Publicly Evaluable Pseudorandom Functions and Their Applications

We put forth the notion of \emph{publicly evaluable} pseudorandom functions (PEPRFs), which can be viewed as a counterpart of standard pseudorandom functions (PRFs) in the public-key setting. Briefly, PEPRFs are defined over domain $X$ containing a language $L$ associated with a hard relation $\mathsf{R}_L$, and each secret key $sk$ is associated with a public key $pk$. For any $x \in L$, in addition to evaluate $\mathsf{F}_{sk}(x)$ using $sk$ as standard PRFs, one is also able to evaluate $\mathsf{F}_{sk}(x)$ with $pk$, $x$ and a witness $w$ for $x \in L$. We consider two security notions for PEPRFs. The basic one is weak pseudorandomness which stipulates a PEPRF cannot be distinguished from a real random function on uniformly random chosen inputs. The strengthened one is adaptive weak pseudorandomness which requires a PEPRF remains weak pseudorandom even when an adversary is given adaptive access to an evaluation oracle. We conduct a formal study of PEPRFs, focusing on applications, constructions, and extensions. We show how to construct chosen-plaintext secure (CPA) and chosen-ciphertext secure (CCA) public-key encryption (PKE) schemes from (adaptive) PEPRFs. The construction is simple, black-box, and admits a direct proof of security. We provide evidence that (adaptive) PEPRFs exist by showing constructions from injective trapdoor functions, hash proof systems, extractable hash proof systems, as well as a construction from puncturable PRFs with program obfuscation. We introduce the notion of publicly sampleable PRFs (PSPRFs), which is a relaxation of PEPRFs, but nonetheless imply PKE. We show (adaptive) PSPRFs are implied by (adaptive) trapdoor relations. This helps us to unify and clarify many PKE schemes from seemingly unrelated general assumptions and paradigms under the notion of PSPRFs. We explore similar extension on recently emerging constrained PRFs, and introduce the notion of publicly evaluable constrained PRFs, which, as an immediate application, implies attribute-based encryption. We propose a twist on PEPRFs, which we call publicly evaluable and verifiable functions (PEVFs). Compared to PEPRFs, PEVFs have an additional promising property named public verifiability while the best possible security degrades to unpredictability. We justify the applicability of PEVFs by presenting a simple construction of ``hash-and-sign\u27\u27 signatures, both in the random oracle model and the standard model

Simulation-Based Selective Opening Security for Receivers under Chosen-Ciphertext Attacks

Security against selective opening attack (SOA) for receivers requires that in a multi-user setting, even if an adversary has access to all ciphertexts, and adaptively corrupts some fraction of the users to obtain the decryption keys corresponding to some of the ciphertexts, the remaining (potentially related) ciphertexts retain their privacy. In this paper, we study simulation-based selective opening security for receivers of public key encryption (PKE) schemes under chosen-ciphertext attacks (RSIM-SO-CCA). Concretely, we first show that some known PKE schemes meet RSIM-SO-CCA security. Then, we introduce the notion of master-key SOA security for identity-based encryption (IBE), and extend the Canetti-Halevi-Katz (CHK) transformation to show generic PKE constructions achieving RSIM-SO-CCA security. Finally, we show how to construct an IBE scheme achieving master-key SOA security

One-round strong oblivious signature-based envelope

Oblivious Signature-Based Envelope (OSBE) has been widely employed for anonymity-orient and privacy-preserving applications. The conventional OSBE execution relies on a secure communication channel to protect against eavesdroppers. In TCC 2012, Blazy, Pointcheval and Vergnaud proposed a framework of OSBE (BPV-OSBE) without requiring any secure channel by clarifying and enhancing the OSBE security notions. They showed how to generically build an OSBE scheme satisfying the new strong security in the standard model with a common-reference string. Their framework requires 2-round interactions and relies on the smooth projective hash function (SPHF) over special languages, i.e., languages from encryption of signatures. In this work, we investigate the study on the strong OSBE and make the following contributions. First, we propose a generic construction of one-round yet strong OSBE system. Compared to the 2-round BPV-OSBE, our one-round construction is more appealing, as its noninteractive setting accommodates more application scenarios in the real word. Moreover, our framework relies on the regular (identity-based) SPHF, which can be instantiated from extensive languages and hence is more general. Second, we also present an efficient instantiation, which is secure under the standard model from classical assumptions, DDH and DBDH, to illustrate the feasibility of our one-round framework. We remark that our construction is the first one-round OSBE with strong securit

