Privacy-Preserving Minimum Spanning Trees through Oblivious Parallel RAM for Secure Multiparty Computation

In this paper, we describe efficient protocols to perform in parallel many reads and writes in private arrays according to private indices. The protocol is implemented on top of the Arithmetic Black Box (ABB) and can be freely composed to build larger privacy-preserving applications. For a large class of secure multiparty computation (SMC) protocols, we believe our technique to have better practical and asymptotic performance than any previous ORAM technique that has been adapted for use in SMC. Our ORAM technique opens up a large class of parallel algorithms for adoption to run on SMC platforms. In this paper, we demonstrate how the minimum spanning tree (MST) finding algorithm by Awerbuch and Shiloach can be executed without revealing any details about the underlying graph (beside its size). The data accesses of this algorithm heavily depend on the location and weight of edges (which are private) and our ORAM technique is instrumental in their execution. Our implementation is probably the first-ever realization of a privacy-preserving MST algorithm

Computationally secure information flow

This thesis presents a definition and a static program analysis for secure information flow. The definition of secure information flow is not based on non-interference, but on the computational independence of the programs public outputs from its secret inputs. Such definition allows cryptographic primitives to be gracefully handled, as their security is usually defined to be only computational, not information-theoretical. The analysis works on a simple imperative programming language containing a cryptographic primitive encryption as a possible operation. The analysis captures the intuitive qualities of the (lack of) information flow from a plaintext to its corresponding ciphertext. We prove the analysis correct with respect to the definition of secure information flow described above. In the proof of correctness we assume that the encryption primitive hides the identity of plaintexts and keys. This thesis also considers the case where the identities of plaintexts and keys are not hidden by encryption, i.e. given two ciphertexts it may be possible to determine whether the corresponding plaintexts are equal or not. We also give an analysis for this case, though it is not a whole program analysis. Namely, we cannot analyse loops. Nevertheless, with the help of the analysis one can check, whether two formal expressions (which are equivalent to the output of programs without loops) have indistinguishable interpretations as bit-strings.In dieser Dissertation wird eine Definition und eine statische Programmanalyse für sicheren Informationsfluss präsentiert. Die Definition des sicheren Informations usses basiert nicht auf der Unbeeinflußbarkeit, sondern auf der komplexitätstheoretischen Unabhängigkeit der öffentlichen Ausgaben des Programms von seinen geheimen Eingaben. Eine solche Definition erlaubt uns, kryptographische Primitiven elegant zu bearbeiten, weil ihre Sicherheit meistens nur komplexitätstheoretisch und nicht informationstheoretisch definiert ist. Die Analyse arbeitet auf einer einfachen imperativen Programmiersprache, die eine kryptographische Primitive Verschlüsselung als eine mögliche Operation enthält. Die Analyse gibt die intuitive Eigenschaft des (nicht vorhandenen) Informationsflusses von einem Klartext zu dem entsprechenden Schlüsseltext wieder. Wir geben den Korrektheitsbeweis der Analyse in Bezug auf die obengegebene Definition des sicheren Informationflusses. Im Beweis nehmen wir an, daß die Verschlüsselungsprimitive die Identität der Klartexte und Schlüssel versteckt. Diese Dissertation behandelt auch den Fall, dass die Verschlüsselungsprimitive die Identität der Klartexte und Schlüssel nicht versteckt, d.h. daß man aus zwei Schlüsseltexten möglicherweise herausfinden kann, ob die entsprechenden Klartexte gleich sind oder nicht. Wir geben eine Analyse auch für diesen Fall an, obwohl sie nicht auf ganze Programme anwendbar ist, da wir keine Schleifen analysieren können. Mit Hilfe dieser Analyse kann man feststellen, ob zwei formale Ausdrücke (die gleichwertig zu der Ausgabe der Programme ohne Schleifen sind) gleiche Interpretation als Bitfolgen haben

