

On Key Recovery Attacks Against Existing Somewhat Homomorphic Encryption Schemes

Contact Info

Product

Resources

About