This dissertation includes four contributions concerning secure multiparty computation. The first contribution is a new lossy threshold encryption scheme. This is the first encryption scheme that is both a lossy and a threshold encryption scheme. The second contribution is a new oblivious transfer protocol secure against erasure-free one-sided active adaptive adversaries. The third contribution is a new two-party computation protocol for the evaluation of boolean circuits that is secure against erasure-free one-sided active adaptive adversaries. As a building block of this protocol, a new cut-and-choose oblivious transfer protocol is designed. The fourth contribution is a new multiparty computation protocol for the evaluation of arithmetic circuits that is secure against covert adversaries. Protocols that are part of the second, third and fourth contributions improve the communication complexity, the number of public key encryption operations and the number of exponentiation operations over existing protocols for the same problems that provide the same or higher levels of security.
This dissertation includes four contributions concerning secure multiparty computation. The first contribution is a new lossy threshold encryption scheme. This is the first encryption scheme that is both a lossy and a threshold encryption scheme. The second contribution is a new oblivious transfer protocol secure against erasure-free one-sided active adaptive adversaries. The third contribution is a new two-party computation protocol for the evaluation of boolean circuits that is secure against erasure-free one-sided active adaptive adversaries. As a building block of this protocol, a new cut-and-choose oblivious transfer protocol is designed. The fourth contribution is a new multiparty computation protocol for the evaluation of arithmetic circuits that is secure against covert adversaries. Protocols that are part of the second, third and fourth contributions improve the communication complexity, the number of public key encryption operations and the number of exponentiation operations over existing protocols for the same problems that provide the same or higher levels of security.
In this dissertation, we address several issues that arise in protecting communication between parties, as well as in the area of secure function evaluation. Intuitively, the notion of secure function evaluation is clear and natural: several parties wish to compute some function of their inputs without revealing any information about the inputs, other than what is implied by the value of the function. Research included in this dissertation follows three main directions, briefly described below. The first direction (Chapters 3 and 4) is the design of efficient protocols for concrete functions of interest. Specifically, we present new, more efficient protocols for securely computing the Greater Than (GT) function on the inputs of two parties. Secure evaluation of GT is frequently needed in financial transactions. We introduce new primitives, which are convenient building blocks for more complex tasks, and generalize our GT solutions to satisfy them. Based on this, we construct secure auction protocols, protocols for determining whether an integer lies on an interval, and others. The second direction (Chapter 5) is a fundamental approach to secure evaluation of any function, given as a boolean circuit. We present a very efficient information-theoretic (IT) reduction from the problem of secure evaluation of a polysize formula (or, equivalently, a log-depth boolean circuit) to Oblivious Transfer (a fundamental well-researched cryptographic primitive). Our cost of evaluating each gate of the formula is quadratic in its depth, while in previous reductions it was exponential. Our constructions imply efficient one-round protocols for evaluation of polysize formulas on the players' inputs. We extend our solutions to evaluation of polysize circuits, at the cost of having only computational security. The third direction (Chapter 6) is research on key exchange (KE). In contrast with the previous two directions, here the goal is for two parties to protect their communication against eavesdropping and active interference of an external attacker. KE is a basic procedure, frequently used to establish secure channels between parties. It is a prerequisite to a large number of protocols, including those of the above two directions. We demonstrate a subtle flaw in a previous family of KE protocols and give new KE definitions for the following practical "bank" setting. Here, a server wishes to exchange a key with a client. They have a shared password, and the client carries a "bank card", capable of storing several cryptographic keys. Finally, we present new, more efficient KE protocols for this setting, and prove their security.
