A Lattice-Based Public-Key Cryptosystem
نویسندگان
چکیده
Ajtai recently found a random class of lattices of integer points for which he could prove the following worst-case/average-case equivalence result: If there is a probabilistic polynomial time algorithm which nds a short vector in a random lattice from the class, then there is also a probabilistic polynomial time algorithm which solves several problems related to the shortest lattice vector problem (SVP) in any n-dimensional lattice. Ajtai and Dwork then designed a public-key cryptosystem which is provably secure unless the worst case of a version of the SVP can be solved in probabilistic polynomial time. However, their cryptosystem suuers from massive data expansion because it encrypts data bit-by-bit. Here we present a public-key cryptosystem based on similar ideas, but with much less data expansion.
منابع مشابه
QTRU: quaternionic version of the NTRU public-key cryptosystems
In this paper we will construct a lattice-based public-key cryptosystem using non-commutative quaternion algebra, and since its lattice does not fully fit within Circular and Convolutional Modular Lattice (CCML), we prove it is arguably more secure than the existing lattice-based cryptosystems such as NTRU. As in NTRU, the proposed public-key cryptosystem relies for its inherent securi...
متن کاملEEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations
GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...
متن کاملA Lattice Based Public Key Cryptosystem Using Polynomial Representations
In Crypto 97, a public key cryptosystem based on the closest vector problem was suggested by Goldreich, Goldwasser and Halevi [4]. In this paper, we propose a public key cryptosystem applying representations of polynomials to the GGH encryption scheme. Its key size is much smaller than the GGH system so that it is a quite practical and efficient lattice based cryptosystem.
متن کاملCryptanalysis of the Cai-Cusick Lattice-based Public-key Cryptosystem
In 1998, Cai and Cusick proposed a lattice-based public-key cryptosystem based on the similar ideas of the Ajtai-Dwork cryptosystem, but with much less data expansion. However, they didn’t give any security proof. In our paper, we present an efficient ciphertext-only attack which runs in polynomial time against the cryptosystem to recover the message, so the Cai-Cusick lattice-based public-key ...
متن کاملImproving GGH Public Key Scheme Using Low Density Lattice Codes
Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based cryptosystem, proposed by McEliece. However, it has a number of drawbacks such as; large public key length and low security level. On the other hand, Low Densi...
متن کاملA Lattice - Based Cryptosystem and Proof of Knowledge on Its Secret Key
We propose a lattice-based cryptosystem by modifying the Regev’05 cryptosystem (STOC 2005), and design a proof of secret-key knowledge. Lattice-based public-key identification schemes have already been proposed, however, it is unknown that their public keys can be used for the public keys of encryption schemes. Our modification admits the proof of knowledge on its secret key, however, we need a...
متن کامل