Efficient asynchronous accumulators for distributed PKI

Cryptographic accumulators are a tool for compact set representation and secure set membership proofs. When an element is added to a set by means of an accumulator, a membership witness is generated. This witness can later be used to prove the membership of the element. Typically, the membership witness has to be synchronized with the accumulator value, and to be updated every time another element is added to the accumulator. In this work we propose an accumulator that, unlike any prior scheme, does not require strict synchronization. In our construction a membership witness needs to be updated only a logarithmic number of times in the number of subsequent element additions. Thus, an out-of-date witness can be easily made current. Vice versa, a verifier with an out-of-date accumulator value can still verify a current membership witness. These properties make our accumulator construction uniquely suited for use in distributed applications, such as blockchain-based public key infrastructures

Studies in authentication

This thesis presents advances in several areas of authentication. First, we consider cryptographic accumulators, which are compact digital objects representing arbitrarily large sets. They support efficient proofs of membership (or, alternatively, of non-membership). We give the first definition of cryptographic accumulators in the UC framework, and construct two new accumulators: one uniquely suited for use in a revokable anonymous credential scheme, and one uniquely suited for use in a distributed system such as a blockchain-based PKI. Next, we consider multi-designated verifier signatures (MDVS). An MDVS is a special kind of signature that can only be verified by parties explicitly specified by the signer; more than that, even if those designated verifiers wanted to prove to an external party (e.g. an adversary) that a certain message was signed by the signer, they should be unable to do so. This is crucial in contexts where off-the-record communication is desirable; the sender may not want to be provably linked to a possibly sensitive message, but still want the intended recipients to be able to verify the authenticity of the message. Existing literature defines and builds limited notions of MDVS, where the off-the-record property only holds when it is conceivable that all verifiers collude. We strengthen this property to support any subset of colluding verifiers, and give two constructions of our stronger notion of MDVS: one from functional encryption, and one from standard primitives (but with a slightly larger signature size). Finally, we consider fuzzy password authenticated key exchange (Fuzzy PAKE). PAKEs are protocols which enable two parties holding the same password (that is, the same potentially low-entropy, non-uniform string) to agree on a (high-entropy, uniform) secret key in a way that resists man-in-the-middle attacks and offline dictionary attacks on the password. We define Fuzzy PAKE, a special kind of PAKE where the passwords used for authentication may contain some errors. We provide the first efficient and general solutions to this problem that enable, for example, key agreement based on commonly used biometrics such as iris scans

Broadcast Secret-Sharing, Bounds and Applications

Consider a sender ? and a group of n recipients. ? holds a secret message ? of length l bits and the goal is to allow ? to create a secret sharing of ? with privacy threshold t among the recipients, by broadcasting a single message ? to the recipients. Our goal is to do this with information theoretic security in a model with a simple form of correlated randomness. Namely, for each subset ? of recipients of size q, ? may share a random key with all recipients in ?. (The keys shared with different subsets ? must be independent.) We call this Broadcast Secret-Sharing (BSS) with parameters l, n, t and q. Our main question is: how large must ? be, as a function of the parameters? We show that (n-t)/q l is a lower bound, and we show an upper bound of ((n(t+1)/(q+t)) -t)l, matching the lower bound whenever t = 0, or when q = 1 or n-t. When q = n-t, the size of ? is exactly l which is clearly minimal. The protocol demonstrating the upper bound in this case requires ? to share a key with every subset of size n-t. We show that this overhead cannot be avoided when ? has minimal size. We also show that if access is additionally given to an idealized PRG, the lower bound on ciphertext size becomes (n-t)/q ? + l - negl(?) (where ? is the length of the input to the PRG). The upper bound becomes ((n(t+1))/(q+t) -t)? + l. BSS can be applied directly to secret-key threshold encryption. We can also consider a setting where the correlated randomness is generated using computationally secure and non-interactive key exchange, where we assume that each recipient has an (independently generated) public key for this purpose. In this model, any protocol for non-interactive secret sharing becomes an ad hoc threshold encryption (ATE) scheme, which is a threshold encryption scheme with no trusted setup beyond a PKI. Our upper bounds imply new ATE schemes, and our lower bound becomes a lower bound on the ciphertext size in any ATE scheme that uses a key exchange functionality and no other cryptographic primitives

Secure Communication in Dynamic Incomplete Networks

In this paper, we explore the feasibility of reliable and private communication in dynamic networks, where in each round the adversary can choose which direct peer-to-peer links are available in the network graph, under the sole condition that the graph is k-connected at each round (for some k). We show that reliable communication is possible in such a dynamic network if and only if k > 2t. We also show that if k = cn > 2 t for a constant c, we can achieve reliable communication with polynomial round and communication complexity. For unconditionally private communication, we show that for a passive adversary, k > t is sufficient (and clearly necessary). For an active adversary, we show that k > 2t is sufficient for statistical security (and clearly necessary), while k > 3t is sufficient for perfect security. We conjecture that, in contrast to the static case, k > 2t is not enough for perfect security, and we give evidence that the conjecture is true. Once we have reliable and private communication between each pair of parties, we can emulate a complete network with secure channels, and we can use known protocols to do secure computation

