The term Federated Learning was coined as recently as 2016 to describe a machine learning setting where multiple entities collaborate in solving a machine learning problem, under the coordination of a central server or service provider. Each client’s raw data is stored locally and not exchanged or transferred; instead, focused updates intended for immediate aggregation are used to achieve the learning objective. Since then, the topic has gathered much interest across many different disciplines and the realization that solving many of these interdisciplinary problems likely requires not just machine learning but techniques from distributed optimization, cryptography, security, differential privacy, fairness, compressed sensing, systems, information theory, statistics, and more. This monograph has contributions from leading experts across the disciplines, who describe the latest state-of-the art from their perspective. These contributions have been carefully curated into a comprehensive treatment that enables the reader to understand the work that has been done and get pointers to where effort is required to solve many of the problems before Federated Learning can become a reality in practical systems. Researchers working in the area of distributed systems will find this monograph an enlightening read that may inspire them to work on the many challenging issues that are outlined. This monograph will get the reader up to speed quickly and easily on what is likely to become an increasingly important topic: Federated Learning.

/pdf/advances-and-open-problems-in-federated-learning-3t0jgb90ia.pdf

Advances and open problems in federated learning

Emerging smart contract systems over decentralized cryptocurrencies allow mutually distrustful parties to transact safely without trusted third parties. In the event of contractual breaches or aborts, the decentralized blockchain ensures that honest parties obtain commensurate compensation. Existing systems, however, lack transactional privacy. All transactions, including flow of money between pseudonyms and amount transacted, are exposed on the blockchain. We present Hawk, a decentralized smart contract system that does not store financial transactions in the clear on the blockchain, thus retaining transactional privacy from the public's view. A Hawk programmer can write a private smart contract in an intuitive manner without having to implement cryptography, and our compiler automatically generates an efficient cryptographic protocol where contractual parties interact with the blockchain, using cryptographic primitives such as zero-knowledge proofs. To formally define and reason about the security of our protocols, we are the first to formalize the blockchain model of cryptography. The formal modeling is of independent interest. We advocate the community to adopt such a formal model when designing applications atop decentralized blockchains.

https://www.the-blockchain.com/docs/Hawk%20-%20The%20Blockchain%20Model%20of%20Cryptography%20and%20Privacy-Preserving%20Smart%20Contracts.pdf

Hawk: The Blockchain Model of Cryptography and Privacy-Preserving Smart Contracts

Bit coin is the first digital currency to see widespread adoption. While payments are conducted between pseudonyms, Bit coin cannot offer strong privacy guarantees: payment transactions are recorded in a public decentralized ledger, from which much information can be deduced. Zero coin (Miers et al., IEEE SaP 2013) tackles some of these privacy issues by unlinking transactions from the payment's origin. Yet, it still reveals payments' destinations and amounts, and is limited in functionality. In this paper, we construct a full-fledged ledger-based digital currency with strong privacy guarantees. Our results leverage recent advances in zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs). First, we formulate and construct decentralized anonymous payment schemes (DAP schemes). A DAP scheme enables users to directly pay each other privately: the corresponding transaction hides the payment's origin, destination, and transferred amount. We provide formal definitions and proofs of the construction's security. Second, we build Zero cash, a practical instantiation of our DAP scheme construction. In Zero cash, transactions are less than 1 kB and take under 6 ms to verify - orders of magnitude more efficient than the less-anonymous Zero coin and competitive with plain Bit coin.

/pdf/zerocash-decentralized-anonymous-payments-from-bitcoin-3npbm68ga9.pdf

Zerocash: Decentralized Anonymous Payments from Bitcoin

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

Advances and Open Problems in Federated Learning

Time-lock puzzles are a mechanism for sending messages “to the future”. A sender can quickly generate a puzzle with a solution s that remains hidden until a moderately large amount of time t has elapsed. The solution s should be hidden from any adversary that runs in time significantly less than t, including resourceful parallel adversaries with polynomially many processors. While the notion of time-lock puzzles has been around for 22 years, there has only been a single candidate proposed. Fifteen years ago, Rivest, Shamir and Wagner suggested a beautiful candidate time-lock puzzle based on the assumption that exponentiation modulo an RSA integer is an “inherently sequential” computation. We show that various flavors of randomized encodings give rise to time-lock puzzles of varying strengths, whose security can be shown assuming the existence of non-parallelizing languages, which are languages that require circuits of depth at least t to decide, in the worstcase. The existence of such languages is necessary for the existence of time-lock puzzles. We instantiate the construction with different randomized encodings from the literature, where increasingly better efficiency is obtained based on increasingly stronger cryptographic assumptions, ranging from one-way functions to indistinguishability obfuscation. We also observe that time-lock puzzles imply one-way functions, and thus the reliance on some cryptographic assumption is necessary. Finally, generalizing the above, we construct other types of puzzles such as proofs of work from randomized encodings and a suitable worst-case hardness assumption (that is necessary for such puzzles to exist). ∗MIT. Email: nirbitan@csail.mit.edu. †MIT and Weizmann Institute. Email: shafi@theory.csail.mit.edu. ‡Johns Hopkins University. Email: abhishek@cs.jhu.edu. §Boston University. Email: omer@bu.edu. Supported by the Simons award for graduate students in theoretical computer science and an NSF Algorithmic foundations grant 1218461. ¶MIT. Email: vinodv@mit.edu. ‖UT Austin. Email: bwaters@cs.utexas.edu.

/pdf/time-lock-puzzles-from-randomized-encodings-krw3cz94zl.pdf

Time-Lock Puzzles from Randomized Encodings.

