Improved identity-based identification using correcting codes

ArXiv, 2020

In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the NP-completeness of R-SDP, via a reduction from the canonical SDP, and describe how information set decoding algorithms can be adapted to solve this new problem. We study the properties of random codes under this new decoding perspective (in the fashion of traditional coding theory results), in order to derive the conditions upon which R-SDP has a unique solution with overwhelming probability. As a concrete application, we describe how Zero-Knowledge Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to compact public keys as well as significantly reduced communication costs. Thus, these schemes offer an improved basis for the construction of code-based digital signature schemes derived from identification sc...

2005

Two identification schemes based on the Maurer-Yacobi ID-based cryptosystem are analysed and shown to suffer from serious security problems.

IEE Proceedings - Communications, 2005

Two identification schemes based on the Maurer-Yacobi ID-based cryptosystem are analysed and shown to suffer from serious security problems.

In 2008, Chin et al. proposed an efficient and provable secure identity-based identification scheme in the standard model. However, we discovered a subtle flaw in the security proof which renders the proof of security useless. While no weakness has been found in the scheme itself, a scheme that is desired would be one with an accompanying proof of security. In this paper, we provide a fix to the scheme to overcome the problem without affecting the efficiency as well as a new proof of security. In particular, we show that only one extra pre-computable pairing operation should be added into the commitment phase of the identification protocol to fix the proof of security under the same hard problems.

We present an efficient and provable secure identity-based identification scheme in the standard model. Our proposed scheme is secure against impersonation under passive attack based on the Computational Diffie-Hellman assumption, and secure under active and concurrent attacks based on the One-More Computational Diffie-Hellman assumption.

In their seminal work for identity-based identification (IBI) schemes in 2004, Bellare et al. left open the question of whether the Beth identification scheme, and consequently the derived IBI scheme, can be proven secure against active and concurrent attackers. In 2008, Crescenzo answered the question in the positive by presenting a modified version of the Beth identification scheme as well as the corresponding derived IBI scheme. In this paper, we show that while the modified version of the Beth identification scheme proposed by Crescenzo is secure, an attack exists on the corresponding Beth-IBI scheme.

An identification scheme allows one party to prove himself or herself (the prover) to another party (the verifier) without revealing any information regarding his or her secret. The traditional public key cryptography setting utilizes certificates to bind a user with his public key, but certificate management has since become a problem on its own. An identity-based identification scheme does away with the certificate management problem by binding a user's public key to his or her identity string. In this paper, we present a k-resilient identity-based identification (IBI) scheme. We provide a reductionist proof of security approach to prove that our scheme is secure up to k-number of passive malicious attackers by assuming the discrete logarithm problem is intractable. Our proof of security is in the standard model -we do not assume that random oracles exist.

Journal of Cryptology, 2009

This paper provides either security proofs or attacks for a large number of identity-based identification and signature schemes defined either explicitly or implicitly in existing literature. Underlying these is a framework that on the one hand helps explain how these schemes are derived, and on the other hand enables modular security analyses, thereby helping to understand, simplify and unify previous work. We also analyze a generic folklore construction that in particular yields identity-based identification and signature schemes without random oracles.

Communications in Computer and Information Science, 2009

We present a new type of Identity-Based Identification (IBI), namely Fuzzy Identity-Based Identification (FIBI). FIBI is an extension of traditional IBI where the identity (ID) is viewed as a set of values. In FIBI, identification is considered successful if and only if the ID set presented by the prover overlaps the verifier's ID set for certain distance metric d. The proposed scheme is secure against impersonation under passive attack based on the discrete logarithm assumption, and is secure against concurrent attack based on the one-more discrete logarithm assumption. We provide the security proof in the fuzzy selective-ID security model.

2011

In this paper we present efficient implementations of several code-based identification schemes, namely the Stern scheme, the Veron scheme and the Cayrel-Veron-El Yousfi scheme. For a security of 80 bits, we obtain a signature in respectively 1.048 ms, 0.987 ms and 0.594 ms.

Lecture Notes in Computer Science, 1998

Signature schemes that are derived from three move identification schemes such as the Fiat-Shamir, Schnorr and modified E1Gamal schemes axe a typical class of the most practical signature schemes. The random oracle paradigm [1, 2, 12] is useful to prove the security of such a class of signature schemes [4, 12]. This paper presents a new key technique, "ID reduction", to show the concrete security result of this class of signature schemes under the random oracle paradigm. First, we apply this technique to the Schnorr and modified E1Gamal schemes, and show the "concrete security analysis" of these schemes. We then apply it to the multi-signature schemes.

Advances in Cryptology — CRYPTO’ 92

This paper presents a three-move interactive identification scheme and proves it to be as secure as t h e discrete logarithm problem. This provably secure scheme is almost as efficient as t,he Schnorr identification scheme, while the Schnorr scheme is not provably secure. This paper also presents another practical identification scheme which is proven to be as secure as the factoring problem arid is almost as efficient as the Guillou-Quisquater identification scheme: the Guillou-Quisquater scheme is not provably secure. We &so propose practical digital signature schemes based on these identification schemes. T h e signature schemes are almost as efficient as the Schnorr and Giiillou-Quisquater signature schemes, while the securit.y assumptions of our signature schemes are weaker than those of the Schnorr and Guillou-Quisquater.signature schemes. This paper also gives a theoretically generalized result: a threemove identification scheme can be constructed which is a s secure as the random-self-reducible problem. Moreover, this paper proposes a variant which is proven to be a s secure as the difficulty of solving both the discrete logarithm problem and the specific factoring problem simultaneously. Some other variants such as an identity-based variant and an elliptic curve variant are also proposed.

Hierarchical identity-based cryptography was introduced with the purpose of reducing the burden of a single Private Key Generator (PKG) and to limit damage to only domains whose lower-level PKGs are compromised. However, until now only security models and concrete schemes for hierarchical identity-based encryption and signature schemes are found in literature. In this paper, we propose the initial idea for hierarchical identity-based identification (HIBI) schemes. We provide the formal definition and security model for HIBI schemes and then proceed to propose a concrete HIBI scheme secure against passive attacks in the random oracle model under the Computational Diffie-Hellman assumption. We also prove the HIBI scheme secure against active and concurrent attacks in the random oracle model under the One-More Computational Diffie-Hellman assumption.

There are a lot of papers on cryptography implementation but mostly on encryption and signature schemes.

In 2010, proposed an identity-based identification (IBI) scheme in the standard model which was resilient to a coalition of attackers conspiring together to break the scheme. They argued that the scheme was desirable due to its proof in the standard model, which is still rare in existing literature. Also desirable was that the proposed scheme was designed without bilinear pairings, which costs greatly in terms of operation costs, thereby allowing the scheme to run more efficiently. However, the proof of security for the proposed scheme was only against impersonation under passive attacks, where the adversary is only allowed to eavesdrop on conversations between honest parties during the identification protocol. In this paper, we upgrade the security proof to prove that the scheme is also secure against impersonation under active and concurrent attacks, showing that the scheme is still secure even if the adversary is to interact with honest parties during the attack.