Secure two-party computation in applied pi-calculus:models and verification

Secure two-party computation allows two mutually distrusting parties to compute a function together, without revealing their secret inputs to each other. Traditionally, the security properties desired in this context, and the corresponding security proofs, are based on a notion of simulation, which can be symbolic or computational. Either way, the proofs of security are intricate, requiring first to find a simulator, and then to prove a notion of indistinguishability. Furthermore, even for classic protocols such as Yao’s (based on garbled circuits and oblivious transfer), we do not have adequate symbolic models for cryptographic primitives and protocol roles, that can form the basis for automated security proofs. We therefore propose new models in applied pi-calculus in order to address these gaps. Our contributions, formulated in the context of Yao’s protocol, include: an equational theory for specifying the primitives of garbled computation and oblivious trans-fer; process specifications for the roles of the two parties in Yao’s protocol; definitions of security that are more clear and direct: result integrity, input agreement (both based on correspondence assertions) and input privacy (based on observational equivalence). We put these models together and illustrate their use with ProVerif, providing a first automated verification of security for Yao’s two-party computation protocol.

Adaptively Secure Multi-Party Computation from LWE (via Equivocal FHE)

Adaptively secure Multi-Party Computation (MPC) is an essential and fundamental notion in cryptography. In this work, we construct Universally Composable (UC) MPC protocols that are adaptively secure against all-but-one corruptions based on LWE. Our protocols have a constant number of rounds and communication complexity dependant only on the length of the inputs and outputs (it is independent of the circuit size). Such protocols were only known assuming an honest majority. Protocols in the dishonest majority setting, such as the work of Ishai et al. (CRYPTO 2008), require communication complexity proportional to the circuit size. In addition, constant-round adaptively secure protocols assuming dishonest majority are known to be impossible in the stand-alone setting with black-box proofs of security in the plain model. Here, we solve the problem in the UC setting using a set-up assumption which was shown necessary in order to achieve dishonest majority. The problem of constructing adaptively secure constant-round MPC protocols against arbitrary corruptions is considered a notorious hard problem. A recent line of works based on indistinguishability obfuscation construct such protocols with near-optimal number of rounds against arbitrary corruptions. However, based on standard assumptions, adaptively secure protocols secure against even just all-but-one corruptions with near-optimal number of rounds are not known. However, in this work we provide a three-round solution based only on LWE and NIZK secure against all-but-one corruptions. In addition, Asharov et al. (EUROCRYPT 2012) and more recently Mukherjee and Wichs (ePrint 2015) presented constant-round protocols based on LWE which are secure only in the presence of static adversaries. Assuming NIZK and LWE their static protocols run in two rounds where the latter one is only based on a common random string. Assuming adaptively secure UC NIZK, proposed by Groth et al. (ACM 2012), and LWE as mentioned above our adaptive protocols run in three rounds. Our protocols are constructed based on a special type of cryptosystem we call equivocal FHE from LWE. We also build adaptively secure UC commitments and UC zero-knowledge proofs (of knowledge) from LWE. Moreover, in the decryption phase using an AMD code mechanism we avoid the use of ZK and achieve communication complexity that does not scale with the decryption circuit

