Born and Raised Distributively: Fully Distributed Non-Interactive Adaptively-Secure Threshold Signatures with Short Shares

International audienceThreshold cryptography is a fundamental distributed computational paradigm for enhancing the availability and the security of cryptographic public-key schemes. It does it by dividing private keys into $n$ shares handed out to distinct servers. In threshold signature schemes, a set of at least $t+1 \leq n$ servers is needed to produce a valid digital signature. Availability is assured by the fact that any subset of $t+1$ servers can produce a signature when authorized. At the same time, the scheme should remain robust (in the fault tolerance sense) and unforgeable (cryptographically) against up to $t$ corrupted servers; {\it i.e.}, it adds quorum control to traditional cryptographic services and introduces redundancy. Originally, most practical threshold signatures have a number of demerits: They have been analyzed in a static corruption model (where the set of corrupted servers is fixed at the very beginning of the attack), they require interaction, they assume a trusted dealer in the key generation phase (so that the system is not fully distributed), or they suffer from certain overheads in terms of storage (large share sizes). In this paper, we construct practical {\it fully distributed} (the private key is born distributed), non-interactive schemes -- where the servers can compute their partial signatures without communication with other servers -- with adaptive security ({\it i.e.}, the adversary corrupts servers dynamically based on its full view of the history of the system). Our schemes are 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 schemes are erasure-free (reliable erasure is a hard to assure and hard to administer property in actual systems). To the best of our knowledge, such a fully distributed highly constrained scheme has been an open problem in the area. In particular, and of special 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 born -- although it is well-known not to ensure uniformly distributed public keys. An advantage of this is that this protocol only takes one round optimistically (in the absence of faulty player)

BADGER - Blockchain Auditable Distributed (RSA) key GEneRation

Migration of security applications to the cloud poses unique challenges in key management and protection: asymmetric keys which would previously have resided in tamper-resistant, on-premise Hardware Security Modules (HSM) now must either continue to reside in non-cloud HSMs (with attendant communication and integration issues) or must be removed from HSMs and exposed to cloud-based threats beyond an organization\u27s control, e.g. accidental loss, warranted seizure, theft etc. Threshold schemes offer a halfway house between traditional HSM-based key protection and native cloud-based usage. Threshold signature schemes allow a set of actors to share a common public key, generate fragments of the private key and to collaboratively sign messages, such that as long as a sufficient quorum of actors sign a message, the partial signatures can be combined into a valid signature. However, threshold schemes, while being a mature idea, suffer from large protocol transcripts and complex communication-based requirements. This consequently makes it a more difficult task for a user to verify that a public key is, in fact, a genuine product of the protocol and that the protocol has been executed validly. In this work, we propose a solution to these auditability and verication problems, reporting on a prototype cloud-based implementation of a threshold RSA key generation and signing system tightly integrated with modern distributed ledger and consensus techniques

PESTO: Proactively Secure Distributed Single Sign-On, or How to Trust a Hacked Server

Single Sign-On (SSO) is becoming an increasingly popular authentication method for users that leverages a trusted Identity Provider (IdP) to bootstrap secure authentication tokens from a single user password. It alleviates some of the worst security issues of passwords, as users no longer need to memorize individual passwords for all service providers, and it removes the burden of these service to properly protect huge password databases. However, SSO also introduces a single point of failure. If compromised, the IdP can impersonate all users and learn their master passwords. To remedy this risk while preserving the advantages of SSO, Agrawal et al. (CCS\u2718) recently proposed a distributed realization termed PASTA (password-authenticated threshold authentication) which splits the role of the IdP across $n$ servers. While PASTA is a great step forward and guarantees security as long as not all servers are corrupted, it uses a rather inflexible corruption model: servers cannot be corrupted adaptively and --- even worse --- cannot recover from corruption. The latter is known as proactive security and allows servers to re-share their keys, thereby rendering all previously compromised information useless. In this work, we improve upon the work of PASTA and propose a distributed SSO protocol with proactive and adaptive security (PESTO), guaranteeing security as long as not all servers are compromised at the same time. We prove our scheme secure in the UC framework which is known to provide the best security guarantees for password-based primitives. The core of our protocol are two new primitives we introduce: partially-oblivious distributed PRFs and a class of distributed signature schemes. Both allow for non-interactive refreshs of the secret key material and tolerate adaptive corruptions. We give secure instantiations based on the gap one-more BDH and RSA assumption respectively, leading to a highly efficient 2-round PESTO protocol. We also present an implementation and benchmark of our scheme in Java, realizing OAuth-compatible bearer tokens for SSO, demonstrating the viability of our approach

