IND-CCA-Secure Key Encapsulation Mechanism in the Quantum Random Oracle Model, Revisited

NTS-KEM is one of the 17 post-quantum public-key encryption (PKE) and key establishment schemes remaining in contention for standardization by NIST. It is a code-based cryptosystem that starts with a combination of the (weakly secure) McEliece and Niederreiter PKE schemes and applies a variant of the Fujisaki-Okamoto (Journal of Cryptology 2013) or Dent (IMACC 2003) transforms to build an IND-CCA secure key encapsulation mechanism (KEM) in the classical random oracle model (ROM). Such generic KEM transformations were also proven to be secure in the quantum ROM (QROM) by Hofheinz et al. (TCC 2017), Jiang et al. (Crypto 2018) and Saito et al. (Eurocrypt 2018). However, the NTS-KEM specification has some peculiarities which means that these security proofs do not directly apply to it.

Selective opening (SO) security is one of the most important securities of public key encryption (PKE) in a multi-user setting. Even though messages and random coins used in some ciphertexts are leaked, SO security guarantees the confidentiality of the other ciphertexts. Actually, it is shown that there exist PKE schemes which meet the standard security such as indistinguishability against chosen ciphertext attacks (IND-CCA security) but do not meet SO security against chosen ciphertext attacks. Hence, it is important to consider SO security in the multi-user setting. On the other hand, many researchers have studied cryptosystems in the security model where adversaries can submit quantum superposition queries (i.e., quantum queries) to oracles. In particular, IND-CCA secure PKE and KEM schemes in the quantum random oracle model have been intensively studied so far.

Code-based public key cryptosystems have been found to be an interesting option in the area of Post-Quantum Cryptography. In this work, we present a key encapsulation mechanism (KEM) using a parity check matrix of the Generalized Srivastava code as the public key matrix. Generalized Srivastava codes are privileged with the decoding technique of Alternant codes as they belong to the family of Alternant codes. We exploit the dyadic structure of the parity check matrix to reduce the storage of the public key. Our encapsulation leads to a shorter ciphertext as compared to DAGS proposed by Banegas et al. in Journal of Mathematical Cryptology which also uses Generalized Srivastava code. Our KEM provides IND-CCA security in the random oracle model. Also, our scheme can be shown to achieve post-quantum security in the quantum random oracle model.

We propose \(\mathsf {FO_\mathsf {AKE}}\), a generic construction of two-message authenticated key exchange (AKE) from any passively secure public key encryption (PKE) in the quantum random oracle model (QROM). Whereas previous AKE constructions relied on a Diffie-Hellman key exchange or required the underlying PKE scheme to be perfectly correct, our transformation allows arbitrary PKE schemes with non-perfect correctness. Dealing with imperfect schemes is one of the major difficulties in a setting involving active attacks. Our direct construction, when applied to schemes such as the submissions to the recent NIST post-quantum competition, is more natural than previous AKE transformations. Furthermore, we avoid the use of (quantum-secure) digital signature schemes which are considerably less efficient than their PKE counterparts. As a consequence, we can instantiate our AKE transformation with any of the submissions to the recent NIST competition, e.g., ones based on codes and lattices.

The post-quantum security of cryptographic schemes assumes that the quantum adversary only receives the classical result of computations with the secret key. Further, it is unknown whether the post-quantum secure schemes still remain secure if the adversary can obtain a superposition state of the results. In this paper, we formalize one class of public-key encryption schemes named oracle-masked schemes. Then we define the plaintext extraction procedure for those schemes and this procedure simulates the quantum-accessible decryption oracle with a certain loss. The construction of the plaintext extraction procedure does not need to take the secret key as input. Based on this property, we prove the IND-qCCA security of the Fujisaki-Okamoto (FO) transformation in the quantum random oracle model (QROM) and our security proof is tighter than the proof given by Zhandry (Crypto 2019). We also give the first IND-qCCA security proof of the REACT transformation in the QROM. Furthermore, our formalization can be applied to prove the IND-qCCA security of key encapsulation mechanisms with explicit rejection. As an example, we present the IND-qCCA security proof of $$\textsf {T}_{\textsf {CH}}$$ transformation, proposed by Huguenin-Dumittan and Vaudenay (Eurocrypt 2022), in the QROM.

We present a quantumly secure identity-based signature scheme based on the standard short integer solution problem, featuring tight security reductions in the quantum and classic random oracle models. The scheme has short signatures. Each signature contains a single lattice vector plus a single bit. Compared to the existing tightly secure, short lattice identity-based signature schemes by Pan and Wagner (PQCrypto’21), our scheme has a shorter signature size (around 30% shorter), stronger unforgeability, relies on a weaker assumption, and has detailed proof in the quantum random oracle model.