Programmeerimiskeeled turvalise ühisarvutuse rakenduste arendamiseks

Turvaline ühisarvutus on tehnoloogia, mis lubab mitmel sõltumatul osapoolel oma andmeid koos töödelda neis olevaid saladusi avalikustamata. Kui andmed on esitatud krüpteeritud kujul, tähendab see, et neid ei dekrüpteerita arvutuse käigus kordagi. Turvalise ühisarvutuse teoreetilised konstruktsioonid on teada olnud juba alates kaheksakümnendatest, kuid esimesed praktilised teostused ja rakendused, mis päris andmeid töötlesid, ilmusid alles natuke enam kui kümme aastat tagasi. Nüüdseks on turvalist ühisarvutust kasutatud mitmes praktilises rakenduses ning sellest on kujunenud oluline andmekaitsetehnoloogia. Turvalise ühisarvutuse rakenduste arendamine on keerukas. Vahendid, mis aitavad kaasa arendusprotsessile, on veel väga uued, ning raamistikud on sageli liiga aeglased praktiliste rakenduste jaoks. Rakendusi on endiselt võimelised arendama ainult krüptograafiaeksperdid. Käesoleva töö eesmärk on teha turvalise ühisarvutuse raamistikke paremaks ning muuta ühisarvutusrakenduste arendamist kergemaks. Väidame, et valdkon- naspetsiifiliste programmeerimiskeelte kasutamine võimaldab turvalise ühisarvu- tuse rakenduste ja raamistike ehitamist, mis on samaaegselt lihtsasti kasutatavad, hea jõudlusega, hooldatavad, usaldusväärsed ja võimelised suuri andmemahtusid töötlema. Peamise tulemusena esitleme kahte uut programmeerimiskeelt, mis on mõeldud turvalise ühisarvutuse jaoks. SecreC 2 on mõeldud turvalise ühisarvutuse rakendus- te arendamise lihtsustamiseks ja aitab kaasa sellele, et rakendused oleks turvalised ja efektiivsed. Teine keel on loodud turvalise ühisarvutuse protokollide arenda- miseks ning selle eesmärk on turvalise ühisarvutuse raamistikke paremaks muuta. Protokollide keel teeb raamistikke kiiremaks ja usaldusväärsemaks ning lihtsustab protokollide arendamist ja haldamist. Kirjeldame mõlemad keeled nii formaalselt kui mitteformaalselt. Näitame, kuidas mitmed rakendused ja prototüübid saavad neist keeltest kasu.Secure multi-party computation is a technology that allows several independent parties to cooperatively process their private data without revealing any secrets. If private inputs are given in encrypted form then the results will also be encrypted, and at no stage during processing are values ever decrypted. As a theoretical concept, the technology has been around since the 1980s, but the first practical implementations arose a bit more than a decade ago. Since then, secure multi-party computation has been used in practical applications, and has been established as an important method of data protection. Developing applications that use secure multi-party computation is challenging. The tools that help with development are still very young and the frameworks are often too slow for practical applications. Currently only experts in cryptography are able to develop secure multi-party applications. In this thesis we look how to improve secure multy-party computation frame- works and make the applications easier to develop. We claim that domain-specific programming languages enable to build secure multi-party applications and frame- works that are at the same time usable, efficient, maintainable, trustworthy, and practically scalable. The contribution of this thesis is the introduction of two new programming languages for secure multi-party computation. The SecreC 2 language makes secure multi-party computation application development easier, ensuring that the applications are secure and enabling them to be efficient. The second language is for developing low-level secure computation protocols. This language was created for improving secure multi-party computation frameworks. It makes the frameworks faster and more trustworthy, and protocols easier to develop and maintain. We give give both a formal and an informal overview of the two languages and see how they benefit multi-party applications and prototypes

New foundations for efficient authentication, commutative cryptography, and private disjointness testing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 105-115).This dissertation presents new constructions and security definitions related to three areas: authentication, cascadable and commutative crytpography, and private set operations. Existing works relevant to each of these areas fall into one of two categories: efficient solutions lacking formal proofs of security or provably-secure, but highly inefficient solutions. This work will bridge this gap by presenting new constructions and definitions that are both practical and provably-secure. The first contribution in the area of efficient authentication is a provably-secure authentication protocol named HB+. The HB+ protocol is efficient enough to be implemented on extremely low-cost devices, or even by a patient human with a coin to flip. The security of HB+ is based on the hardness of a long-standing learning problem that is closely related to coding theory. HB+ is the first authentication protocol that is both practical for low-cost devices, like radio frequency identification (RFID) tags, and provably secure against active adversaries. The second contribution of this work is a new framework for defining and proving the security of cascadable cryptosystems, specifically commutative cryptosystems.(cont.) This new framework addresses a gap in existing security definitions that fail to handle cryptosystems where ciphertexts produced by cascadable encryption and decryption perations may contain some message-independent history. Several cryptosystems, including a new, practical commutative cryptosystem, are proven secure under this new framework. Finally, a new and efficient private disjointness testing construction named HW is offered. Unlike previous constructions, HW is secure in the face of malicious parties, but without the need for random oracles or expensive zero-knowledge protocols. HW is as efficient as previous constructions and may be implemented using standard software libraries. The security of HW is based on a novel use of subgroup assumptions. These assumptions may prove useful in solving many other private set operation problems.by Stephen A. Weis.Ph.D

Verified Implementations for Secure and Verifiable Computation

Formal verification of the security of software systems is gradually moving from the traditional focus on idealized models, to the more ambitious goal of producing verified implementations. This trend is also present in recent work targeting the verification of cryptographic software, but the reach of existing tools has so far been limited to cryptographic primitives, such as RSA-OAEP encryption, or standalone protocols, such as SSH. This paper presents a scalable approach to formally verifying implementations of higher-level cryptographic systems, directly in the computational model. We consider circuit-based cloud-oriented cryptographic protocols for secure and verifiable computation over encrypted data. Our examples share as central component Yao\u27s celebrated transformation of a boolean circuit into an equivalent garbled form that can be evaluated securely in an untrusted environment. We leverage the foundations of garbled circuits set forth by Bellare, Hoang, and Rogaway (CCS 2012, ASIACRYPT 2012) to build verified implementations of garbling schemes, a verified implementation of Yao\u27s secure function evaluation protocol, and a verified (albeit partial) implementation of the verifiable computation protocol by Gennaro, Gentry, and Parno (CRYPTO 2010). The implementations are formally verified using EasyCrypt, a tool-assisted framework for building high-confidence cryptographic proofs, and critically rely on two novel features: a module and theory system that supports compositional reasoning, and a code extraction mechanism for generating implementations from formalizations

