Code-based public-key encryption schemes (PKE) are the candidates for post-quantum cryptography, since they are believed to resist the attacks using quantum algorithms. The most famous such schemes are the McEliece encryption and the Niederreiter encryption. In this paper, we present the zero-knowledge (ZK) proof systems for proving statements about data encrypted using these schemes. Specifically, we present a proof of plaintext knowledge for both PKE's, and also a verifiable McEliece PKE. The main ingredients of our constructions are the ZK identification schemes by Stern from Crypto'93 and by Jain, Krenn, Pietrzak, and Tentes from Asiacrypt'12.
Code-based public-key encryption schemes (PKE) are the candidates for post-quantum cryptography, since they are believed to resist the attacks using quantum algorithms. The most famous such schemes are the McEliece encryption and the Niederreiter encryption. In this paper, we present the zero-knowledge (ZK) proof systems for proving statements about data encrypted using these schemes. Specifically, we present a proof of plaintext knowledge for both PKE's, and also a verifiable McEliece PKE. The main ingredients of our constructions are the ZK identification schemes by Stern from Crypto'93 and by Jain, Krenn, Pietrzak, and Tentes from Asiacrypt'12.
The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail to hold since, in the quantum setting, the concept of rewinding is not generally applicable. Moreover, known classical techniques that avoid rewinding have various shortcomings in the quantum setting. We propose new techniques for building quantum zero-knowledge (QZK) protocols, which remain secure even under (active) quantum attacks. We obtain computational QZK proofs and perfect QZK arguments for any NP language in the common reference string model. This is based on a general method converting an important class of classical honest-verifier ZK (HVZK) proofs into QZK proofs. This leads to quite practical protocols if the underlying HVZK proof is efficient. These are the first proof protocols enjoying these properties, in particular the first to achieve perfect QZK. As part of our construction, we propose a general framework for building unconditionally hiding (trapdoor) string commitment schemes, secure against quantum attacks, as well as concrete instantiations based on specific (believed to be) hard problems. This is of independent interest, as these are the first unconditionally hiding string commitment schemes withstanding quantum attacks. Finally, we give a partial answer to the question whether QZK is possible in the plain model. We propose a new notion of QZK, non-oblivious verifier QZK, which is strictly stronger than honest-verifier QZK but weaker than full QZK, and we show that this notion can be achieved by means of efficient (quantum) protocols.
In the quantum era, the advent of quantum computers poses significant threats to the security of current cryptosystems. Therefore, designing quantum-resistant cryptoschemes becomes important to guarantee information security. This work concentrates on the development of the post-quantum public key encryption (PKE) scheme. Non-commutative cryptography (NCC) has entered the field of post-quantum cryptography. We utilize the TSPEM problem with asymmetric structures (which serve as a potential candiate for resisting quantum attacks) to construct two PKE schemes which are demonstrated to be CPA security under the DTSPEM assumption. By representing the plaintext as a matrix, these schemes can effectively encrypt a significant amount of information in a single operation. Assuming an equal amount of messages for encryption, the proposed schemes acheive superior efficiency compared to existing PKE schemes. Structurally, our systems exhibit a level of synchronization and coexistence due to the distinct public keys $ (P) $ and ciphertexts $ (C_{1}) .Theefficiencyanalysisisconductedbycomparingknownschemesfromtheaspectofspecificcryptographicindicators.Generally,theproposedonesofferseveraladvantagesincludingprovablesecurity,highefficiency,potentialquantum−resistant,andrelativeeaseofimplementation;alongwithsynchronizationandcoexistence.OurinvestigationhasestablishedthefeasibilityofconstructingPKEschemesbasedontheTSPEMproblem,specificallyforasymmetriccommunicationscenarios.ThepreliminaryresultspavethewayforfurtherexplorationoftheTSPEMproblem ' $s potential in developing other cryptosystems suitable for quantum computing environments.
Lattice-based cryptography is one of the most promising candidates for designing post-quantum cryptographic algorithms that resist emerging quantum computing attacks. The recent NIST PQC standardization process is nearing its completion, with practical lattice-based algorithms for basic cryptographic functionalities (namely digital signature and public-key encryption) selected for standardization in the near future. However, practical lattice-based solutions for more advanced privacy-preserving protocols, in particular, Zero-Knowledge Proofs (ZKPs), have only emerged recently and are an active area of research. We discuss some recent developments in design and analysis of practical lattice-based post-quantum ZKPs and their applications. In particular, we review some challenges that arise in designing ZKPs in the lattice setting and some recent progress on efficient lattice-based Schnorr-like proofs for important relations, such as binary/range proofs, one-out-of-many proofs and rounding proofs [1, 2, 4]. We discuss applications and optimization of such proof systems as building blocks for practical advanced cryptographic protocols such as ring signatures and balance proofs for privacy-preserving cryptocurrency payment protocols [2, 3]. We also discuss our recent work on succinct designated-verifier ZKPs (DV-ZKSNARKS) for verifying correctness of general delegated computations [5].
A concept named induced trapdoor one-way quantum transformation (OWQT) has been introduced, and a theoretical framework of public-key encryption (PKE) of quantum message is presented based on it. Then several kinds of quantum public-key encryption (QPKE) protocols, such as quantum version PKE of RSA, ElGamal, Goldwasser-Micali, elliptic curve, McEliece, Niederreiter and Okamoto-Tanaka-Uchiyama, are given within this framework. Though all of these protocols are only computationally secure, the last three are probably secure in post-quantum era. Besides, theoretical frameworks for public-key authentication and signature of quantum message are also given based on the induced trapdoor OWQT. As examples, a public-key authentication protocol of quantum message based on SN-S authentication scheme and two quantum digital signature protocols based on RSA and McEliece algorithms respectively are presented.
This thesis considers cryptographic systems that use public key encryption (PKE) as a building block in a larger system. We call these cryptosystems and develop a framework for describing such protocols that provides a clear way of describing the role of PKE in the PKE-hybrid protocol. By clarifying and generalizing the role of PKE in such protocols, we are able to state and prove a powerful lemma for proving the security of PK-hybrid protocols. We then show how this lemma can be used in a proof of security for the standard technique of hybrid encryption, substantially simplifying earlier proofs by Cramer and Shoup and by Abe, et al. In addressing these protocols we make improvements to a previously published protocol for Generalized Non-Interactive Oblivious Transfer (GNIOT) due to Gunupudi and Tate, and use our new security framework to correct a subtle error in the original security proof provided for GNIOT.
This work is focused on the description of one verifiable encryption scheme, specifically a zero-knowledge proof of knowledge protocol. Verifiable encryption allows us to prove properties of data without revealing its content. The main goal of the presented method is verification of knowledge of a secret key. This method can be used for group signa- tures, multiple steps secret sharing, key escrow protocols, and many others cryptographic protocols. It is based on the hardness of the Ring-LWE problem and problems of finding solutions to linear relations over some ring. It uses the principle of rejection sampling. The method is build on two closely described cryptographic protocols, Ring-LWE and Fiat-Shamir with aborts. It uses the construction of polynomial rings R = Z[x]/(xn + 1) a Rq = Zq[x]/(xn + 1). 1