An Introduction to Probabilistic Encryption

An introduction to probabilistic encryption is given, presenting the first probabilistic cryptosystem by Goldwasser and Micali. Furthermore, the required number-theoretic concepts are discussed and the notion of semantic security is presented in an informal way. The article should be comprehensible to students with basic mathematical knowledge

Signatures courtes sur chiffrés randomizables

International audienceRandomizable encryption lets anyone randomize a ciphertext so it is distributed like a fresh encryption of the same plaintext. Signatures on randomizable cipher-texts (SoRC), introduced by Blazy et al. (PKC'11), let one adapt a signature on a ciphertext to a randomization of the latter. Since signatures can only be adapted to ciphertexts that encrypt the same message as the signed ciphertext, signatures obliviously authenticate plaintexts. SoRC have been used as a building block in e-voting, blind signatures and (delegatable) anonymous credentials. We observe that SoRC can be seen as signatures on equivalence classes (JoC'19), another primitive with many applications to anonymous authentication, and that SoRC provide better anonymity guarantees. We first strengthen the unforgeability notion for SoRC and then give a scheme that provably achieves it in the generic group model. Signatures in our scheme consist of 4 bilinear-group elements, which is considerably more efficient than prior schemes

Constant-Size Structure-Preserving Signatures: Generic Constructions and Simple Assumptions

This paper presents efficient structure-preserving signature schemes based on assumptions as simple as Decision-Linear. We first give two general frameworks for constructing fully secure signature schemes from weaker building blocks such as variations of one-time signatures and random-message secure signatures. They can be seen as refinements of the Even-Goldreich-Micali framework, and preserve many desirable properties of the underlying schemes such as constant signature size and structure preservation. We then instantiate them based on simple (i.e., not q-type) assumptions over symmetric and asymmetric bilinear groups. The resulting schemes are structure-preserving and yield constant-size signatures consisting o

Security Analysis and Improvements for the IETF MLS Standard for Group Messaging

Secure messaging (SM) protocols allow users to communicate securely over untrusted infrastructure. In contrast to most other secure communication protocols (such as TLS, SSH, or Wireguard), SM sessions may be long-lived (e.g., years) and highly asynchronous. In order to deal with likely state compromises of users during the lifetime of a session, SM protocols do not only protect authenticity and privacy, but they also guarantee forward secrecy (FS) and post-compromise security (PCS). The former ensures that messages sent and received before a state compromise remain secure, while the latter ensures that users can recover from state compromise as a consequence of normal protocol usage. SM has received considerable attention in the two-party case, where prior work has studied the well-known double-ratchet paradigm in particular and SM as a cryptographic primitive in general. Unfortunately, this paradigm does not scale well to the problem of secure group messaging (SGM). In order to address the lack of satisfactory SGM protocols, the IETF has launched the message-layer security (MLS) working group, which aims to standardize an eponymous SGM protocol. In this work we analyze the TreeKEM protocol, which is at the core of the SGM protocol proposed by the MLS working group. On a positive note, we show that TreeKEM achieves PCS in isolation (and slightly more). However, we observe that the current version of TreeKEM does not provide an adequate form of FS. More precisely, our work proceeds by formally capturing the exact security of TreeKEM as a so-called continuous group key agreement (CGKA) protocol, which we believe to be a primitive of independent interest. To address the insecurity of TreeKEM, we propose a simple modification to TreeKEM inspired by recent work of Jost et al. (EUROCRYPT \u2719) and an idea due to Kohbrok (MLS Mailing List). We then show that the modified version of TreeKEM comes with almost no efficiency degradation but achieves optimal (according to MLS specification) CGKA security, including FS and PCS. Our work also lays out how a CGKA protocol can be used to design a full SGM protocol. Finally, we propose and motivate an extensive list of potential future research directions for the area

Breaking and Fixing Anonymous Credentials for the Cloud

In an attribute-based credential (ABC) system, users obtain a digital certificate on their personal attributes, and can later prove possession of such a certificate in an unlinkable way, thereby selectively disclosing chosen attributes to the service provider. Recently, the concept of encrypted ABCs (EABCs) was introduced by Krenn et al. at CANS 2017, where virtually all computation is outsourced to a semi-trusted cloud-provider called wallet, thereby overcoming existing efficiency limitations on the user’s side, and for the first time enabling “privacy-preserving identity management as a service”. While their approach is highly relevant for bringing ABCs into the real world, we present a simple attack allowing the wallet to learn a user\u27s attributes when colluding with another user -- a scenario which is not covered by their modeling but which needs to be considered in practice. We then revise the model and construction of Krenn et al. in various ways, such that the above attack is no longer possible. Furthermore, we also remove existing non-collusion assumptions between wallet and service provider or issuer from their construction. Our protocols are still highly efficient in the sense that the computational effort on the end user side consists of a single exponentiation only, and otherwise efficiency is comparable to the original work of Krenn et al

