This paper proposes a fast algorithm for computing multiplicative inverses in GF(2m) using normal bases. Normal bases have the following useful property: In the case that an element x in GF(2”‘) is… (More)

In a modern network system, data security technologies such as cryptosystems, signature schemes, etc., are indispensable for reliable data transmission. In particular, for a large-scale network,… (More)

In this paper we provide a new cryptographic primitive that generalizes several existing zero-knowledge proofs and show that if a languageL induces the primitive, then there exists a perfect… (More)

Informally, private information retrieval for k >= 1 databases (k-PIR) is an interactive scheme that enables a user to make access to (separated) k replicated copies of a database and privately… (More)

Private information retrieval for k ≥ 1 databases (denoted by (k, )-PIR for short) is a protocol that (1) a user sends an tuple query to each of k noncommunicating replicated databases; (2) each… (More)

Let N(d,d<sup>perp</sup>) denote the minimum length n of a linear code C with d and d<sup>perp</sup>, where d is the minimum Hamming distance of C and d<sup>perp</sup> is the minimum Hamming distance… (More)

A (k, δ, ε)-locally decodable code C : Fnq → F N q is an error-correcting code that encodes each message ~x = (x1, x2, . . . , xn) ∈ F n q to a codeword C(~x) ∈ F N q and has the following property:… (More)

A k-query locally decodable code (LDC) C : Σ n → Γ N encodes each message x into a codeword C(x) such that each symbol of x can be probabilistically recovered by querying only k coordinates of C(x),… (More)