Abstract. We introduce a new approach to multiparty computation (MPC) basing it on homomorphic threshold crypto-systems. We show that given keys for any sufficiently efficient system of this type, general MPC protocols for n parties can be devised which are secure against an active adversary that corrupts any minority of the parties. The total number of bits broadcast is O(nk|C|), where k is the security parameter and |C | is the size of a (Boolean) circuit computing the function to be securely evaluated. An earlier proposal by Franklin and Haber with the same complexity was only secure for passive adversaries, while all earlier protocols with active security had complexity at least quadratic in n. We give two examples of threshold cryptosystems that can support our construction and lead to the claimed complexities. 1
Secure two-party computation allows two parties to evaluate a function on their private inputs while keeping all information private except what can be inferred from the outputs. A major building block and the foundation for many efficient secure computation protocols is oblivious transfer (OT). In an OT protocol a sender inputs two messages (x_{0}, x_{1}) while a receiver with choice bit c wants to receive message x_{c}.The OT protocol execution guarantees that the sender learns no information about c and the receiver learns no information about x_{1−c}. This thesis focuses on the efficient generation of OTs and their use in secure computation. In particular, we show how to compute OTs more efficiently, improve generic secure computation protocols which can be used to securely evaluate any functionality, and develop highly efficient special-purpose protocols for private set intersection (PSI). We outline our contributions in more detail next. More Efficient OT Extensions. The most efficient OT protocols are based on public-key cryptography and require a constant number of exponentiations per OT. However, for many practical applications where millions to billions of OTs need to be computed, these exponentiations become prohibitively slow. To enable these applications, OT extension protocols [Bea96, IKNP03] can be used, which extend a small number of public-key-based OTs to an arbitrarily large number using cheap symmetric-key cryptography only. We improve the computation and communication efficiency of OT extension protocols and show how to achieve security against malicious adversaries, which can arbitrarily deviate from the protocol, at low overhead. Our resulting protocols can compute several million of OTs per second and we show that, in contrast to previous belief, the local computation overhead for computing OTs is so low that the main bottleneck is the network bandwidth. Parts of these results are published in: • G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More Efficient Oblivious Transfer and Extensions for Faster Secure Computation. In 20th ACM Conference on Computer and Communications Security (CCS’13). • G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More Efficient Oblivious Transfer Extensions with Security for Malicious Adversaries. In 34th Advances in Cryptology – EUROCRYPT’15. • G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More Efficient Oblivious Transfer Extensions. To appear in Journal of Cryptology. Online at http://eprint.iacr.org/2016/602. Communication-Efficient Generic Secure Two-Party Computation. Generic secure two-party computation techniques allow to evaluate a function, represented as a circuit of linear (XOR) and non-linear (AND) gates. One of the most prominent generic secure two-party computation protocols is Yao’s garbled circuits [Yao86], for which many optimizations have been proposed. Shortly after Yao’s protocol, the generic secure protocol by Goldreich-Micali-Wigderson (GMW) [GMW87] was introduced. The GMW protocol requires a large number of OTs and was believed to be less efficient for secure two-party computation than Yao’s protocol [HL10, CHK+12]. We improve the efficiency of the GMW protocol and show that it can outperform Yao’s garbled circuits protocol in settings with low bandwidth. Furthermore, we utilize the flexibility of OT and outline special-purpose constructions that can be used within the GMW protocol and which improve its efficiency even further. Parts of these results are published in: • T. Schneider, M. Zohner. GMW vs. Yao? Efficient Secure Two-Party Computation with Low Depth Circuits. In 17th International Conference on Financial Cryptography and Data Security (FC’13). • D. Demmler, T. Schneider, M. Zohner. ABY - A Framework for Efficient Mixed-Protocol Secure Two-Party Computation. In 22th Network and Distributed System Security Symposium (NDSS’15). • G. Dessouky, F. Koushanfar, A.-R. Sadeghi, T. Schneider, S. Zeitouni, M. Zohner. Pushing the Communication Barrier in Secure Computation using Lookup Tables. In 24th Network and Distributed System Security Symposium (NDSS’17). Faster Private Set Intersection (PSI). PSI allows two parties to compute the intersection of their private sets without revealing any element that is not in the intersection. PSI is a well-studied problem in secure computation and many special-purpose protocols have been proposed. However, existing PSI protocols are several orders of magnitude slower than an insecure naive hashing solution that is used in practice. In addition, many protocols were compared in a biased fashion, which makes it difficult to identify the most promising solution for a particular scenario. We systematize the progress made on PSI protocols by reviewing, optimizing, and comparing existing PSI protocols. We then introduce a novel PSI protocol that is based on our efficiency improvements in OT extension protocols and which outperforms existing protocols by up to two orders of magnitude. Parts of these results are published in: • B. Pinkas, T. Schneider, M. Zohner. Faster Private Set Intersection Based on OT Extension. In 23th USENIX Security Symposium (USENIX Security’14). • B. Pinkas, T. Schneider, G. Segev, M. Zohner. Phasing: Private Set Intersection using Permutation-based Hashing. In 24th USENIX Security Symposium (USENIX Security’15). • B. Pinkas, T. Schneider, M. Zohner. Scalable Private Set Intersection Based on OT Extension. Journal paper. In submission. Online at http://iacr.eprint.org/2016/930.