Subversion-Resistant Simulation (Knowledge) Sound NIZKs

In ASIACRYPT 2016, Bellare, Fuchsbauer, and Scafuro studied the security of non-interactive zero-knowledge (NIZK) arguments in the face of parameter subversion. They showed that achieving subversion soundness (soundness without trusting to the third party) and standard zero-knowledge is impossible at the same time. On the positive side, in the best case, they showed that one can achieve subversion zero-knowledge (zero-knowledge without trusting to the third party) and soundness at the same time. In this paper, we show that one can amplify their best positive result and construct NIZK arguments that can achieve subversion zero-knowledge and $\textit{simulation}$ (knowledge) soundness at the same time. Simulation (knowledge) soundness is a stronger notion in comparison with (knowledge) soundness, as it also guarantees non-malleability of proofs. Such a stronger security guarantee is a must in practical systems. To prove the result, we show that given a NIZK argument that achieves Sub-ZK and (knowledge) soundness, one can use an OR-based construction to define a new language and build a NIZK argument that will guarantee Sub-ZK and $\textit{simulation}$ (knowledge) soundness at the same time. We instantiate the construction with the state-of-the-art zk-SNARK proposed by Groth [Eurocrypt 2016] and obtain an efficient SNARK that guarantees Sub-ZK and simulation knowledge soundness

Structure-Preserving Signatures on Equivalence Classes From Standard Assumptions

Structure-preserving signatures on equivalence classes (SPS-EQ) introduced at ASIACRYPT 2014 are a variant of SPS where a message is considered as a projective equivalence class, and a new representative of the same class can be obtained by multiplying a vector by a scalar. Given a message and corresponding signature, anyone can produce an updated and randomized signature on an arbitrary representative from the same equivalence class. SPS-EQ have proven to be a very versatile building block for many cryptographic applications. In this paper, we present the first EUF-CMA secure SPS-EQ scheme under standard assumptions. So far only constructions in the generic group model are known. One recent candidate under standard assumptions are the weakly secure equivalence class signatures by Fuchsbauer and Gay (PKC\u2718), a variant of SPS-EQ satisfying only a weaker unforgeability and adaption notion. Fuchsbauer and Gay show that this weaker unforgeability notion is sufficient for many known applications of SPS-EQ. Unfortunately, the weaker adaption notion is only proper for a semi-honest (passive) model and as we show in this paper, makes their scheme unusable in the current models for almost all of their advertised applications of SPS-EQ from the literature. We then present a new EUF-CMA secure SPS-EQ scheme with a tight security reduction under the SXDH assumption providing the notion of perfect adaption (under malicious keys). To achieve the strongest notion of perfect adaption under malicious keys, we require a common reference string (CRS), which seems inherent for constructions under standard assumptions. However, for most known applications of SPS-EQ we do not require a trusted CRS (as the CRS can be generated by the signer during key generation). Technically, our construction is inspired by a recent work of Gay et al. (EUROCRYPT\u2718), who construct a tightly secure message authentication code and translate it to an SPS scheme adapting techniques due to Bellare and Goldwasser (CRYPTO\u2789)

On QA-NIZK in the BPK Model

Recently, Bellare et al. defined subversion-resistance (security in the case the CRS creator may be malicious) for NIZK. In particular, a Sub-ZK NIZK is zero-knowledge, even in the case of subverted CRS. We study Sub-ZK QA-NIZKs, where the CRS can depend on the language parameter. First, we observe that subversion zero-knowledge (Sub-ZK) in the CRS model corresponds to no-auxiliary-string non-black-box NIZK in the Bare Public Key model, and hence, the use of non-black-box techniques is needed to obtain Sub-ZK. Second, we give a precise definition of Sub-ZK QA-NIZKs that are (knowledge-)sound if the language parameter but not the CRS is subverted and zero-knowledge even if both are subverted. Third, we prove that the most efficient known QA-NIZK for linear subspaces by Kiltz and Wee is Sub-ZK under a new knowledge assumption that by itself is secure in (a weaker version of) the algebraic group model. Depending on the parameter setting, it is (knowledge-)sound under different non-falsifiable assumptions, some of which do not belong to the family of knowledge assumptions

Succinct Malleable NIZKs and an Application to Compact Shuffles

Depending on the application, malleability in cryptography can be viewed as either a flaw or — especially if sufficiently understood and restricted — a feature. In this vein, Chase, Kohlweiss, Lysyanskaya, and Meiklejohn recently defined malleable zero-knowledge proofs, and showed how to control the set of allowable transformations on proofs. As an application, they construct the first compact verifiable shuffle, in which one such controlled-malleable proof suffices to prove the correctness of an entire multi-step shuffle. Despite these initial steps, a number of natural open problems remain: (1) their construction of controlled-malleable proofs relies on the inherent malleability of Groth-Sahai proofs and is thus not based on generic primitives; (2) the classes of allowable transformations they can support are somewhat restrictive; and (3) their construction of a compactly verifiable shuffle has proof size O(N 2 + L) (where N is the number of votes and L is the number of mix authorities), whereas in theory such a proof could be of size O(N + L). In this paper, we address these open problems by providing a generic construction of controlledmalleable proofs using succinct non-interactive arguments of knowledge, or SNARGs for short. Our construction has the advantage that we can support a very general class of transformations (as we no longer rely on the transformations that Groth-Sahai proofs can support), and that we can use it to obtain a proof of size O(N + L) for the compactly verifiable shuffle