By a generic transformation by Canetti, Halevi, and Katz (CHK) every Identity-based encryption (IBE) scheme implies a chosen-ciphertext secure public-key encryption (PKE) scheme. In the same work it is claimed that this transformation maps the two existing IBE schemes to two new and different chosen-ciphertext secure encryption schemes, each with individual advantages over the other.In this work we reconsider one of the two specific instantiations of the CHK transformation (when applied to the “second Boneh/Boyen IBE scheme”). We demonstrate that by applying further simplifications the resulting scheme can be proven secure under a weaker assumption than the underlying IBE scheme.Surprisingly, our simplified scheme nearly converges to a recent encryption scheme due to Boyen, Mei, and Waters which itself was obtained from the other specific instantiation of the CHK transformation (when applied to the “first Boneh/Boyen IBE scheme”). We find this particularly interesting since the two underlying IBE schemes are completely different.The bottom line of this paper is that the claim made by Canetti, Halevi, and Katz needs to be reformulated to: the CHK transformation maps the two known IBE schemes to nearly one single encryption scheme.KeywordsEncryption SchemeMessage Authentication CodeChallenge CiphertextChoose Ciphertext AttackBilinear GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The famous Fiat-Shamir transformation turns any public-coin three-round interactive proof, i.e., any so-called sigma-protocol, into a non-interactive proof in the random-oracle model. We study this transformation in the setting of a quantum adversary that in particular may query the random oracle in quantum superposition. Our main result is a generic reduction that transforms any quantum dishonest prover attacking the Fiat-Shamir transformation in the quantum random-oracle model into a similarly successful quantum dishonest prover attacking the underlying sigma-protocol (in the standard model). Applied to the standard soundness and proof-of-knowledge definitions, our reduction implies that both these security properties, in both the computational and the statistical variant, are preserved under the Fiat-Shamir transformation even when allowing quantum attacks. Our result improves and completes the partial results that have been known so far, but it also proves wrong certain claims made in the literature. In the context of post-quantum secure signature schemes, our results imply that for any sigma-protocol that is a proof-of-knowledge against quantum dishonest provers (and that satisfies some additional natural properties), the corresponding Fiat-Shamir signature scheme is secure in the quantum random-oracle model. For example, we can conclude that the non-optimized version of Fish, which is the bare Fiat-Shamir variant of the NIST candidate Picnic, is secure in the quantum random-oracle model.

The Fujisaki-Okamoto (FO) conversion is a generic conversion to enhance a public key encryption scheme with security of one-way against chosen plaintext attacks (OW-CPA) to security of indistinguishable against adaptive chosen ciphertext attacks (IND-CCA) in the random oracle model. Existing works have shown that the FO conversion also can generically upgrade the security of the identity-based encryption (IBE) schemes or certificateless public key encryption (CL-PKE) schemes. However, it is still unknown if the same holds for certificate-based encryption (CBE) schemes. In this paper, we investigate the generic security of the CBE scheme obtained by applying the FO conversion to an arbitrary underlying OW-CBE-CPA secure CBE scheme and confirm that the FO conversion can generically convert any OW-CBE-CPA secure CBE into an IND-CBE-CCA secure CBE. We also note that the straightforward application of the FO conversion only leads to a CBE scheme with a loose reduction. To solve this problem, we propose an enhanced FO conversion which just introduces minor extra computation overhead, but results in considerably more efficient security reduction.

The concept of policy-based cryptography is a promising paradigm for trust establishment and authorization in largescale open environments like the Internet and Mobile Networks. It aims at providing a framework for performing cryptographic operations with respect to policies formalized as monotone Boolean expressions written in standard normal forms. A policy involves conjunctions and disjunctions of conditions where each condition is fulfilled by a digital credential representing the signature of a specific credential issuer on a set of statements about a certain entity. Therefore, an entity fulfills a policy if any only if it has been issued a set of credentials fulfilling the combination of conditions specified by the policy.In this work, we focus on policy-based encryption schemes which allow to encrypt a message according to a policy so that only entities fulfilling the policy are able to decrypt the message. More generally, policy-based encryption belongs to an emerging family of encryption schemes sharing the ability to integrate encryption with access control structures. This ability is mainly enabled by bilinear pairings over elliptic curves and allows for several interesting applications in different contexts.A policy-based encryption scheme has to fulfill two primary requirements: on one hand, provable security under well defined attack models. On the other hand, efficiency, especially when dealing with the conjunctions and disjunctions of credential-based conditions.The contributions of our research work are twofold:1. The standard acceptable notion of security for public-key encryption schemes is indistinguishability against chosen ciphertext attacks. Hence, it is natural to require that a policy-based encryption scheme also satisfies this strong notion of security. However, the definition of this security notion must be adapted to the policy-based setting. Our first contribution is the definition of policy-oriented security model for policy-based encryption schemes as well as the development of an efficient policy-based encryption scheme that is provably secure under our security model in the random oracle model.2. Policy-based encryption schemes may suffer from the key-escrow property i.e. in addition to the legitimate holder of the credentials fulfilling the encryption policy, any collusion of credential issuers who are able to issue a set of credentials fulfilling the policy can decrypt the message. Our second contribution is to address this issue through the notion of policy-based public-key encryption. The latter allows encrypting a message not only with respect to a policy but also according to a public-key so that only an entity fulfilling the policy and having access to the corresponding private-key is able to decrypt the message. We developed a policy-based public-key encryption scheme from bilinear pairings and proved its security under the corresponding security model. Our proposal improves related work in terms of both security and efficiency.