We introduce a new approach to multiparty computation (MPC) basing it on homomorphic threshold crypto-systems. We show that given keys for any sufficiently efficient system of this type, general MPC protocols for n players can be devised which are secure against an active adversary that corrupts any minority of the players. The total number of bits sent is O(nk|C|), where k is the security parameter and |C| is the size of a (Boolean) circuit computing the function to be securely evaluated. An earlier proposal by Franklin and Haber with the same complexity was only secure for passive adversaries, while all earlier protocols with active security had complexity at least quadratic in n. We give two examples of threshold cryptosystems that can support our construction and lead to the claimed complexities.
Multiparty Computation (hereafter MPC) is a technique for allowing a set ofparticipants to run a secure computation with the assurance that the output is (1) correct, and (2) that a malicious party did not learn anything about the inputs of the honest parties besides what it can glean from the output. Impor- tantly much of cryptography is based on the assumption that an honest party has a private and secret input, and if the adversary learns this input the security of the scheme is broken. Then naturally the techniques of MPC can be applied to create threshold protocols for these cryptographic schemes to ensure that the secret inputs are not leaked and moreover that no group of parties smaller than the threshold know the input at all. While we have known how to generically evaluate MPC for any function since the 80s the question of efficiency still drives progress to this day. This thesis looks at two approaches for making secure com- putation more practical to deploy: developing specialized protocols for appli- cations such as distributed key generation and signing with RSA and ECDSA; and improving the state of the art of maliciously secure generic boolean-circuit MPC. We first look at work that produced a distributed key generation protocol for RSA that utilizes a novel candidate sampling mechanism to reduce waste in primality testing. The second work builds a threshold scheme for symmetric cryptographic primitives such as AES and SHA where there is limited algebraic structure to exploit by efficiently converting a generic n-of-n MPC protocol into a threshold t-of-n MPC protocol. Future directions in this thesis are in combin- ing techniques from the prior works to create a blind signature scheme for the Elliptic Curve Digital Signature Algorithm (ECDSA) that requires both alge- braic operations over elliptic curves and additionally symmetric evaluations of the SHA2 hash function.--Author's abstract
Secure multi-party computation (MPC) enables distrustful parties to jointly perform computations while guaranteeing both the privacy of their inputs and the correctness of the computation.
This thesis explores two aspects of secure multi-party computation: adaptive security and round efficiency. Adaptive security is concerned with an adversary that adaptively determines who and when to corrupt during the course of the computation. Even though this is a very natural and realistic assumption about the adversary, most of the MPC literature addresses security only against a static adversary — an adversary that chooses (and fixes) which parties to corrupt before the protocol starts executing. A protocol is called round-efficient if it runs in a small number of rounds. Constructing such protocols is important since efficiency of a protocol is greatly influenced by its round complexity.
The security in this thesis is formulated in the universal composability (UC) framework introduced by Canetti [Can01]. Protocols secure in the UC framework remain secure even when executed concurrently with other arbitrary protocols running in some larger network, and can be used as subroutines of larger protocols in a modular fashion. This property is important considering that nowadays many protocols are executed concurrently with others in the Internet.
With the focus on adaptive security and round efficiency, we obtain the following results:
(1) We show that with access to an ideal commitment functionality, there exists a protocol that UC realizes any well-formed multi-party functionality against a malicious, adaptive adversary that may corrupt any number of parties, with black-box access to any protocol that UC realizes oblivious transfer against a semi-honest, adaptive adversary.
(2) We show that there exists a protocol that UC realizes oblivious transfer against a semi-honest, adaptive adversary, with black-box access to a cryptographic primitive called a trapdoor simulatable cryptosystem, which is a natural relaxation of a simulatable cryptosystem introduced by Damgard and Nielsen [3N00].
We also show that the primitive can be constructed based on hardness of factoring.
(3) We present a single-message protocol that UC realizes two-party computing with encrypted data (a variant of secure two-party computation), based on the DDH assumption and non- interactive zero-knowledge arguments. The protocol achieves security against a malicious, static adversary.
(4) We present two round-efficient protocols that UC realize multi-party computing with encrypted data (a variant of secure multi-party computation), based on the DDH assumption and non-interactive zero-knowledge arguments. The first (resp. second) protocol requires one round (resp. two rounds) with appropriate preprocessing, which is independent of the exact circuit and actual inputs of the specific instance problem to solve — only the bound on the circuit size is known. Although the first protocol is more round-efficient, the preprocessing of the second is sometimes better under some efficiency considerations. Both protocols achieve security against a malicious, static adversary that may corrupt up to all but one parties.