On the Theory and Practice of Personal Digital Signatures

(Full version of a PKC 2009 paper) We take a step towards a more realistic modeling of personal digital signatures, where a human user, his mobile equipment, his PC and a server are all considered as independent players in the protocol, and where only the human user is assumed incorruptible. We then propose a protocol for issuing digital signatures on behalf of the user. This protocol is proactively UC-secure assuming at most one player is corrupted in every operational phase. In more practical terms, this means that one can securely sign using terminals (PC’s) that are not necessarily trusted, as long as the mobile unit and the PC are not both corrupted at the same time. In other words, our solution cannot be broken by phising or key-logging via the PC. The protocol allows for mobile units with very small computing power by securely outsourcing computation to the PC and also allows usage of any PC that can communicate properly. Finally, we report on the results of a prototype implementation of our solution

Self-healing in unattended wireless sensor networks

Wireless sensor networks (WSNs) appeal to a wide range of applications that involve the monitoring of various physical phenomena. However, WSNs are subject to many threats. In particular, lack of pervasive tamper-resistant hardware results in sensors being easy targets for compromise. Having compromised a sensor, the adversary learns all the sensor secrets, allowing it to later encrypt/decrypt or authenticate messages on behalf of that sensor. This threat is particularly relevant in the novel unattended wireless sensor networks (UWSNs) scenario. UWSNs operate without constant supervision by a trusted sink. UWSN?s unattended nature and increased exposure to attacks prompts the need for special techniques geared towards regaining security after being compromised. In this article, we investigate cooperative self-healing in UWSNs and propose various techniques to allow unattended sensors to recover security after compromise. Our techniques provide seamless healing rates even against a very agile and powerful adversary. The effectiveness and viability of our proposed techniques are assessed by thorough analysis and supported by simulation results. Finally, we introduce some real-world issues affecting UWSN deployment and provide some solutions for them as well as a few open problems calling for further investigation

Two results on spontaneous anonymous group signatures.