Liskov proposed several weakened versions of the random oracle model, called weakened random oracle models (WROMs), to capture the vulnerability of ideal compression functions, which are expected to have the standard security of hash functions, i.e., collision resistance, second-preimage resistance, and one-wayness properties. The WROMs offer additional oracles to break such properties of the random oracle. In this paper, we investigate whether public-key encryption schemes in the random oracle model essentially require the standard security of hash functions by the WROMs. In particular, we deal with four WROMs associated with the standard security of hash functions; the standard, collision tractable, second-preimage tractable, first-preimage tractable ones (ROM, CT-ROM, SPT-ROM, and FPT-ROM, respectively), done by Numayama et al. for digital signature schemes in the WROMs. We obtain the following results: (1) The OAEP is secure in all the four models. (2) The encryption schemes obtained by the Fujisaki-Okamoto conversion (FO) are secure in the SPT-ROM. However, some encryption schemes with FO are insecure in the FPT-ROM. (3) We consider two artificial variants wFO and dFO of FO for separation of the WROMs in the context of encryption schemes. The encryption schemes with wFO (dFO, respectively) are secure in the CT-ROM (ROM, respectively). However, some encryption schemes obtained by wFO (dFO, respectively) are insecure in the SPT-ROM (CT-ROM, respectively). These results imply that standard encryption schemes such as the OAEP and FO-based one do not always require the standard security of hash functions. Moreover, in order to make our security proofs complete, we construct an efficient sampling algorithm for the binomial distribution with exponentially large parameters, which was left open in Numayama et al.’s paper.

Many of the recent advanced lattice-based \(\varSigma \)-/public-coin honest verifier (HVZK) interactive protocols based on the techniques developed by Lyubashevsky (Asiacrypt’09, Eurocrypt’12) can be transformed into a non-interactive zero-knowledge (NIZK) proof in the random oracle model (ROM) using the Fiat-Shamir transform. Unfortunately, although they are known to be secure in the classical ROM, existing proof techniques are incapable of proving them secure in the quantum ROM (QROM). Alternatively, while we could instead rely on the Unruh transform (Eurocrypt’15), the resulting QROM secure NIZK will incur a large overhead compared to the underlying interactive protocol.

We study a scheme of Bai and Galbraith (CT-RSA’14), also known as TESLA. TESLA was thought to have a tight security reduction from the learning with errors problem (LWE) in the random oracle model (ROM). Moreover, a variant using chameleon hash functions was lifted to the quantum random oracle model (QROM). However, both reductions were later found to be flawed and hence it remained unresolved until now whether TESLA can be proven to be tightly secure in the (Q)ROM.

In this paper, we study the problem of secure integrating public key encryption with keyword search (PEKS) with public key data encryption (PKE). We argue the previous security model is not complete regarding keyword privacy and the previous constructions are secure only in the random oracle model. We solve these problems by first defining a new security model, then give a generic construction which is secure in the new security model without random oracles. Our construction is based on secure PEKS and tag-KEM/DEM schemes and achieves modular design. We also give some applications and extensions for our construction. For example, instantiate our construction with proper components, we have a concrete scheme without random oracles, whose performance is even competitive to the previous schemes with random oracles.

A leakage-resilient public-key encryption (PKE) scheme provides security even if an adversary obtains some information on the secret key. In recent years, much attention has been focused on designing provably secure PKE in the presence of key-leakage and almost all the constructions rely on an important building block namely hash proof system (HPS). However, in the setting of adaptive chosen-ciphertext attacks (CCA2), there are not many HPS-based leakage-resilient PKE schemes available. Moreover, most of them have an unsatisfactory leakage rate. In this study, the authors propose a new method of constructing leakage-resilient CCA2-secure PKE scheme from any tag-based strongly universal 2 HPS. The striking advantage of the authors scheme is the leakage rate, which is the best one among all known HPS-based indistinguishability key leakage CCA2-secure constructions. In particular, they present an instantiation under the n -linear assumption. In the cases of n = 1 (resp. n = 2), they actually obtain a decisional Diffie-Hellman (DDH)-based [resp. decisional linear (DLIN)-based] PKE scheme, where the leakage rate can be made to 1/4 (resp. 1/6). The authors DDH-based scheme achieves the best leakage rate among all known DDH-based (Cramer-Shoup-type) schemes. Their DLIN-based scheme is the first one that can achieve leakage of L /6 bits without pairing, where L is the length of the secret key.