Fully Homomorphic Encryption over the Integers with Shorter Public Keys

نویسندگان

  • Jean-Sébastien Coron
  • Avradip Mandal
  • David Naccache
  • Mehdi Tibouchi
چکیده

At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme over the integers. The main appeal of this scheme (compared to Gentry’s) is its conceptual simplicity. This simplicity comes at the expense of a public key size in Õ(λ) which is too large for any practical system. In this paper we reduce the public key size to Õ(λ) by encrypting with a quadratic form in the public key elements, instead of a linear form. We prove that the scheme remains semantically secure, based on a stronger variant of the approximate-GCD problem, already considered by van Dijk et al. We also describe the first implementation of the resulting fully homomorphic scheme. Borrowing some optimizations from the recent Gentry-Halevi implementation of Gentry’s scheme, we obtain roughly the same level of efficiency. This shows that fully homomorphic encryption can be implemented using simple arithmetic operations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Improved Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Fully homomorphic encryption (FHE) is a “holy grail” of cryptography. However, it is not yet adopted in practice because no known scheme is efficient. In this paper, we mainly focus on how to reduce the public key sizes in FHE. Based on Dijk et al.’s FHE scheme (DGHV) and Gentry’s fully homomorhpic technology, we propose two schemes with shorter public keys by encrypting with a combination of t...

متن کامل

Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes

We present a fully homomorphic encryption scheme which has both relatively small key and ciphertext size. Our construction follows that of Gentry by producing a fully homomorphic scheme from a “somewhat” homomorphic scheme. For the somewhat homomorphic scheme the public and private keys consist of two large integers (one of which is shared by both the public and private key) and the ciphertext ...

متن کامل

Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

We describe a compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan’s (DGHV) fully homomorphic scheme over the integers from Õ(λ) to Õ(λ). Our variant remains semantically secure, but in the random oracle model. We obtain an implementation of the full scheme with a 10.1 MB public key instead of 802 MB using similar parameters as in [7]. Additional...

متن کامل

Accelerating Fully Homomorphic Encryption over the Integers with Super-size Hardware Multiplier and Modular Reduction

A fully homomorphic encryption (FHE) scheme is envisioned as being a key cryptographic tool in building a secure and reliable cloud computing environment, as it allows arbitrarily evaluation of a ciphertext without revealing the plaintext. However, existing FHE implementations remain impractical due to their very high time and resource costs. Of the proposed schemes that can perform FHE to date...

متن کامل

Batch Fully Homomorphic Encryption over the Integers

We extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) into a batch fully homomorphic encryption scheme, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintexts as a single ciphertext. We present two variants in which the semantic security is based on different assumptions. The first variant is based on a new decisio...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011