Distributed (Correlation) Samplers: How to Remove a Trusted Dealer in One Round

Structured random strings (SRSs) and correlated randomness are important for many cryptographic protocols. In settings where interaction is expensive, it is desirable to obtain such randomness in as few rounds of communication as possible; ideally, simply by exchanging one reusable round of messages which can be considered public keys. In this paper, we describe how to generate any SRS or correlated randomness in such a single round of communication, using, among other things, indistinguishability obfuscation. We introduce what we call a distributed sampler, which enables $n$ parties to sample a single public value (SRS) from any distribution. We construct a semi-malicious distributed sampler in the plain model, and use it to build a semi-malicious public-key PCF (Boyle et al, FOCS 2020) in the plain model. A public-key PCF can be thought of as a distributed correlation sampler; instead of producing a public SRS, it gives each party a private random value (where the values satisfy some correlation). We introduce a general technique called an anti-rusher which compiles any one-round protocol with semi-malicious security without inputs to a similar one-round protocol with active security by making use of a programmable random oracle. This gets us actively secure distributed samplers and public-key PCFs in the random oracle model. Finally, we explore some tradeoffs. Our first PCF construction is limited to reverse-sampleable correlations (where the random outputs of honest parties must be simulatable given the random outputs of corrupt parties); we additionally show a different construction without this limitation, but which does not allow parties to hold secret parameters of the correlation. We also describe how to avoid the use of a random oracle at the cost of relying on sub-exponentially secure indistinguishability obfuscation

A Decentralized Public Key Infrastructure with Identity Retention

Public key infrastructures (PKIs) enable users to look up and verify one another\u27s public keys based on identities. Current approaches to PKIs are vulnerable because they do not offer sufficiently strong guarantees of \emph{identity retention}; that is, they do not effectively prevent one user from registering a public key under another\u27s already-registered identity. In this paper, we leverage the consistency guarantees provided by cryptocurrencies such as Bitcoin and Namecoin to build a PKI that ensures identity retention. Our system, called Certcoin, has no central authority and thus requires the use of secure distributed dictionary data structures to provide efficient support for key lookup

Threshold-Optimal MPC With Friends and Foes

Alon et. al (Crypto 2020) initiated the study of MPC with Friends and Foes (FaF) security, which captures the desirable property that even up to $h^{*}$ honest parties should learn nothing additional about other honest parties’ inputs, even if the $t$ corrupt parties send them extra information. Alon et. al describe two flavors of FaF security: weak FaF, where the simulated view of up to $h^{*}$ honest parties should be indistinguishable from their real view, and strong FaF, where the simulated view of the honest parties should be indistinguishable from their real view even in conjunction with the simulated / real view of the corrupt parties. They give several initial FaF constructions with guaranteed output delivery (GOD); however, they leave some open problems. Their only construction which supports the optimal corruption bounds of $2t+h^{*} < n$ (where $n$ denotes the number of parties) only offers weak FaF security and takes much more than the optimal three rounds of communication. In this paper, we describe two new constructions with GOD, both of which support $2t+h^{*} < n$. Our first construction, based on threshold FHE, is the first three-round construction that matches this optimal corruption bound (though it only offers weak FaF security). Our second construction, based on a variant of BGW, is the first such construction that offers strong FaF security (though it requires more than three rounds, as well as correlated randomness). Our final contribution is further exploration of the relationship between FaF security and similar security notions. In particular, we show that FaF security does not imply mixed adversary security (where the adversary can make $t$ active and $h^{*}$ passive corruptions), and that Best of Both Worlds security (where the adversary can make $t$ active or $t+h^{*}$ passive corruptions, but not both) is orthogonal to both FaF and mixed adversary security

Constant-Round YOSO MPC Without Setup

YOSO MPC (Gentry et al., Crypto 2021) is a new MPC framework where each participant can speak at most once. This models an adaptive adversary’s ability to watch the network and corrupt or destroy parties it deems significant based on their communication. By using private channels to anonymous receivers (e.g. by encrypting to a public key whose owner is unknown), the communication complexity of YOSO MPC can scale sublinearly with the total number N of available parties, even when the adversary’s corruption threshold is linear in N (e.g. just under N/2). It was previously an open problem whether YOSO MPC can achieve guaranteed output delivery in a constant number of rounds without relying on trusted setup. In this work, we show that this can indeed be accomplished. We demonstrate three different approaches: the first two (which we call YaOSO and YOSO-GLS) use two and three rounds of communication, respectively. Our third approach (which we call YOSO-LHSS) uses O(d) rounds, where d is the multiplicative depth of the circuit being evaluated; however, it can be used to bootstrap any constant-round YOSO protocol that requires setup, by generating that setup within YOSO-LHSS. Though YOSO-LHSS requires more rounds than our first two approaches, it may be more practical, since the zero knowledge proofs it employs are more efficient to instantiate. As a contribution of independent interest, we introduce a verifiable state propagation UC functionality, which allows parties to send private message which are verifiably derived in the “correct” way (according to the protocol in question) to anonymous receivers. This is a natural functionality to build YOSO protocols on top of

Stronger Notions and a More Efficient Construction of Threshold Ring Signatures

We consider threshold ring signatures (introduced by Bresson et al. [BSS02], where any t signers can sign a message while anonymizing themselves within a larger (size-n) group. The signature proves that t members of the group signed, without revealing anything else about their identities. Our contributions in this paper are two-fold. First, we strengthen existing definitions of threshold ring signatures in a natural way; we demand that a signer cannot be de-anonymized even by their fellow signers. This is crucial, since in applications where a signer\u27s anonymity is important, we do not want anonymity to be compromised by a single insider. Our definitions demand non-interactive signing, which is important for anonymity, since truly anonymous interaction is difficult or impossible in many scenarios. Second, we give the first rigorous construction of a threshold ring signature with size independent of n, the number of users in the larger group. Instead, our signatures have size linear in t, the number of signers. This is also a very important contribution; signers should not have to choose between achieving their desired degree of anonymity (possibly very large n) and their need for communication efficiency