Opening talk of the NIST Threshold Cryptography Workshop (NTCW) 2019, explaining the scope of the project and showing the agenda for the workshop.

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Abstract: The trend in trust decentralization together with the ever increasing value of digital assets (cryptocurrencies, blockchains, mega data repositories, key (mis)management, intellectual property, privacy, etc.) and the need to protect these assets for secrecy and availability, make threshold cryptography a most relevant technology whose time has come. We need to see more targeted applications as well as software platforms on which to build solutions that take into account real-world considerations such as asynchronous networks, support for diversified architectures, hardware enclaves, and more. Additionally, we need to refresh the set of techniques supporting threshold cryptography with advances in areas such as multi-party computation, quantum-resistant primitives, and blockchain-inspired consensus protocols. In addition to arguing these points, the talk will discuss some recent applications of threshold cryptography in the domain of key and password management, blockchain, and how threshold cryptography can be relevant to the #metoo movement.

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Joint work with Christian Cachin, Hugo Krawczyk, Tal Rabin, Chrysoula Stathakopoulou

Partial abstract: We introduce ‘PROTECT’ a Platform for Robust Threshold Cryptography. It’s a freely available open-source project [1], and it can be readily deployed to implement a number of threshold-secure services. PROTECT implements cryptographic functionality as operations on shares of a physically distributed key. The implementation is robust in the sense that it tolerates and recovers from Byzantine faults, while preserving availability and confidentiality of the shared secret through share recovery and proactive share renewal operations.

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Joint work with: Michael Kraitsberg, Yehuda Lindell, Valery Osheter, Younes Talibi Alaoui.

Abstract: We show how to build distributed key generation and distributed decryption procedures for the LIMA Ring-LWE based post-quantum cryptosystem. Our protocols implement the CCA variants of distributed decryption and are actively secure (with abort) in the case of three parties and honest majority. Our protocols make use of a combination of problem specific MPC protocols, generic garbled circuit based MPC and generic Linear Secret Sharing based MPC. We also, as a by-product, report on the first run-times for the execution of the SHA-3 function in an MPC system.

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Joint work with: Benoı̂t Libert, Marc Joye, Moti Yung.

Partial Abstract. We present a practical fully distributed non-interactive scheme — where the servers can compute their partial signatures without communication with other servers —with adaptive security (i.e., the adversary corrupts servers dynamically based on its full view of the history of the system). Our scheme is very efficient in terms of computation, communication, and scalable storage (with private key shares of size O(1), where certain solutions incur O(n) storage costs at each server). Unlike other adaptively secure schemes, our scheme is erasure-free. Of particular interest is the fact that Pedersen’s traditional distributed key generation (DKG) protocol can be safely employed in the initial key generation phase when the system is set up although it is well-known not to ensure uniformly distributed public keys. An advantage of this is that this protocol only takes one round in the absence of faulty player.

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Joint work with: Jack Doerner, Eysa Lee, abhi Shelat

Note: this also counted as the 1st (out of three) introductory presentation to the panel "Threshold Protocols for the Digital Signature Standard"

Partial abstract: This paper reports on new protocols (appearing in [DKLs18, DKLs19]) for multi-party ECDSA key-generation and signing with arbitrary thresholds, that are secure against malicious adversaries in the Random Oracle Model assuming only the Computational Die-Hellman Assumption. We instantiate our protocols using the same hash function and elliptic curve group used by the ECDSA signature being computed. Our threshold t scheme requires log(t) + 6 rounds of communication with scope for adjustment to constant rounds if desired, and when t = 2 we provide an optimized two message protocol. We evaluate our implementations and nd that the wall-clock time for computing a signature through our two-party protocol comes to within a factor of 18 of local signatures. Concretely, two parties can jointly sign a message in just over three milliseconds. We also demonstrate the feasibility of signing with a low-power device (as in the setting of 2-factor authentication) by computing a signature between two Raspberry Pi devices in under 60 milliseconds.

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This was the 2nd of three introductory talks in the panel discussion "Threshold Protocols for the Digital Signature Standard".

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This was the 3rd of three introductory talks in the panel discussion "Threshold Protocols for the Digital Signature Standard".

