Non-interactive half-aggregation of EdDSA and variants of Schnorr signatures

Schnorr\u27s signature scheme provides an elegant method to derive signatures with security rooted in the hardness of the discrete logarithm problem, which is a well-studied assumption and conducive to efficient cryptography. However, unlike pairing-based schemes which allow arbitrarily many signatures to be aggregated to a single constant sized signature, achieving significant non-interactive compression for Schnorr signatures and their variants has remained elusive. This work shows how to compress a set of independent EdDSA/Schnorr signatures to roughly half their naive size. Our technique does not employ generic succinct proofs; it is agnostic to both the hash function as well as the specific representation of the group used to instantiate the signature scheme. We demonstrate via an implementation that our aggregation scheme is indeed practical. Additionally, we give strong evidence that achieving better compression would imply proving statements specific to the hash function in Schnorr\u27s scheme, which would entail significant effort for standardized schemes such as SHA2 in EdDSA. Among the others, our solution has direct applications to compressing Ed25519-based blockchain blocks because transactions are independent and normally users do not interact with each other

Two-Round Stateless Deterministic Two-Party Schnorr Signatures From Pseudorandom Correlation Functions

Schnorr signatures are a popular choice due to their simplicity, provable security, and linear structure that enables relatively easy threshold signing protocols. The deterministic variant of Schnorr (where the nonce is derived in a stateless manner using a PRF from the message and a long term secret) is widely used in practice since it mitigates the threats of a faulty or poor randomness generator (which in Schnorr leads to catastrophic breaches of security). Unfortunately, threshold protocols for the deterministic variant of Schnorr have so far been quite inefficient, as they make non black-box use of the PRF involved in the nonce generation. In this paper, we present the first two-party threshold protocol for Schnorr signatures, where signing is stateless and deterministic, and only makes black-box use of the underlying cryptographic algorithms. We present a protocol from general assumptions which achieves covert security, and a protocol that achieves full active security under standard factoring-like assumptions. Our protocols make crucial use of recent advances within the field of pseudorandom correlation functions (PCFs). As an additional benefit, only two-rounds are needed to perform distributed signing in our protocol, connecting our work to a recent line of research on the trade-offs between round complexity and cryptographic assumptions for threshold Schnorr signatures

Integration of Hardware Security Modules and Permissioned Blockchain in Industrial IoT Networks

Hardware Security Modules (HSM) serve as a hardware based root of trust that offers physical protection while adding a new security layer in the system architecture. When combined with decentralized access technologies as Blockchain, HSM offers robustness and complete reliability enabling secured end-toend mechanisms for authenticity, authorization and integrity. This work proposes an ef cient integration of HSM and Blockchain technologies focusing on, mainly, public-key cryptography algorithms and standards, that result crucial in order to achieve a successful combination of the mentioned technologies to improve the overall security in Industrial IoT systems. To prove the suitability of the proposal and the interaction of an IoT node and a Blockchain network using HSM a proof of concept is developed. Results of time performance analysis of the prototype reveal how promising the combination of HSMs in Blockchain environments is.Infineon Technologies AGEuropean Union's Horizon 2020 Research and Innovation Program through the Cyber Security 4.0: Protecting the Industrial Internet of Things (C4IIoT) 833828FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades B-TIC-588-UGR2

