International Association
for Cryptologic Research

In this paper, we study the design of efficient signature and public-key encryption (PKE) schemes in the presence of both leakage and tampering attacks. Firstly, we formalize the strong leakage and tamper-resilient (sLTR) security model for signature, which provides strong existential unforgeability, and deals with bounded leakage and restricted tampering attacks, as a counterpart to the sLTR security introduced by Sun et al. (ACNS 2019) for PKE. Then, we present direct constructions of signature and chosen-ciphertext attack (CCA) secure PKE schemes in the sLTR model, based on the matrix decisional Diffie-Hellman (MDDH) assumptions (which covers the standard symmetric external DH (SXDH) and k-Linear assumptions) over asymmetric pairing groups. Our schemes avoid the use of heavy building blocks such as the true-simulation extractable non-interactive zero-knowledge proofs (tSE-NIZK) proposed by Dodis et al. (ASIACRYPT 2010), which are usually needed in constructing schemes with leakage and tamper-resilience. Especially, our SXDH-based signature and PKE schemes are more efficient than the existing schemes in the leakage and tamper-resilient setting: our signature scheme has only 4 group elements in the signature, which is about 5×~8× shorter, and our PKE scheme has only 6 group elements in the ciphertext, which is about 1.3×~3.3× shorter. Finally, we note that our signature scheme is the {\it first} one achieving strong existential unforgeability in the leakage and tamper-resilient setting, where strong existential unforgeability has important applications in building more complex primitives such as signcryption and authenticated key exchange.

Proxy re-encryption (PRE) allows a proxy to transform a ciphertext intended for Alice (delegator) to another ciphertext intended for Bob (delegatee) without revealing the underlying message. Recently, a new variant of PRE, namely fine-grained PRE (FPRE), was proposed in [Zhou et al., Asiacrypt 2023]. Generally, FPRE is designed for a function family F: each re-encryption key rk_{A→B}^f is associated with a function f ∈ F, and with rk_{A→B}^f, a proxy can transform Alice's ciphertext encrypting m to Bob's ciphertext encrypting f(m). However, their scheme only supports single-hop re-encryption and achieves only CPA security. In this paper, we formalize {\it multi-hop} FPRE (mFPRE) that supports multi-hop re-encryptions in the fine-grained setting, and propose two mFPRE schemes achieving CPA security and stronger HRA security (security against honest re-encryption attacks), respectively. -- For multi-hop FPRE, we formally define its syntax and formalize a set of security notions including CPA security, HRA security, undirectionality and ciphertext unlinkablity. HRA security is stronger and more reasonable than CPA security, and ciphertext unlinkablity blurs the proxy relations among a chain of multi-hop re-encryptions, hence providing better privacy. We establish the relations between these security notions. -- Our mFPRE schemes support fine-grained re-encryptions for bounded linear functions and have security based on the learning-with-errors (LWE) assumption in the standard model. In particular, one of our schemes is HRA secure and enjoys all the aforementioned desirable securities. To achieve CPA security and HRA security for mFPRE, we extend the framework of [Jafargholi et al., Crypto 2017] and the technique of the [Fuchsbauer et al., PKC 2019].

In this paper, we construct the first password authenticated key exchange (PAKE) scheme from isogenies with Universal Composable (UC) security in the random oracle model (ROM). We also construct the first two PAKE schemes with UC security in the quantum random oracle model (QROM), one is based on the learning with error (LWE) assumption, and the other is based on the group-action decisional Diffie-Hellman (GA-DDH) assumption in the isogeny setting. To obtain our UC-secure PAKE scheme in ROM, we propose a generic construction of PAKE from basic lossy public key encryption (LPKE) and CCA-secure PKE. We also introduce a new variant of LPKE, named extractable LPKE (eLPKE). By replacing the basic LPKE with eLPKE, our generic construction of PAKE achieves UC security in QROM. The LPKE and eLPKE have instantiations not only from LWE but also from GA-DDH, which admit four specific PAKE schemes with UC security in ROM or QROM, based on LWE or GA-DDH.

