On the Asymptotic Idealness of the Asmuth-Bloom Threshold Secret Sharing Scheme

A necessary and sufficient condition for the asymptotic idealness of the Asmuth-Bloom threshold secret sharing scheme is proposed. Apart from this, a comprehensive analysis of the known variants of the Asmuth-Bloom threshold secret sharing scheme is provided, clarifying the security properties achieved by each of them

Asymptotically Ideal CRT-based Secret Sharing Schemes for Multilevel and Compartmented Access Structures

Multilevel and compartmented access structures are two important classes of access structures where participants are grouped into levels/compartments with different degrees of trust and privileges. The construction of secret sharing schemes for such access structures has been in the attention of researchers for a long time. Two main approaches have been taken so far: one of them is based on polynomial interpolation and the other one is based on the Chinese Remainder Theorem (CRT). In this paper we propose the first asymptotically ideal CRT-based secret sharing schemes for (disjunctive, conjunctive) multilevel and compartmented access structures. Our approach is compositional and it is based on a variant of the Asmuth-Bloom secret sharing scheme where some participants may have public shares. Based on this, we show that the proposed secret sharing schemes for multilevel and compartmented access structures are asymptotically ideal if and only if they are based on 1-compact sequences of co-primes

Private votes on untrusted platforms: models, attacks and provable scheme

International audienceModern e-voting systems deploy cryptographic protocols on a complex infrastructure involving different computing platforms and agents. It is crucial to have appropriate specification and evaluation methods to perform rigorous analysis of such systems, taking into account the corruption and computational capabilities of a potential attacker. In particular, the platform used for voting may be corrupted, e.g. infected by malware, and we need to ensure privacy and integrity of votes even in that case. We propose a new definition of vote privacy, formalized as a computational indistinguishability game, that allows to take into account such refined attacker models; we show that the definition captures both known and novel attacks against several voting schemes; and we propose a scheme that is provably secure in this setting. We moreover formalize and machine-check the proof in the EasyCrypt theorem prover

Machine-checked proofs for electronic voting: privacy and verifiability for Belenios

International audienceWe present a machine-checked security analysis of Belenios-a deployed voting protocol used already in more than 200 elections. Belenios extends Helios with an explicit registration authority to obtain eligibility guarantees. We offer two main results. First, we build upon a recent framework for proving ballot privacy in EasyCrypt. Inspired by our application to Belenios, we adapt and extend the privacy security notions to account for protocols that include a registration phase. Our analysis identifies a trust assumption which is missing in the existing (pen and paper) analysis of Belenios: ballot privacy does not hold if the registrar misbehaves, even if the role of the registrar is seemingly to provide eligibility guarantees. Second, we develop a novel framework for proving strong verifiability in EasyCrypt and apply it to Belenios. In the process, we clarify several aspects of the pen-and-paper proof, such as how to deal with revote policies. Together, our results yield the first machine-checked analysis of both ballot privacy and verifiability properties for a deployed electronic voting protocol. Perhaps more importantly, we identify several issues regarding the applicability of existing definitions of privacy and verifiability to systems other than Helios. While we show how to adapt the definitions to the particular case of Belenios, our findings indicate the need for more general security notions for electronic voting protocols with registration authorities

Mechanised Models and Proofs for Distance-Bounding

In relay attacks, a man-in-the-middle adversary impersonates a legitimate party and makes it this party appear to be of an authenticator, when in fact they are not. In order to counteract relay attacks, distance-bounding protocols provide a means for a verifier (e.g., an payment terminal) to estimate his relative distance to a prover (e.g., a bankcard). We propose FlexiDB, a new cryptographic model for distance bounding, parameterised by different types of fine-grained corruptions. FlexiDB allows to consider classical cases but also new, generalised corruption settings. In these settings, we exhibit new attack strategies on existing protocols. Finally, we propose a proof-of-concept mechanisation of FlexiDB in the interactive cryptographic prover EasyCrypt. We use this to exhibit a flavour of man-in-the-middle security on a variant of MasterCard\u27s contactless-payment protocol

