We give the first proof of security for an identity-based encryption scheme in the quantum random oracle model. This is the first proof of security for any scheme in this model that requires no additional assumptions. Our techniques are quite general and we use them to obtain security proofs for two random oracle hierarchical identity-based encryption schemes and a random oracle signature scheme, all of which have previously resisted quantum security proofs, even using additional assumptions. We also explain how to remove the extra assumptions from prior quantum random oracle model proofs. We accomplish these results by developing new tools for arguing that quantum algorithms cannot distinguish between two oracle distributions. Using a particular class of oracle distributions, so called semi-constant distributions, we argue that the aforementioned cryptosystems are secure against quantum adversaries.
We give the first proof of security for an identity-based encryption scheme in the quantum random oracle model. This is the first proof of security for any scheme in this model that requires no additional assumptions. Our techniques are quite general and we use them to obtain security proofs for two random oracle hierarchical identity-based encryption schemes and a random oracle signature scheme, all of which have previously resisted quantum security proofs, even using additional assumptions. We also explain how to remove the extra assumptions from prior quantum random oracle model proofs. We accomplish these results by developing new tools for arguing that quantum algorithms cannot distinguish between two oracle distributions. Using a particular class of oracle distributions, so called semi-constant distributions, we argue that the aforementioned cryptosystems are secure against quantum adversaries.
We give the first proof of security for an identity-based encryption (IBE) scheme in the quantum random oracle model. This is the first proof of security for any scheme in this model that does not rely on the assumed existence of so-called quantum-secure pseudorandom functions (PRFs). Our techniques are quite general and we use them to obtain security proofs for two random oracle hierarchical IBE schemes and a random oracle signature scheme, all of which have previously resisted quantum security proofs, even assuming quantum-secure PRFs. We also explain how to remove quantum-secure PRFs from prior quantum random oracle model proofs. We accomplish these results by developing new tools for arguing that quantum algorithms cannot distinguish between two oracle distributions. Using a particular class of oracle distributions that we call semi-constant distributions, we argue that the aforementioned cryptosystems are secure against quantum adversaries.
Recent developments in quantum computers pose an imminent threat to cryptography since many widely used cryptographic schemes will no longer be secure. This worrisome scenario motivated a growing interest in the field of post-quantum cryptography, which aims to design cryptosystems that are postquantum secure, i.e. secure against quantum-capable adversaries. While finding post-quantum computational hardness assumptions is pivotal to achieve this goal, an issue that is often overlooked is provable security. In fact, to prove that the post-quantum computational hardness necessarily implies post-quantum security of the derived cryptosystem, the reduction argument that establishes this implication also needs to be post-quantum. As such, many new methods have been devised in the last few years to handle this adaptation to the quantum setting. In particular, the quantum analogue of the Random Oracle Model has garnered special interest, as it is the foundation of many cryptographic schemes, from public-key encryption to digital signatures. It is also very problematic and usually the main culprit of the failure of security proofs when transitioning to the quantum setting. This work offers a comprehensive exposition on the most influential techniques developed in the last decade to enable or facilitate the construction of security proofs in the Quantum Random Oracle Model (QROM). Each presented technique offers an unique purpose and a solution to a problem provoked by the QROM, and, as such, as a whole, this works allows for an understanding of the most common strategies to construct these type of security proofs. This is accomplished by presenting and analyzing the security proof of three cryptographic schemes set in this model, which underlines the central role these techniques take in provable quantum security.
With the development of quantum computation, quantum computers will break the almost classical cryptography. It is imminent to design post-quantum cryptography algorithm that could resist quantum adversaries. Lattice-based problem has been verified that could resist quantum attacks. Our goal is to design a signature and try to prove it is secure in the quantum random oracle model. Our new signature scheme is redesigned based on the signature proposed by Lyu, but that scheme only proved secure in the random oracle model. The difference between the two signature is that we introduce the middle-product operation. So our signature is based on middle-product LWE hard assumption, which enjoys a security proof from PL WE. Then we combine the secure chameleon hash function and our new scheme, prove that our new combined signature is still secure in the quantum random oracle model.
In Asiacrypt 2003, Al-Riyami and Paterson proposed the notion of certificateless cryptography, a technique to remove key escrow from traditional identity-based cryptography as well as circumvent the certificate management problem of traditional public key cryptography.Subsequently much research has been done in the realm of certificateless encryption and signature schemes, but little to no work has been done for the identification primitive until 2013 when Chin et al. rigorously defined certificateless identification and proposed a concrete scheme.However Chin et al.'s scheme was proven in the random oracle model and Canetti et al. has shown that certain schemes provable secure in the random oracle model can be insecure when random oracles are replaced with actual hash functions.Therefore while having a proof in the random oracle model is better than having no proof at all, a scheme to be proven in the standard model would provide stronger security guarantees.In this paper, we propose the first certificateless identification scheme that is both efficient and show our proof of security in the standard model, that is without having to assume random oracles exist.
This paper investigates a Hierarchical Identity Based Encryption () scheme, with emphasis on the construction of D. Cash, D. Hofheinz, E. Kiltz, and Ch. Peikert. The scheme is founded on -ary lattices and its security relies on the hardness of the Learning With Errors () problem, which is regarded as resistant to all known quantum algorithms. We propose a modified variant of the original design and provide a formal security analysis in the random oracle model, confirming that the modification preserves its theoretical guarantees. The central contribution of the study, however, lies in the implementation. We evaluate the scheme with respect to correctness, execution time, and computational overhead, offering a concrete assessment of its efficiency and scalability. The results show that the modified scheme combines post-quantum security with practical performance, making it a compelling candidate for applications that require hierarchical key management in a quantum aware environment.
With the rapid advance in quantum computing, quantum security is now an indispensable property for any cryptographic system. In this paper, we study how to prove the security of a complex cryptographic system in the quantum random oracle model. We first give a variant of Zhandry’s compressed quantum random oracle (CStO), called compressed quantum random oracle with adaptive special points (CStOs). Then, we extend the on-line extraction technique of Don et al (EUROCRYPT’22) from CStO to CStOs. We also extend the random experiment technique of Liu and Zhandry (CRYPTO’19) for extracting the CStO query that witnesses the future adversarial output. With these preparations, a systematic security proof in the quantum random oracle model can start with a random CStO experiment (that extracts the witness for the future adversarial output) and then convert this game to one involving CStOs. Next, the on-line extraction technique for CStOs can be applied to extract the witness for any on-line commitment. With this strategy, we give a security proof of our recent compact multi-signature framework that is converted from any weakly secure linear ID scheme. We also prove the quantum security of our recent lattice realization of this linear ID scheme, by iteratively applying the weakly collapsing protocol technique of Liu and Zhandry (CRYPTO 2019). Combining these two results, we obtain the first quantum security proof for a compact multi-signature.