Password Authenticated Key Exchange (PAKE) allows two parties to establish a secure session key with a shared low-entropy password $pw$. Asymmetric PAKE (aPAKE) extends PAKE in the client-server setting, and the server only stores a password file instead of the plain password so as to provide additional security guarantee when the server is compromised. In this paper, we propose a novel generic compiler from PAKE to aPAKE in the Universal Composable (UC) framework by making use of Key Encapsulation Mechanism (KEM) and Authenticated Encryption (AE). -- Our compiler admits efficient instantiations from lattice to yield lattice-based post-quantum secure aPAKE protocols. When instantiated with Kyber (the standardized KEM algorithm by the NIST), the performances of our compiler outperform other lattice-based compilers (Gentry et al. CRYPTO 2006) in all aspects, hence yielding the most efficient aPAKE compiler from lattice. In particular, when applying our compiler to the UC-secure PAKE schemes (Santos et al. EUROCRYPT 2023, Beguinet et al. ACNS 2023), we obtain the most efficient UC-secure aPAKE schemes from lattice. -- Moreover, the instantiation of our compiler from the tightly-secure matrix DDH (MDDH)-based KEM (Pan et al. CRYPTO 2023) can compile the tightly-secure PAKE scheme (Liu et al. PKC 2023) to a tightly-secure MDDH-based aPAKE, which serves as the first tightly UC-secure aPAKE scheme.

Anamorphic encryptions and anamorphic signatures assume a double key pre-shared between two parties so as to enable the transmission of covert messages. How to securely and efficiently distribute a double key under the dictator's surveillance is a central problem for anamorphic cryptography, especially when the users are forced to surrender their long-term secret keys or even the randomness used in the algorithms to the dictator. In this paper, we propose Anamorphic Authentication Key Exchange (AM-AKE) to solve the problem. Similar to anamorphic encryption, AM-AKE contains a set of anamorphic algorithms besides the normal algorithms. With the help of the anamorphic algorithms in AM-AKE, the initiator and the responder are able to exchange not only a session key but also a double key. We define robustness and security notions for AM-AKE, and also prove some impossibility results on plain AM-AKE whose anamorphic key generation algorithm only outputs a key-pair. To bypass the impossibility results, we work on two sides. -- On the one side, for plain AM-AKE, the securities have to be relaxed to resist only passive attacks from the dictator. Under this setting, we propose a generic construction of two-pass plain AM-AKE from a two-pass AKE with partially randomness-recoverable algorithms. -- On the other side, we consider (non-plain) AM-AKE whose key generation algorithm also outputs an auxiliary trapdoor besides the key-pairs. We ask new properties from AKE: its key generation algorithm has secret extractability and other algorithms have separability. Based on such a two-pass AKE, we propose a generic construction of two-pass (non-plain) AM-AKE. The resulting AM-AKE enjoys not only robustness but also the strong security against any dictator knowing both users' secret keys and even the internal randomness of the AKE algorithms and implementing active attacks. Finally, we present concrete AM-AKE schemes from the popular SIG+KEM paradigm and three-KEM paradigm for constructing AKE.

(Asymmetric) Password-based Authenticated Key Exchange ((a)PAKE) protocols allow two parties establish a session key with a pre-shared low-entropy password. In this paper, we show how Encrypted Key Exchange (EKE) compiler [Bellovin and Merritt, S&P 1992] meets tight security in the Universally Composable (UC) framework. We propose a strong 2DH variant of EKE, denoted by 2DH-EKE, and prove its tight security in the UC framework based on the CDH assumption. The efficiency of 2DH-EKE is comparable to the original EKE, with only O(\lambda) bits growth in communication (\lambda the security parameter), and two (resp., one) extra exponentiation in computation for client (resp., server). We also develop an asymmetric PAKE scheme 2DH-aEKE from 2DH-EKE. The security reduction loss of 2DH-aEKE is N, the total number of client-server pairs. With a meta-reduction, we formally prove that such a factor N is inevitable in aPAKE. Namely, our 2DH-aEKE meets the optimal security loss. As a byproduct, we further apply our technique to PAKE protocols like SPAKE2 and PPK in the relaxed UC framework, resulting in their 2DH variants with tight security from the CDH assumption.

In this paper, we propose a new type of non-interactive zero-knowledge (NIZK), called Fine-grained Verifier NIZK (FV-NIZK), which provides more flexible and more fine-grained verifiability of proofs than standard NIZK that supports public verifiability and designated-verifier NIZK (DV-NIZK) that supports private verifiability. FV-NIZK has two statistically equivalent verification approaches: -- a master verification using the master secret key msk; -- a fine-grained verification using a derived secret key sk_d, which is derived from msk w.r.t. d (which may stand for user identity, email address, vector, etc.). We require unbounded simulation soundness (USS) of FV-NIZK to hold, even if an adversary obtains derived secret keys sk_d with d of its choices, and define proof pseudorandomness which stipulates the pseudorandomness of proofs for adversaries that are not given any secret key. We present two instantiations of FV-NIZK for linear subspace languages, based on the matrix decisional Diffie-Hellman (MDDH) assumption. One of the FV-NIZK instantiations is pairing-free and achieves almost tight USS and proof pseudorandomness. We illustrate the usefulness of FV-NIZK by showing two applications and obtain the following pairing-free schemes: -- the first almost tightly multi-challenge CCA (mCCA)-secure inner-product functional encryption (IPFE) scheme without pairings; -- the first public-key encryption (PKE) scheme that reconciles the inherent contradictions between public verifiability and anonymity. We formalize such PKE as Fine-grained Verifiable PKE (FV-PKE), which derives a special key from the decryption secret key, such that for those who obtain the derived key, they can check the validity of ciphertexts but the anonymity is lost from their views (CCA-security still holds for them), while for others who do not get the derived key, they cannot do the validity check but the anonymity holds for them. Our FV-PKE scheme achieves almost tight mCCA-security for adversaries who obtain the derived keys, and achieves almost tight ciphertext pseudorandomness (thus anonymity) for others who do not get any derived key.