Cryptographic techniques for hardware security

Traditionally, cryptographic algorithms are designed under the so-called black-box model, which considers adversaries that receive black-box access to the hardware implementation. Although a "black-box" treatment covers a wide range of attacks, it fails to capture reality adequately, as real-world adversaries can exploit physical properties of the implementation, mounting attacks that enable unexpected, non-black-box access, to the components of the cryptographic system. This type of attacks is widely known as physical attacks, and has proven to be a significant threat to the real-world security of cryptographic systems. The present dissertation is (partially) dealing with the problem of protecting cryptographic memory against physical attacks, via the use of non-malleable codes, which is a notion introduced in a preceding work, aiming to provide privacy of the encoded data, in the presence of adversarial faults. In the present thesis we improve the current state-of-the-art on non-malleable codes and we provide practical solutions for protecting real-world cryptographic implementations against physical attacks. Our study is primarily focusing on the following adversarial models: (i) the extensively studied split-state model, which assumes that private memory splits into two parts, and the adversary tampers with each part, independently, and (ii) the model of partial functions, which is introduced by the current thesis, and models adversaries that access arbitrary subsets of codeword locations, with bounded cardinality. Our study is comprehensive, covering one-time and continuous, attacks, while for the case of partial functions, we manage to achieve a stronger notion of security, that we call non-malleability with manipulation detection, that in addition to privacy, it also guarantees integrity of the private data. It should be noted that, our techniques are also useful for the problem of establishing, private, keyless communication, over adversarial communication channels. Besides physical attacks, another important concern related to cryptographic hardware security, is that the hardware fabrication process is assumed to be trusted. In reality though, when aiming to minimize the production costs, or whenever access to leading-edge manufacturing facilities is required, the fabrication process requires the involvement of several, potentially malicious, facilities. Consequently, cryptographic hardware is susceptible to the so-called hardware Trojans, which are hardware components that are maliciously implanted to the original circuitry, having as a purpose to alter the device's functionality, while remaining undetected. Part of the present dissertation, deals with the problem of protecting cryptographic hardware against Trojan injection attacks, by (i) proposing a formal model for assessing the security of cryptographic hardware, whose production has been partially outsourced to a set of untrusted, and possibly malicious, manufacturers, and (ii) by proposing a compiler that transforms any cryptographic circuit, into another, that can be securely outsourced

Omniring: Scaling Up Private Payments Without Trusted Setup - Formal Foundations and Constructions of Ring Confidential Transactions with Log-size Proofs

Monero is the largest cryptocurrency with built-in cryptographic privacy features. The transactions are authenticated using spend proofs, which provide a certain level of anonymity by hiding the source accounts from which the funds are sent among a set (known as a ring) of other accounts. Due to its similarities to ring signatures, this core cryptographic component is called Ring Confidential Transactions (RingCT). Because of its practical relevance, several works attempt to analyze the security of RingCT. However, due to the complexity of RingCT they are either informal, miss fundamental functionalities, or introduce undesirable trusted setup assumptions. Regarding efficiency, Monero currently deploys a scheme in which the size of the spend proof is linear in the ring size. This limits the ring size to only a few accounts, which in turn limits the acquired anonymity significantly and facilitates de-anonymization attacks. As a solution to these problems, we present the first complete rigorous formalization of RingCT as a cryptographic primitive. We then propose a generic construction of RingCT and prove it secure in our formal security model. By instantiating our generic construction with new efficient zero-knowledge proofs we obtain Omniring, a fully-fledged RingCT scheme in the discrete logarithm setting that provides the highest concrete and asymptotic efficiency as of today. Omniring is the first RingCT scheme which 1) does not require a trusted setup or pairing-friendly elliptic curves, 2) has a proof size logarithmic in the size of the ring, and 3) allows to share the same ring between all source accounts in a transaction, thereby enabling significantly improved privacy level without sacrificing performance. Our zero-knowledge proofs rely on novel enhancements to the Bulletproofs framework (S&P 2018), which we believe are of independent interest

Non-Malleable Codes for Partial Functions with Manipulation Detection

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs (ICS \u2710) and its main application is the protection of cryptographic devices against tampering attacks on memory. In this work, we initiate a comprehensive study on non-malleable codes for the class of partial functions, that read/write on an arbitrary subset of codeword bits with specific cardinality. Our constructions are efficient in terms of information rate, while allowing the attacker to access asymptotically almost the entire codeword. In addition, they satisfy a notion which is stronger than non-malleability, that we call non-malleability with manipulation detection, guaranteeing that any modified codeword decodes to either the original message or to $\bot$. Finally, our primitive implies All-Or-Nothing Transforms (AONTs) and as a result our constructions yield efficient AONTs under standard assumptions (only one-way functions), which, to the best of our knowledge, was an open question until now. In addition to this, we present a number of additional applications of our primitive in tamper resilience

CCA-Secure IB-KEM from Identity-Based Extractable Hash Proof Systems

Abstract. In this paper, we introduce a general paradigm called identity-based extractable hash proof system (IB-EHPS), which is an extension of extractable hash proof system (EHPS) proposed by Wee (CRYPTO ’10). We show how to construct identity-based key encapsulation mechanism (IB-KEM) from IB-EHPS in a simple and modular fashion. Our construction provides a generic method of building and interpreting CCA-secure IB-KEMs based on computational assumptions. As instantiations, we realize IB-EHPS from the bilinear Diffie-Hellman assumption and the modified bilinear Diffie-Hellman assumption, respectively. Key words: identity-based extractable hash proof, identity-based key encapsulation mechanism, CCA security, BDH assumption