Chan Kwok Leong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 72-78).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Preliminaries --- p.4Chapter 2.1 --- Notation --- p.4Chapter 2.2 --- Cryptographic Primitives --- p.5Chapter 2.2.1 --- Symmetric Key Cryptography --- p.5Chapter 2.2.2 --- Asymmetric Key Cryptosystem --- p.6Chapter 2.2.3 --- Secure Hash Function --- p.7Chapter 2.2.4 --- Digital Signature --- p.8Chapter 2.2.5 --- Digital Certificate and Public Key Infrastructure --- p.8Chapter 2.3 --- Provable Security and Security Model --- p.9Chapter 2.3.1 --- Mathematics Background --- p.9Chapter 2.3.2 --- One-Way Function --- p.10Chapter 2.3.3 --- Candidate One-way Functions --- p.12Chapter 2.4 --- Proof Systems --- p.15Chapter 2.4.1 --- Zero-knowledge Protocol --- p.15Chapter 2.4.2 --- Proof-of-Knowledge Protocol --- p.17Chapter 2.4.3 --- Honest-Verifier Zero-Knowledge (HVZK) Proof of Knowl- edge Protocols (PoKs) --- p.18Chapter 2.5 --- Security Model --- p.19Chapter 2.5.1 --- Random Oracle Model --- p.19Chapter 2.5.2 --- Generic group model (GGM) --- p.20Chapter 3 --- Signature Scheme --- p.21Chapter 3.1 --- Introduction --- p.21Chapter 3.2 --- Security Notation for Digital Signature --- p.23Chapter 3.3 --- Security Proof for Digital Signature --- p.24Chapter 3.3.1 --- Random Oracle Model for Signature Scheme --- p.24Chapter 3.3.2 --- Adaptive Chosen Message Attack --- p.24Chapter 3.4 --- Schnorr Identification and Schnorr Signature --- p.25Chapter 3.4.1 --- Schnorr's ROS assumption --- p.26Chapter 3.5 --- Blind Signature --- p.27Chapter 4 --- Spontaneous Anonymous Group (SAG) Signature --- p.30Chapter 4.1 --- Introduction --- p.30Chapter 4.2 --- Background --- p.30Chapter 4.2.1 --- Group Signature --- p.30Chapter 4.2.2 --- Threshold Signature --- p.31Chapter 4.3 --- SAG signatures --- p.33Chapter 4.4 --- Formal Definitions and Constructions --- p.35Chapter 4.4.1 --- Ring-type construction --- p.36Chapter 4.4.2 --- CDS-type construction --- p.36Chapter 4.5 --- Discussion --- p.37Chapter 5 --- Blind Spontaneous Anonymous Signature --- p.39Chapter 5.1 --- Introduction --- p.39Chapter 5.2 --- Definition --- p.40Chapter 5.2.1 --- Security Model --- p.41Chapter 5.2.2 --- Definitions of security notions --- p.41Chapter 5.3 --- Constructing blind SAG signatures --- p.43Chapter 5.3.1 --- Blind SAG signature: CDS-type [1] --- p.43Chapter 5.3.2 --- "Blind SAG signature: ring-type [2, 3]" --- p.44Chapter 5.4 --- Security Analysis --- p.44Chapter 5.4.1 --- Multi-key parallel one-more unforgeability of blind signature --- p.45Chapter 5.4.2 --- Security of our blind SAG signatures --- p.47Chapter 5.5 --- Discussion --- p.49Chapter 6 --- Linkable Spontaneous Anonymous Group Signature --- p.51Chapter 6.1 --- introduction --- p.51Chapter 6.2 --- Related work --- p.51Chapter 6.3 --- Basic Building Blocks --- p.52Chapter 6.3.1 --- Proving the Knowledge of Several Discrete Logarithms --- p.53Chapter 6.3.2 --- Proving the Knowledge of d Out of n Equalities of Discrete Logarithms --- p.55Chapter 6.4 --- Security Model --- p.57Chapter 6.4.1 --- Syntax --- p.57Chapter 6.4.2 --- Notions of Security --- p.59Chapter 6.5 --- Our Construction --- p.63Chapter 6.5.1 --- An Linkable Threshold SAG Signature Scheme --- p.63Chapter 6.5.2 --- Security --- p.65Chapter 6.5.3 --- Discussions --- p.67Chapter 7 --- Conclusion --- p.70Bibliography --- p.7

Asynchronous Proactive RSA

Nowadays, to model practical systems better, such as the Internet network and ad hoc networks, researchers usually regard these systems as asynchronous networks. Meanwhile, proactive secret sharing schemes are often employed to tolerate a mobile adversary. Considering both aspects, an asynchronous proactive threshold signature scheme is needed to keep computer systems secure. So far, two asynchronous proactive secret sharing schemes have been proposed. One is proposed by Zhou in 2001, which is for RSA schemes. The other scheme is proposed by Cachin in 2002, which is a proactive secret sharing scheme for discrete-log schemes. There exist several drawbacks in both schemes. In Zhou¡¯s scheme, the formal security proof of this scheme is missing. Furthermore, Zhou¡¯s scheme needs to resort to the system administrator as the trusted third party for further run when some Byzantine errors occur. In Cachin¡¯s scheme, the building block is based on the threshold RSA scheme proposed by Shoup. However, how to proactivize Shoup¡¯s scheme is omitted in Cachin¡¯s scheme, so this scheme is incomplete. In this paper, we present a complete provably secure asynchronous proactive RSA scheme (APRS). Our paper has four contributions. Firstly, we present a provably secure asynchronous verifiable secret sharing for RSA schemes (asynchronous verifiable additive secret sharing, AVASS), which is based on a verifiable additive secret sharing over integers. Secondly, we propose an asynchronous threshold RSA signature scheme that is based on the AVASS scheme and the random oracle model, and is capable of being proactivized. Thirdly, we present a provably secure threshold coin-tossing scheme on the basis of the above threshold RSA scheme. Fourthly, we propose an asynchronous proactive secret sharing based on the threshold RSA scheme and the coin-tossing scheme. Finally, combining the proactive secret sharing scheme and the threshold RSA scheme, we achieve a complete provably secure asynchronous proactive RSA scheme