Machine-Checked Proofs of Privacy for Electronic Voting Protocols

International audienceWe provide the first machine-checked proof of privacy-related properties (including ballot privacy) for an electronic voting protocol in the computational model. We target the popular Helios family of voting protocols, for which we identify appropriate levels of abstractions to allow the simplification and convenient reuse of proof steps across many variations of the voting scheme. The resulting framework enables machine-checked security proofs for several hundred variants of Helios and should serve as a stepping stone for the analysis of further variations of the scheme. In addition, we highlight some of the lessons learned regarding the gap between pen-and-paper and machine-checked proofs, and report on the experience with formalizing the security of protocols at this scale

Private votes on untrusted platforms: models, attacks and provable scheme

International audienceModern e-voting systems deploy cryptographic protocols on a complex infrastructure involving different computing platforms and agents. It is crucial to have appropriate specification and evaluation methods to perform rigorous analysis of such systems, taking into account the corruption and computational capabilities of a potential attacker. In particular, the platform used for voting may be corrupted, e.g. infected by malware, and we need to ensure privacy and integrity of votes even in that case. We propose a new definition of vote privacy, formalized as a computational indistinguishability game, that allows to take into account such refined attacker models; we show that the definition captures both known and novel attacks against several voting schemes; and we propose a scheme that is provably secure in this setting. We moreover formalize and machine-check the proof in the EasyCrypt theorem prover

Hierarchical Attribute-based Signatures. 17th International Conference, CANS 2018, Naples, Italy, September 30 – October 3, 2018

Attribute-based Signatures (ABS) are a powerful tool allowing users with attributes issued by authorities to sign messages while also proving that their attributes satisfy some policy. ABS schemes provide a exible and privacy-preserving approach to authentication since the signer's identity and attributes remain hidden within the anonymity set of users sharing policy-conform attributes. Current ABS schemes exhibit some limitations when it comes to the management and issue of attributes. In this paper we address the lack of support for hierarchical attribute management, a property that is prevalent in traditional PKIs where certification authorities are organised into hierarchies and signatures are verified along roots of trust. Hierarchical Attribute-based Signatures (HABS) introduced in this work support delegation of attributes along paths from the top-level authority down to the users while also ensuring that signatures produced by these users do not leak their delegation paths, thus extending the original privacy guarantees of ABS schemes. Our generic HABS construction also ensures unforgeability of signatures in the presence of collusion attacks and contains an extended traceability property allowing a dedicated tracing authority to identify the signer and reveal its attribute delegation paths. We include a public verification procedure for the accountability of the tracing authority. We anticipate that HABS will be useful for privacy-preserving authentication in applications requiring hierarchical delegation of attribute-issuing rights and where knowledge of delegation paths might leak information about signers and their attributes, e.g., in intelligent transport systems where vehicles may require certain attributes to authenticate themselves to the infrastructure but remain untrackable by the latter

Biometric-Authenticated Searchable Encryption

We introduce Biometric-Authenticated Keyword Search (BAKS), a novel searchable encryption scheme that relieves clients from managing cryptographic keys and relies purely on client's biometric data for authenticated outsourcing and retrieval of files indexed by encrypted keywords. BAKS utilises distributed trust across two servers and the liveness assumption which models physical presence of the client; in particular, BAKS security is guaranteed even if clients' biometric data, which often has low entropy, becomes public. We formalise two security properties, Authentication and Indistinguisha-bility against Chosen Keyword Attacks, which ensure that only a client with a biometric input sufficiently close to the registered template is considered legitimate and that neither of the two servers involved can learn any information about the encrypted keywords. Our BAKS construction further supports outsourcing and retrieval of files using multiple keywords and flexible search queries (e.g., conjunction, disjunction and subset-type queries). An additional update mechanism allows clients to replace their registered biometrics without requiring re-encryption of outsourced keywords , which enables smooth user migration across devices supporting different types of biometrics