Computationally secure information flow

This thesis presents a definition and a static program analysis for secure information flow. The definition of secure information flow is not based on non-interference, but on the computational independence of the programs public outputs from its secret inputs. Such definition allows cryptographic primitives to be gracefully handled, as their security is usually defined to be only computational, not information-theoretical. The analysis works on a simple imperative programming language containing a cryptographic primitive encryption as a possible operation. The analysis captures the intuitive qualities of the (lack of) information flow from a plaintext to its corresponding ciphertext. We prove the analysis correct with respect to the definition of secure information flow described above. In the proof of correctness we assume that the encryption primitive hides the identity of plaintexts and keys. This thesis also considers the case where the identities of plaintexts and keys are not hidden by encryption, i.e. given two ciphertexts it may be possible to determine whether the corresponding plaintexts are equal or not. We also give an analysis for this case, though it is not a whole program analysis. Namely, we cannot analyse loops. Nevertheless, with the help of the analysis one can check, whether two formal expressions (which are equivalent to the output of programs without loops) have indistinguishable interpretations as bit-strings.In dieser Dissertation wird eine Definition und eine statische Programmanalyse für sicheren Informationsfluss präsentiert. Die Definition des sicheren Informations usses basiert nicht auf der Unbeeinflußbarkeit, sondern auf der komplexitätstheoretischen Unabhängigkeit der öffentlichen Ausgaben des Programms von seinen geheimen Eingaben. Eine solche Definition erlaubt uns, kryptographische Primitiven elegant zu bearbeiten, weil ihre Sicherheit meistens nur komplexitätstheoretisch und nicht informationstheoretisch definiert ist. Die Analyse arbeitet auf einer einfachen imperativen Programmiersprache, die eine kryptographische Primitive Verschlüsselung als eine mögliche Operation enthält. Die Analyse gibt die intuitive Eigenschaft des (nicht vorhandenen) Informationsflusses von einem Klartext zu dem entsprechenden Schlüsseltext wieder. Wir geben den Korrektheitsbeweis der Analyse in Bezug auf die obengegebene Definition des sicheren Informationflusses. Im Beweis nehmen wir an, daß die Verschlüsselungsprimitive die Identität der Klartexte und Schlüssel versteckt. Diese Dissertation behandelt auch den Fall, dass die Verschlüsselungsprimitive die Identität der Klartexte und Schlüssel nicht versteckt, d.h. daß man aus zwei Schlüsseltexten möglicherweise herausfinden kann, ob die entsprechenden Klartexte gleich sind oder nicht. Wir geben eine Analyse auch für diesen Fall an, obwohl sie nicht auf ganze Programme anwendbar ist, da wir keine Schleifen analysieren können. Mit Hilfe dieser Analyse kann man feststellen, ob zwei formale Ausdrücke (die gleichwertig zu der Ausgabe der Programme ohne Schleifen sind) gleiche Interpretation als Bitfolgen haben

Combining Differential Privacy and Secure Multiparty Computation

We consider how to perform privacy-preserving analyses on private data from different data providers and containing personal information of many different individuals. We combine differential privacy and secret sharing in the same system to protect the privacy of both the data providers and the individuals. We have implemented a prototype of this combination and the overhead of adding differential privacy to secret sharing is small enough to be usable in practice

Universally composable privacy preserving finite automata execution with low online and offline complexity

In this paper, we propose efficient protocols to obliviously execute non-deterministic and deterministic finite automata (NFA and DFA) in the arithmetic black box (ABB) model. In contrast to previous approaches, our protocols do not use expensive public-key operations, relying instead only on computation with secret-shared values. Additionally, the complexity of our protocols is largely offline. In particular, if the DFA is available during the precomputation phase, then the online complexity of evaluating it on an input string requires a small constant number of operations per character. This makes our protocols highly suitable for certain outsourcing applications

Privacy-preserving Frequent Itemset Mining for Sparse and Dense Data

Frequent itemset mining is a task that can in turn be used for other purposes such as associative rule mining. One problem is that the data may be sensitive, and its owner may refuse to give it for analysis in plaintext. There exist many privacy-preserving solutions for frequent itemset mining, but in any case enhancing the privacy inevitably spoils the efficiency. Leaking some less sensitive information such as data density might improve the efficiency. In this paper, we devise an approach that works better for sparse matrices and compare it to the related work that uses similar security requirements on similar secure multiparty computation platform

Automatic Proofs of Privacy of Secure Multi-Party Computation Protocols Against Active Adversaries

We describe an automatic analysis to check secure multiparty computation protocols against privacy leaks. The analysis is sound --- a protocol that is deemed private does not leak anything about its private inputs, even if active attacks are performed against it. Privacy against active adversaries is an essential ingredient in constructions aiming to provide security (privacy + correctness) in adversarial models of intermediate (between passive and active) strength. Using our analysis we are able to show that the protocols used by the Sharemind secure multiparty computation platform are actively private