In this paper, we consider tight multi-user security under adaptive corruptions, where the adversary can adaptively corrupt some users and obtain their secret keys. We propose generic constructions for a bunch of primitives, and the instantiations from the matrix decision Diffie-Hellman (MDDH) assumptions yield the following schemes: (1) the first digital signature (SIG) scheme achieving almost tight strong EUF-CMA security in the multi-user setting with adaptive corruptions in the standard model; (2) the first public-key encryption (PKE) scheme achieving almost tight IND-CCA security in the multi-user multi-challenge setting with adaptive corruptions in the standard model; (3) the first signcryption (SC) scheme achieving almost tight privacy and authenticity under CCA attacks in the multi-user multi-challenge setting with adaptive corruptions in the standard model. As byproducts, our SIG and SC naturally derive the first strongly secure message authentication code (MAC) and the first authenticated encryption (AE) schemes achieving almost tight multi-user security under adaptive corruptions in the standard model. We further optimize constructions of SC, MAC and AE to admit better efficiency. Furthermore, we consider key leakages besides corruptions, as a natural strengthening of tight multi-user security under adaptive corruptions. This security considers a more natural and more complete "all-or-part-or-nothing" setting, where secret keys of users are either fully exposed to adversary ("all"), or completely hidden to adversary ("nothing"), or partially leaked to adversary ("part"), and it protects the uncorrupted users even with bounded key leakages. All our schemes additionally support bounded key leakages and enjoy full compactness. This yields the first SIG, PKE, SC, MAC, AE schemes achieving almost tight multi-user security under both adaptive corruptions and leakages.

In this work, we construct the {\it first} digital signature (SIG) and public-key encryption (PKE) schemes with almost tight multi-user security under adaptive corruptions based on the learning-with-errors (LWE) assumption in the standard model. Our PKE scheme achieves almost tight IND-CCA security and our SIG scheme achieves almost tight strong EUF-CMA security, both in the multi-user setting with adaptive corruptions. The security loss is quadratic in the security parameter, and independent of the number of users, signatures or ciphertexts. Previously, such schemes were only known to exist under number-theoretic assumptions or in classical random oracle model, thus vulnerable to quantum adversaries. To obtain our schemes from LWE, we propose new frameworks for constructing SIG and PKE with a core technical tool named {\it probabilistic} quasi-adaptive hash proof system (pr-QA-HPS). As a new variant of HPS, our pr-QA-HPS provides {\it probabilistic} public and private evaluation modes that may toss coins. This is in stark contrast to the traditional HPS [Cramer and Shoup, Eurocrypt 2002] and existing variants like approximate HPS [Katz and Vaikuntanathan, Asiacrypt 2009], whose public and private evaluations are deterministic in their inputs. Moreover, we formalize a new property called evaluation indistinguishability by requiring statistical indistinguishability of the two probabilistic evaluation modes, even in the presence of the secret key. The evaluation indistinguishability, as well as other nice properties resulting from the probabilistic features of pr-QA-HPS, are crucial for the multi-user security proof of our frameworks under adaptive corruptions. As for instantiations, we construct pr-QA-HPS from the LWE assumption and prove its properties with almost tight reductions, which admit almost tightly secure LWE-based SIG and PKE schemes under our frameworks. Along the way, we also provide new almost-tight reductions from LWE to multi-secret LWE, which may be of independent interest.