Bootstrapping Cryptography on the Internet

This thesis focuses on bootstrapping cryptography, taking it from a theoretical algorithm to something we can use on the Internet. We summarize the requirement and define five pillars that build the foundation of successfully deployed cryptographic algorithms: computational performance, usability, transport, key management, and randomness. While there is a lot of research around the computational performance and usability of cryptographic algorithms, we focus on the other pillars. For transport, we explore two obstacles that interfere with the development of practical, real-world secure computation applications. We show the importance of the selection of suitable transport layers. Our evaluations show how Transmission Control Protocol (TCP) does not fully utilize the bandwidth for Two Party Computation (2PC) implementations. We evaluate three transport layers protocols for different applications and show that no protocol is suited for every scenario. In our evaluations, we use various protocols and network conditions in multiple regions to highlight the effects on the performance of 2PC applications. We propose an extendable framework that integrates the (initially) three transport layer protocols: User Datagram Protocol (UDP), TCP, and UDP-based Data Transfer Protocol (UDT). The framework's task is to identify the most suitable transport layer protocol depending on the current TCP application and the network conditions. For key management, we show how to manipulate a domain validation mechanism. We developed a BGP simulator to evaluate BGP paths on the Internet. Our simulator is high performant and respects relationships between CAs. In combination with our simulator, we analyze the resilience of the domains ecosystem to attacks against domain validation. Our measurements show that the domains ecosystem is not resilient to prefix hijacks and reveal that only a few ASes own most domains. We discuss possible mitigations and propose the distributed domain validation as a drop-in replacement for the standard domain validation. It allows strong resistance against MitM attackers. Additionally, we show that many IPs are anycast which is beneficial for distributed domain validation. We also analyze the validations agents' placement on the Internet and demonstrate a method to determine good ASes for agent placement. For randomness, we propose an alternative approach for generating pseudorandom strings, using the distributed nature of the Internet for collecting randomness from public services on the Internet. We develop our Distributed Pseudorandom Generator (DPRG) and demonstrate how it guarantees security against strong practical attackers and how it addresses the main shortcomings in existing PRGs. It uses AES encryption in CBC mode and an HDKF to extract randomness and inputs for handshakes. We analyze the distribution of different randomness sources like HTTP, SMTPS, SSH, and TOR and present an implementation of DPRG using the TOR network. We analyze the quality of randomness and performance of our DPRG and show that we can achieve highly secure randomness only from user space

Threshold Schnorr with Stateless Deterministic Signing from Standard Assumptions

Schnorr\u27s signature scheme permits an elegant threshold signing protocol due to its linear signing equation. However each new signature consumes fresh randomness, which can be a major attack vector in practice. Sources of randomness in deployments are frequently either unreliable, or require state continuity, i.e. reliable fresh state resilient to rollbacks. State continuity is a notoriously difficult guarantee to achieve in practice, due to system crashes caused by software errors, malicious actors, or power supply interruptions (Parno et al., S&P \u2711). This is a non-issue for Schnorr variants such as EdDSA, which is specified to derive nonces deterministically as a function of the message and the secret key. However, it is challenging to translate these benefits to the threshold setting, specifically to construct a threshold Schnorr scheme where signing neither requires parties to consume fresh randomness nor update long-term secret state. In this work, we construct a dishonest majority threshold Schnorr protocol that enables such stateless deterministic nonce derivation using standardized block ciphers. Our core technical ingredients are new tools for the zero-knowledge from garbled circuits (ZKGC) paradigm to aid in verifying correct nonce derivation: - A mechanism based on UC Commitments that allows a prover to commit once to a witness, and prove an unbounded number of statements online with only cheap symmetric key operations. - A garbling gadget to translate intermediate garbled circuit wire labels to arithmetic encodings. Our scheme prioritizes computation cost, with each proof requiring only a small constant number of exponentiations

Measuring and characterizing weak RSA keys across PKI ecosystem

The insecurities of public-key infrastructure on the Internet have been the focus of research for over a decade. The extensive presence of broken, weak, and vulnerable cryptographic keys has been repeatedly emphasized by many studies. Analyzing the security implications of cryptographic keys' vulnerabilities, several studies noted the presence of public key reuse. While the phenomenon of private key sharing was extensively studied, the prevalence of public key sharing on the Internet remains largely unknown. This work performs a large-scale analysis of public key reuse within the PKI ecosystem. This study investigates the presence and distribution of duplicate X.509 certificates and reused RSA public keys across a large collection containing over 315 million certificates and over 13 million SSH keys collected over several years. This work analyzes the cryptographic weaknesses of duplicate certificates and reused keys and investigates the reasons and sources of reuse. The results reveal that certificate and key sharing are common and persistent. The findings show over 10 million certificates and 17 million public keys are reused across time and shared between the collections. Observations show keys with non-compliant cryptographic elements stay available for an extended period of time. The widespread adoption of Android apps has led to increasing concerns about the reuse of digital certificates. Android app developers frequently depend on digital certificates to sign their applications, and users place their trust in an app when they recognize the owner provided by the same certificate. Although the presence of cryptographic misuse has been acknowledged by several studies, its extent and characteristics are not well understood. This study performs a detailed analysis of code-signing certificate reuse across the Android ecosystem and malware binaries on a collection of over 19 million certificates and over 9 million keys extracted from PE files and Android applications collected over several years. The results reveal that despite the growing nature of the Android ecosystem, the misuse of cryptographic elements is common and persistent. The findings uncover several issues and enable us to provide a series of applicable solutions to the seen security flaws