An obfuscator O is Virtual Grey Box (VGB) for a class C of circuits if, for any C ∈ C and any predicate π, deducing π(C) given O(C) is tantamount to deducing π(C) given unbounded computational resources and polynomially many oracle queries to C. VGB obfuscation is often significantly more meaningful than indistinguishability obfuscation (IO). In fact, for some circuit families of interest VGB is equivalent to full-fledged Virtual Black Box obfuscation. We investigate the feasibility of obtaining VGB obfuscation for general circuits. We first formulate a natural strengthening of IO, called strong IO (SIO). Essentially, O is SIO for class C if O(C) ≈ O(C ′) whenever the pair (C,C ′) is taken from a distribution over C where, for all x, C(x) 6= C ′(x) only with negligible probability. We then show that an obfuscator is VGB for a class C if and only if it is SIO for C. This result is unconditional and holds for any C. We also show that, for some circuit collections, SIO implies virtual black-box obfuscation. Finally, we formulate a slightly stronger variant of the semantic security property of graded encoding schemes [Pass-Seth-Telang Crypto 14], and show that existing obfuscators, such as the obfuscator of Barak et al. [Eurocrypt 14], are SIO for all circuits in NC, assuming that the underlying graded encoding scheme satisfies our variant of semantic security. Put together, we obtain VGB obfuscation for all NC circuits under assumptions that are almost the same as those used by Pass et al. to obtain IO for NC circuits. We also show that semantic security is in essence necessary for showing VGB obfuscation. ∗A preliminary version of this work appears in the proceedings of CRYPTO 2014. †Tel Aviv University. Email: nirbitan@tau.ac.il. Supported by an IBM Ph.D. Fellowship, the Check Point Institute for Information Security, and The Israeli Ministry of Science and Technology. ‡Boston University and Tel Aviv University. Email: canetti@bu.edu. Supported by the Check Point Institute for Information Security, an ISF grant 20006317, an NSF EAGER grant, and an NSF Algorithmic foundations grant 1218461. §Microsoft Research ¶Boston University. Email: omer@bu.edu. Supported by the Simons award for graduate students in theoretical computer science and an NSF Algorithmic foundations grant 1218461.

/pdf/on-virtual-grey-box-obfuscation-for-general-circuits-3rfn59j817.pdf

On Virtual Grey Box Obfuscation for General Circuits.

We consider the problem of amplifying two-party coin-tossing protocols: given a protocol where it is possible to bias the common output by at most ρ, we aim to obtain a new protocol where the output can be biased by at most ρ < ρ. We rule out the existence of a natural type of amplifiers called oblivious amplifiers for every ρ < ρ. Such amplifiers ignore the way that the underlying ρ-bias protocol works and can only invoke an oracle that provides ρ-bias bits. We provide two proofs of this impossibility. The first is by a reduction to the impossibility of deterministic randomness extraction from Santha-Vazirani sources. The second is a direct proof that is more general and also rules outs certain types of asymmetric amplification. In addition, it gives yet another proof for the Santha-Vazirani impossibility. 2012 ACM Subject Classification Theory of computation → Cryptographic protocols; Theory of computation → Oracles and decision trees

On Oblivious Amplification of Coin-Tossing Protocols.

A function f is extractable if it is possible to algorithmically “extract,” from any adversarial program that outputs a value y in the image of f, a preimage of y. When combined with hardness properties such as one-wayness or collision-resistance, extractability has proven to be a powerful tool. However, so far, extractability has not been explicitly shown. Instead, it has only been considered as a non-standard knowledge assumption on certain functions. We make two headways in the study of the existence of extractable one-way functions (EOWFs). On the negative side, we show that if there exist indistinguishability obfuscators for a certain class of circuits then there do not exist EOWFs where extraction works for any adversarial program with auxiliary-input of unbounded polynomial length. On the positive side, for adversarial programs with bounded auxiliary-input (and unbounded polynomial running time), we give the first construction of EOWFs with an explicit extraction procedure, based on relatively standard assumptions (e.g., sub-exponential hardness of Learning with Errors). We then use these functions to construct the first 2-message zero-knowledge arguments and 3-message zeroknowledge arguments of knowledge, against the same class of adversarial verifiers, from essentially the same assumptions. ∗This is a merged version of two works: “How to construct extractable one-way functions against uniform adversaries” (IACR Eprint 2013/468) and “Indistinguishability obfuscation vs. Extractable one-way functions: One must fall” (IACR Eprint 2013/641). An extended abstract of this work appears in STOC 2014. †Tel Aviv University. Email: nirbitan@tau.ac.il. Supported by an IBM Ph.D. Fellowship and the Check Point Institute for Information Security. ‡Boston University and Tel Aviv University. Email: canetti@bu.edu. Supported by the Check Point Institute for Information Security, an NSF EAGER grant, and NSF Algorithmic foundations grant 1218461. §Boston University. Email: omer@bu.edu. Supported by the Simons award for graduate students in theoretical computer science and an NSF Algorithmic foundations grant 1218461. ¶Efi Arazi School of Computer Science, IDC Herzliya, Israel. Email: alon.rosen@idc.ac.il. Supported by ISF grant no. 1255/12 and by the ERC under the EU’s Seventh Framework Programme (FP/2007-2013) ERC Grant Agreement n. 307952.

/pdf/on-the-existence-of-extractable-one-way-functions-2xdxdvgjrw.pdf

On the Existence of Extractable One-Way Functions.

/pdf/from-point-obfuscation-to-3-round-zero-knowledge-50be8k68h6.pdf

From Point Obfuscation To 3-round Zero-Knowledge.

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