Proactive Refresh for Accountable Threshold Signatures

An accountable threshold signature (ATS) is a threshold signature scheme where every signature identifies the quorum of signers who generated that signature. They are widely used in financial settings where signers need to be held accountable for threshold signatures they generate. In this paper we initiate the study of proactive refresh for accountable threshold signatures. Proactive refresh is a protocol that lets the group of signers refresh their shares of the secret key, without changing the public key or the threshold. We give several definitions for this notion achieving different levels of security. We observe that certain natural constructions for an ATS cannot be proactively refreshed because the secret key generated at setup is needed for accountability. We then construct three types of ATS schemes with proactive refresh. The first is a generic construction that is efficient when the number of signers is small. The second is a hybrid construction that performs well for a large number of signers and satisfies a strong security definition. The third is a collection of very practical constructions derived from ATS versions of the Schnorr and BLS signature schemes; however these practical constructions only satisfy our weaker notion of security

A Survey on Wireless Security: Technical Challenges, Recent Advances and Future Trends

This paper examines the security vulnerabilities and threats imposed by the inherent open nature of wireless communications and to devise efficient defense mechanisms for improving the wireless network security. We first summarize the security requirements of wireless networks, including their authenticity, confidentiality, integrity and availability issues. Next, a comprehensive overview of security attacks encountered in wireless networks is presented in view of the network protocol architecture, where the potential security threats are discussed at each protocol layer. We also provide a survey of the existing security protocols and algorithms that are adopted in the existing wireless network standards, such as the Bluetooth, Wi-Fi, WiMAX, and the long-term evolution (LTE) systems. Then, we discuss the state-of-the-art in physical-layer security, which is an emerging technique of securing the open communications environment against eavesdropping attacks at the physical layer. We also introduce the family of various jamming attacks and their counter-measures, including the constant jammer, intermittent jammer, reactive jammer, adaptive jammer and intelligent jammer. Additionally, we discuss the integration of physical-layer security into existing authentication and cryptography mechanisms for further securing wireless networks. Finally, some technical challenges which remain unresolved at the time of writing are summarized and the future trends in wireless security are discussed.Comment: 36 pages. Accepted to Appear in Proceedings of the IEEE, 201

STROBE: Stake-based Threshold Random Beacons

We revisit decentralized random beacons with a focus on practical distributed applications. Decentralized random beacons (Beaver and So, Eurocrypt 1993) provide the functionality for $n$ parties to generate an unpredictable sequence of bits in a way that cannot be biased, which is useful for any decentralized protocol requiring trusted randomness. Existing beacon constructions are highly inefficient in practical settings where protocol parties need to rejoin after crashes or disconnections, and more significantly where smart contracts may rely on arbitrary index points in high-volume streams. For this, we introduce a new notion of history-generating decentralized random beacons (HGDRBs). Roughly, the history-generation property of HGDRBs allows for previous beacon outputs to be efficiently generated knowing only the current value and the public key. At application layers, history-generation supports registering a sparser set of on-chain values if desired, so that apps like lotteries can utilize on-chain values without incurring high-frequency costs, enjoying all the benefits of DRBs implemented off-chain or with decoupled, special-purpose chains. Unlike rollups, HG is tailored specifically to recovering and verifying pseudorandom bit sequences and thus enjoys unique optimizations investigated in this work. We introduce STROBE: an efficient HGDRB construction which generalizes the original squaring-based RSA approach of Beaver and So. STROBE enjoys several useful properties that make it suited for practical applications that use beacons: - history-generating: it can regenerate and verify high-throughput beacon streams, supporting sparse (thus cost-effective) ledger entries; - concisely self-verifying: NIZK-free, with state and validation employing a single ring element; - eco-friendly: stake-based rather than work based; - unbounded: refresh-free, addressing limitations of Beaver and So; - delay-free: results are immediately available