Proxy re-encryption (PRE) allows a proxy with a re-encryption key to translate a ciphertext intended for Alice (delegator) to another ciphertext intended for Bob (delegatee) without revealing the underlying message. However, with PRE, Bob can obtain the whole message from the re-encrypted ciphertext, and Alice cannot take flexible control of the extent of the message transmitted to Bob. In this paper, we propose a new variant of PRE, called Fine-Grained PRE (FPRE), to support fine-grained re-encryptions. An FPRE is associated with a function family F, and each re-encryption key rk_{A→B}^f is associated with a function f ∈ F. With FPRE, Alice now can authorize re-encryption power to proxy by issuing rk_{A→B}^f to it, with f chosen by herself. Then the proxy can translate ciphertext encrypting m to Bob's ciphertext encrypting f(m) with such a fine-grained re-encryption key, and Bob only obtains a function of message m. In this way, Alice can take flexible control of the message spread by specifying functions. For FPRE, we formally define its syntax and formalize security notions including CPA security, ciphertext pseudo-randomness, unidirectionality, non-transitivity, collusion-safety under adaptive corruptions in the multi-user setting. Moreover, we propose a new security notion named {\it ciphertext unlinkability}, which blurs the link between a ciphertext and its re-encrypted ciphertext to hide the proxy connections between users. We establish the relations between those security notions. As for constructions, we propose two FPRE schemes, one for bounded linear functions and the other for deletion functions, based on the learning-with-errors (LWE) assumption. Our FPRE schemes achieve all the aforementioned desirable securities under adaptive corruptions in the standard model. As far as we know, our schemes provide the {\it first} solution to PRE with security under adaptive corruptions in the standard model.

Privacy-Preserving Authenticated Key Exchange (PPAKE) provides protection both for the session keys and the identity information of the involved parties. In this paper, we introduce the concept of robustness into PPAKE. Robustness enables each user to confirm whether itself is the target recipient of the first round message in the protocol. With the help of robustness, a PPAKE protocol can successfully avoid the heavy redundant communications and computations caused by the ambiguity of communicants in the existing PPAKE, especially in broadcast channels. We propose a generic construction of robust PPAKE from key encapsulation mechanism (KEM), digital signature (SIG), message authentication code (MAC), pseudo-random generator (PRG) and symmetric encryption (SE). By instantiating KEM, MAC, PRG from the DDH assumption and SIG from the CDH assumption, we obtain a specific robust PPAKE scheme in the standard model, which enjoys forward security for session keys, explicit authentication and forward privacy for user identities. Thanks to the robustness of our PPAKE, the number of broadcast messages per run and the computational complexity per user are constant, and in particular, independent of the number of users in the system.

Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization. To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What's worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions. In this work, we introduce a new security notion for PKE called ANON-RSO$_{k}\&$C security, capturing anonymity under corruptions. We also introduce SIM-RSO$_{k}\&$C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with \emph{compact} ciphertexts. Furthermore, for some PKE instantiation, its security reduction is \emph{tight}.

We construct the first authenticated key exchange protocols that achieve tight security in the standard model. Previous works either relied on techniques that seem to inherently require a random oracle, or achieved only “Multi-Bit-Guess” security, which is not known to compose tightly, for instance, to build a secure channel. Our constructions are generic, based on digital signatures and key encapsulation mechanisms (KEMs). The main technical challenges we resolve is to determine suitable KEM security notions which on the one hand are strong enough to yield tight security, but at the same time weak enough to be efficiently instantiable in the standard model, based on standard techniques such as universal hash proof systems. Digital signature schemes with tight multi-user security in presence of adaptive corruptions are a central building block, which is used in all known constructions of tightly-secure AKE with full forward security. We identify a subtle gap in the security proof of the only previously known efficient standard model scheme by Bader et al. (TCC 2015). We develop a new variant, which yields the currently most efficient signature scheme that achieves this strong security notion without random oracles and based on standard hardness assumptions.

For Key Encapsulation Mechanism (KEM) deployed in a multi-user setting, an adversary may corrupt some users to learn their secret keys, and obtain some encapsulated keys due to careless key managements of users. To resist such attacks, we formalize Enhanced security against Chosen Plaintext/Ciphertext Attack (ECPA/ECCA), which ask the pseudorandomness of unrevealed encapsulated keys under uncorrupted users. This enhanced security for KEM serves well for the security of a class of Authenticated Key Exchange protocols built from KEM. In this paper, we study the achievability of tight ECPA and ECCA security for KEM in the multi-user setting, and present an impossibility result and an optimal security loss factor that can be obtained. The existing meta-reduction technique due to Bader et al. (EUROCRYPT 2016) rules out some KEMs, but many well-known KEMs, e.g., Cramer-Shoup KEM (SIAM J. Comput. 2003), Kurosawa-Desmedt KEM (CRYPTO 2004), run out. To solve this problem, we develop a new technique tool named rank of KEM and a new secret key partitioning strategy for meta-reduction. With this new tool and new strategy, we prove that KEM schemes with polynomially-bounded ranks have no tight ECPA and ECCA security from non-interactive complexity assumptions, and the security loss is at least linear in the number n of users. This impossibility result covers lots of well-known KEMs, including the Cramer-Shoup KEM, Kurosawa-Desmedt KEM and many others. Moreover, we show that the linear security loss is optimal by presenting concrete KEMs with security loss Θ(n). This is justified by a non-trivial security reduction with linear loss factor from ECPA/ECCA security to the traditional multi-challenge CPA/CCA security.