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Partial abstract from the panel proposal: Due to the intense commercial interest in threshold protocols for DSA based signatures, we believe that a panel on the status of threshold protocols for DSA, and its maturity for standardization would be a very relevant and interesting addition to the NIST Workshop.

The panel, introduced by Hugo Krawczyk (IBM Research, USA), was composed of three introductory talks (the first of which is from the previous session, by Yashvanth Kondi), followed by a panel discussion.

Introduction talks:

1. [Merged with previous session] A Multiparty Computation Approach to Threshold ECDSA. Speaker: Yashvanth Kondi. Joint work with: Jack Doerner, Eysa Lee, abhi shelat. (Northeastern University, USA).
2. Fast Secure Multiparty ECDSA. Speaker: Samuel Ranellucci (Unbound Tech, Israel).
3. Fast Multiparty Threshold ECDSA with Fast Trustless Setup. Speaker: Rosario Gennaro (CUNY, USA). Joint work with Steven Goldfeder.

Panel discussion. Moderator: Hugo Krawczyk (IBM Research, USA). Panelists: Samuel Ranellucci (Unbound Tech, Israel); Rosario Gennaro (CUNY, USA); abhi shelat (Northeastern University, USA).

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Joint work with: Dušan Božilov, Miroslav Knežević.

Abstract. Threshold implementation (TI) is a popular hardware masking technique, being used in some of the current most efficient side-channel secure designs. Earlier versions of TI are characterized by the number of input shares being dependant on both security order d and algebraic degree of a function t, namely td + 1. Later, the bound was reduced to d + 1, with the cost of increasing the number of output shares and requirements of the input shares. In this work, we utilize the optimized sharing method to investigate the impact of the number of S-box stages on the area and latency of the final design, with the two extreme cases of fully decomposed S-box and a single stage S-box. Finally, we show the trade-off on d+1 and td + 1 TI, for first- and second-order secure, low-latency and low-energy implementations of the PRINCE block cipher.

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Joint work with: Karine Villegas, Claudio Favi.

Partial abstract. This presentation will discuss the interaction between side channel protections and high-speed hardware implementations; we will show that in some way these objectives are contradictory by discussing concrete examples. By deriving conclusions, we will state an important open problem, that we think must be considered in the threshold standardization effort.

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Partial abstract. In this talk we will discuss two recent proposals in this area: CAPA and M&M, which both start from passively secure threshold schemes and extend those with information-theoretic MAC tags for protection against active adversaries. While similar in their most basic structure, the two proposals explore very different adversary models and thus employ completely different implementation techniques. CAPA considers the field-probe-and-fault model, which is the embedded analogue of multiple parties jointly computing a function with at least one of the parties honest. Accordingly, CAPA is strongly based on the actively secure MPC protocol SPDZ and inherits its provable security properties in this model. Since this results in very expensive implementations, M&M works in a similar but more realistic adversary model and uses existing building blocks from previous passively secure implementations to build more efficient actively secure threshold cryptography.

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Joint work with: Sveta Nikova, Vincent Rijmen.

Abstract. Masking is a widely used countermeasure against Side-Channel Attacks, nonetheless, the implementation of these countermeasures is challenging. Experimental security evaluation requires special equipment, a considerable amount of time, and extensive technical knowledge. Therefore, to automate and to speed up this process, a formal verification can be performed to asses the security of a design. In this work we present VerMI, a verification tool in the form of a logic simulator that checks the properties defined in Threshold Implementations to address the security of a hardware implementation for meaningful orders of security. The tool is designed so that any masking scheme can be evaluated. It accepts combinational and sequential logic and is able to analyze an entire cipher in short time. With the tool we have managed to spot a flaw in the round-based KECCAK implementation by Gross et al., published in DSD 2017.

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Partial abstract (from the proposal): The panel will include panelists from industry, academia and security evaluation labs. We aim to discus the security levels and cost efficiency associated with such countermeasures from industry point of view and recent on research challenges and opportunities for standardization.

Moderators: Svetla Nikova (KU Leuven, Belgium); Vincent Rijmen (KU Leuven, Belgium).

