A new zero-knowledge code based identification scheme with reduced communication

Abstract

In this paper we present a new 5-pass identification scheme with asymptotic cheating probability 1 2 based on the syndrome decoding problem. Our protocol is related to the Stern identification scheme but has a reduced communication cost compared to previous code-based zeroknowledge schemes, moreover our scheme permits to obtain a very low size of public key and secret key. The contribution of this paper is twofold, first we propose a variation on the Stern authentication scheme which permits to decrease asymptotically the cheating probability to 1/2 rather than 2/3 (and very close to 1/2 in practice) but with less communication. Our solution is based on deriving new challenges from the secret key through cyclic shifts of the initial public key syndrome; a new proof of soundness for this case is given Secondly we propose a new way to deal with hashed commitments in zero-knowledge schemes based on Stern's scheme, so that in terms of communication, on the average, only one hash value is sent rather than two or three. Overall our new scheme has the good features of having a zero-knowledge security proof based on well known hard problem of coding theory, a small size of secret and public key (a few hundred bits), a small calculation complexity, for an overall communication cost of 19kb for authentication (for a 2 16 security) and a signature of size of 93kb (11.5kB) (for security 2 80 ), an improvement of 40% compared to previous schemes based on coding theory.

Improved Veron Identification and Signature Schemes in the Rank Metric

“…where the Stern protocol is converted from Hamming to rank metric and the function Π P,Q (see Section 3 above) is introduced, and from [5], where the cheating probability of the Veron protocol is improved from 2/3 to 1/2 using the double circulant technique in the Hamming metric. In [5], the intermediate challenge is a random parallel left rotation. To better exploit the rank metric properties, and to make it more difficult to guess the challenge for an attacker, we instead consider a random linear combination of all possible parallel left rotations.…”

“…2 into a signature scheme, to which we will refer to as Rank Veron Double Circulant (RVDC) Signature scheme, using a generalization of the Fiat-Shamir transform, introduced in [17]. The signature size of the scheme can be reduced by applying the commitment compression technique used in [5]. We will call the scheme resulting from this variation compressed Rank Veron Double Circulant (cRVDC) scheme.…”

Novel Trusted Hierarchy Construction for RFID Sensor–Based MANETs Using ECCs

“…After generating codes and a key pair, identification marks to nodes are assigned using Algorithm 1. The approach of Aguilar and others of the double-circulant protocol (DCP) for zero-knowledge code-based identification with reduced communication is modified with an encryption/decryption process [43].…”

An Improved Zero-knowledge Identification Scheme based on Quasi-Dyadic Codes

“…Fortunately, there are no quantum attacks known for code-based cryptosystems, which means these cryptosystems can possibly resist to a quantum computer. And code-based cryptosystems [2] are very fast and easy to implement compared to number theory based systems. The first code-based public key cryptographic system [3] was published by McEliece in 1978.…”

“…There has been a number of identification schemes proposed these years [2,[12][13][14][15]. In 1993, Stern [13] proposed the first zero-knowledge identification schemes based on hard problem from syndrome decoding.…”