We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the $${\text {DDH}} $$ DDH assumption hold for them. Our first construction is symmetric and comes with a $$\kappa $$ κ -linear map $$\mathbf{e }: {{\mathbb {G}}}^\kappa \longrightarrow {\mathbb {G}}_T$$ e : G κ ⟶ G T for prime-order groups $${\mathbb {G}}$$ G and $${\mathbb {G}}_T$$ G T . To establish the hardness of the $$\kappa $$ κ -linear $${\text {DDH}} $$ DDH problem, we rely on the existence of a base group for which the $$\kappa $$ κ -strong $${\text {DDH}} $$ DDH assumption holds. Our second construction is for the asymmetric setting, where $$\mathbf{e }: {\mathbb {G}}_1 \times \cdots \times {\mathbb {G}}_{\kappa } \longrightarrow {\mathbb {G}}_T$$ e : G 1 × ⋯ × G κ ⟶ G T for a collection of $$\kappa +1$$ κ + 1 prime-order groups $${\mathbb {G}}_i$$ G i and $${\mathbb {G}}_T$$ G T , and relies only on the 1-strong $${\text {DDH}} $$ DDH assumption in its base group. In both constructions, the linearity $$\kappa $$ κ can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness-indistinguishability, and zero knowledge), and additively homomorphic encryption for the group $$\mathbb {Z}_N^{+}$$ Z N + . At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups and show the equivalence of PIO and multilinear maps under the existence of the aforementioned primitives.

We propose the concept of quasi-adaptive hash proof system (QAHPS), where the projection key is allowed to depend on the specific language for which hash values are computed. We formalize leakage-resilient(LR)-ardency for QAHPS by defining two statistical properties, including LR-$$\langle \mathscr {L}_0, \mathscr {L}_1 \rangle $$-universal and LR-$$\langle \mathscr {L}_0, \mathscr {L}_1 \rangle $$-key-switching.We provide a generic approach to tightly leakage-resilient CCA (LR-CCA) secure public-key encryption (PKE) from LR-ardent QAHPS. Our approach is reminiscent of the seminal work of Cramer and Shoup (Eurocrypt’02), and employ three QAHPS schemes, one for generating a uniform string to hide the plaintext, and the other two for proving the well-formedness of the ciphertext. The LR-ardency of QAHPS makes possible the tight LR-CCA security. We give instantiations based on the standard k-Linear (k-LIN) assumptions over asymmetric and symmetric pairing groups, respectively, and obtain fully compact PKE with tight LR-CCA security. The security loss is $${{O}}(\log {Q_{{e}}})$$ where $${Q_{{e}}}$$ denotes the number of encryption queries. Specifically, our tightly LR-CCA secure PKE instantiation from SXDH has only 4 group elements in the public key and 7 group elements in the ciphertext, thus is the most efficient one.

Selective opening security (SO security) is desirable for public key encryption (PKE) in a multi-user setting. In a selective opening attack, an adversary receives a number of ciphertexts for possibly correlated messages, then it opens a subset of them and gets the corresponding messages together with the randomnesses used in the encryptions. SO security aims at providing security for the unopened ciphertexts. Among the existing simulation-based, selective opening, chosen ciphertext secure (SIM-SO-CCA secure) PKEs, only one (Libert et al. Crypto’17) enjoys tight security, which is reduced to the Non-Uniform LWE assumption. However, their public key and ciphertext are not compact.In this work, we focus on constructing PKE with tight SIM-SO-CCA security based on standard assumptions. We formalize security notions needed for key encapsulation mechanism (KEM) and show how to transform these securities into SIM-SO-CCA security of PKE through a tight security reduction, while the construction of PKE from KEM follows the general framework proposed by Liu and Paterson (PKC’15). We present two KEM constructions with tight securities based on the Matrix Decision Diffie-Hellman assumption. These KEMs in turn lead to two tightly SIM-SO-CCA secure PKE schemes. One of them enjoys not only tight security but also compact public key.