Panelists: Nigel Smart (KU Leuven, Belgium); Ventzislav Nikov (NXP Semiconductors, Belgium); Mike Hutter (Rambus, USA); Junfeng Fan (Open Security Research, China); Ruggero Susella (ST Microelectronics, Italy); Emmanuel Prouff (ANSSI, France).

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Joint work with: Peihan Miao (UC Berkeley, USA), Akshayaram Srinivasan (UC Berkeley, USA).

Partial abstract. In this work, we present local leakage resilient threshold secret sharing schemes with constant rate for any threshold. Furthermore, our scheme has optimal leakage-resilience rate, i.e., the ratio between the leakage tolerated and the size of each share can be made arbitrarily close to 1. We implement a variant of our scheme (that has worse rate and leakage-resilience rate, but better computational efficiency), and present comparisons of its performance to that of Shamir’s secret sharing scheme (Shamir, Commun. ACM 1979). Our construction generalizes to a rate-preserving compiler that adds local leakage-resilience to any secret sharing scheme for any monotone access structure.

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Joint work with: Payman Mohassel (Visa Research, USA), Pratyay Mukherjee (Visa Research, USA), Peter Rindal (Visa Research, USA)

Partial abstract: We put forth the first formal treatment for distributed symmetric-key encryption, proposing new notions of correctness, privacy and authenticity in presence of malicious attackers. We provide strong and intuitive game-based definitions that are easy to understand and yield efficient constructions. We propose a generic construction of threshold authenticated encryption based on any distributed pseudorandom function (DPRF). When instantiated with the two different DPRF constructions proposed by Naor, Pinkas and Reingold (Eurocrypt 1999) and our enhanced versions, we obtain several efficient constructions meeting different security definitions. We implement these variants and provide extensive performance comparisons. Our most efficient instantiation uses only symmetric-key primitives and achieves a throughput of upto 1 million encryptions/decryptions per seconds, or alternatively a sub-millisecond latency with upto 18 participating parties.

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Abstract: Bitcoin, started in 2009, is a digital currency in which all activity is publicly verifiable. Coins are controlled by spending policies expressed in Bitcoin Script, a simple stack-based programming language which supports hash preimage challenges and digital signatures. Included in Bitcoin Script is a basic form of threshold ECDSA signature: a list of public keys and a threshold is specified; the coins can then be moved if threshold-many valid ECDSA signatures are provided in sequence.

This threshold scheme is inefficient in terms of both signature size and verification time (both linear in the threshold size), which are the two most important considerations for cryptosystems designed for inclusion on blockchains. Being explicitly specified, they also represent a fungibility loss as threshold-controlled coins are visibly distinct from non-threshold-controlled coins. However, they achieve several practical goals which have proved difficult to preserve in more efficient threshold schemes: they are noninteractive; they require no persistent state during signing; they work in the plain public-key model and require no interactive key setup; their security follows immediately from the security of the underlying ECDSA scheme even when signing counterparties are considered to be adversarial.

In this talk we describe our work in developing a multisignature scheme for Bitcoin, called MuSig, which supports an extension to threshold signatures, over the last several years. We describe how consideration of both practical use cases and formal security models guided the evolution of our goals, and the unexpected tradeoffs that we found ourselves forced to make.

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Partial abstract: Cybernetica would like to present the case study of the SplitKey Authentication and Digital Signature Platform, which is based on the threshold cryptography digital signature scheme. The document outlines the cryptographical design of the scheme, the key pair generation and the signing and also explains how the security of SplitKey has been formally evaluated.

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Abstract. In this presentation we report on the efforts of Danish company Sepior on commercializing solutions based on Threshold Cryptography (TC). The contribution of this presentation is to:

1. Present the “historical” lineage of Sepior going back to the sugar beet auction in 2008 [8]
2. Two commercial case studies for TC
3. Discuss challenges for commercial application of TC

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Abstract. This talk will make recommendations for the standardization of Threshold Cryptography (TC) based on experiences of investigating and designing uses of TC in deployed software systems. The talk will present representative examples of TC solutions considered for deployed software systems. In most cases, these solutions were not chosen, and the talk will present an analysis of the reasons for this. Finally, this talk will discuss recommendations for standardization of TC motivated by these lessons learned.

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Thank you notes; a recollection of the discussed topics; an opportunity for final remarks by the audience.

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