(Public) Verifiability For Composable Protocols Without Adaptivity Or Zero-Knowledge

The Universal Composability (UC) framework (FOCS \u2701) is the current standard for proving security of cryptographic protocols under composition. It allows to reason about complex protocol structures in a bottom-up fashion: any building block that is UC-secure can be composed arbitrarily with any other UC-secure construction while retaining their security guarantees. Unfortunately, some protocol properties such as the verifiability of outputs require excessively strong tools to achieve in UC. In particular, ``obviously secure\u27\u27 constructions cannot directly be shown to be UC-secure, and verifiability of building blocks does not easily carry over to verifiability of the composed construction. In this work, we study Non-Interactive (Public) Verifiability of UC protocols, i.e. under which conditions a verifier can ascertain that a party obtained a specific output from the protocol. The verifier may have been part of the protocol execution or not, as in the case of public verifiability. We consider a setting used in a number of applications where it is ok to reveal the input of the party whose output gets verified and analyze under which conditions such verifiability can generically be achieved using ``cheap\u27\u27 cryptographic primitives. That is, we avoid having to rely on adaptively secure primitives or heavy computational tools such as NIZKs. As Non-Interactive Public Verifiability is crucial when composing protocols with a public ledger, our approach can be beneficial when designing these with provably composable security and efficiency in mind

Privacy enhancing technologies : protocol verification, implementation and specification

In this thesis, we present novel methods for verifying, implementing and specifying protocols. In particular, we focus properties modeling data protection and the protection of privacy. In the first part of the thesis, the author introduces protocol verification and presents a model for verification that encompasses so-called Zero-Knowledge (ZK) proofs. These ZK proofs are a cryptographic primitive that is particularly suited for hiding information and hence serves the protection of privacy. The here presented model gives a list of criteria which allows the transfer of verification results from the model to the implementation if the criteria are met by the implementation. In particular, the criteria are less demanding than the ones of previous work regarding ZK proofs. The second part of the thesis contributes to the area of protocol implementations. Hereby, ZK proofs are used in order to improve multi-party computations. The third and last part of the thesis explains a novel approach for specifying data protection policies. Instead of relying on policies, this approach relies on actual legislation. The advantage of relying on legislation is that often a fair balancing is introduced which is typically not contained in regulations or policies.In dieser Arbeit werden neue Methoden zur Verifikation, Implementierung und Spezifikation im von Protokollen vorgestellt. Ein besonderer Fokus liegt dabei auf Datenschutz-Eigenschaften und dem Schutz der Privatsph¨are. Im ersten Teil dieser Arbeit geht der Author auf die Protokoll- Verifikation ein und stellt ein Modell zur Verifikation vor, dass sogenannte Zero-Knowledge (ZK) Beweise enth¨alt. Diese ZK Beweise sind ein kryptographisches primitiv, dass insbesondere zum Verstecken von Informationen geeignet ist und somit zum Schutz der Privatsph¨are dient. Das hier vorgestellte Modell gibt eine Liste von Kriterien, welche eine Implementierung der genutzten kryptographischen Primitive erf¨ullen muss, damit die verifikationen im Modell sich auf Implementierungen ¨ubertragen lassen. In Bezug auf ZK Beweise sind diese Kriterien sch¨acher als die vorangegangener Arbeiten. Der zweite Teil der Arbeit wendet sich der Implementierung von Protokollen zu. Hierbei werden dann ZK Beweise verwendet um sichere Mehrparteienberechnungen zu verbessern. Im dritten und letzten Teil der Arbeit wird eine neuartige Art der Spezifikation von Datenschutz-Richtlinien erl¨autert. Diese geht nicht von Richtlinien aus, sondern von der Rechtsprechung. Der Vorteil ist, dass in der Rechtsprechung konkrete Abw¨agungen getroffen werden, die Gesetze und Richtlinien nicht enthalten

From Input Private to Universally Composable Secure Multiparty Computation Primitives

Secure multiparty computation systems are commonly built form a small set of primitive components. Composability of security notions has a central role in the analysis of such systems, since it allows us to deduce security properties of complex protocols from the properties of its components. We show that the standard notions of universally composable security are overly restrictive in this context and can lead to protocols with sub-optimal performance. As a remedy, we introduce a weaker notion of privacy that is satisfied by simpler protocols and is preserved by composition. After that we fix a passive security model and show how to convert a private protocol into a universally composable protocol. As a result, we obtain modular security proofs without performance penalties