Algorithm-Substitution Attacks on Cryptographic Puzzles

In this work, we study and formalize security notions for algorithm substitution attacks (ASAs) on em cryptographic puzzles. Puzzles are difficult problems that require an investment of computation, memory, or some other related resource. They are heavily used as a building block for the consensus networks used by cryptocurrencies. These include primitives such as proof-of-work, proof-of-space, and verifiable delay functions (VDFs). Due to economies of scale, these networks increasingly rely on a small number of companies to construct opaque hardware or software (e.g., GPU or FPGA images): this dependency raises concerns about cryptographic subversion. Unlike the algorithms considered by previous ASAs, cryptographic puzzles do not rely on secret keys and thus enable a very different set of attacks. We first explore the threat model for these systems and then propose concrete attacks that (1) selectively reduce a victim\u27s solving capability ( e.g., hashrate) and (2) exfiltrate puzzle solutions to an attacker. We then propose defenses, several of which can be applied to existing cryptocurrency hardware with minimal changes. We also find that mining devices for many major proof-of-work cryptocurrencies already demonstrate errors exactly how a potentially subverted device would. Given that these attacks are relevant to all proof of work cryptocurrencies that have a combined market capitalization of around a few hundred billion dollars (2022), we recommend that all vulnerable mining protocols consider making the suggested adaptations today

Trading Accumulation Size for Witness Size: A Merkle Tree Based Universal Accumulator Via Subset Differences

Merkle-type trees are widely used to design cryptographic accumulators. The primary advantage in using Merkle tree for accumulators is that they only assume existence of collision-resistant hash functions. Merkle tree based accumulators produces constant size accumulation values. But, the size of the witness is always logarithmic in the number of values accumulated, opposed to the constant size witness as exhibited by some of the other popular accumulators that uses number theoretic techniques and problems. Surprisingly, there exists no Merkle tree based accumulator that provides a trade-off between accumulation size and witness size. Such a trade-off is warranted, as argued in this paper, in a situation where witnesses are stored in memory constrained devices and are being moved around continuously, as opposed to the accumulation values that remain stationary, often in devices with moderate storage capacity. In this paper we propose a Merkle-tree based accumulator scheme assuming only collision-resistant hash functions exist. Our scheme allows witness of size that is in general strictly less than logarithmic in the number of values accumulated, and in some cases reduces to constant size. The trade-off cost results in an increased accumulation size

SoK: Privacy-Preserving Signatures

Modern security systems depend fundamentally on the ability of users to authenticate their communications to other parties in a network. Unfortunately, cryptographic authentication can substantially undermine the privacy of users. One possible solution to this problem is to use privacy-preserving cryptographic authentication. These protocols allow users to authenticate their communications without revealing their identity to the verifier. In the non-interactive setting, the most common protocols include blind, ring, and group signatures, each of which has been the subject of enormous research in the security and cryptography literature. These primitives are now being deployed at scale in major applications, including Intel\u27s SGX software attestation framework. The depth of the research literature and the prospect of large-scale deployment motivate us to systematize our understanding of the research in this area. This work provides an overview of these techniques, focusing on applications and efficiency

MinRoot: Candidate Sequential Function for Ethereum VDF

We present a candidate sequential function for a VDF protocol to be used within the Ethereum ecosystem. The new function, called MinRoot, is an optimized iterative algebraic transformation and is a strict improvement over competitors VeeDo and Sloth++. We analyze various attacks on sequentiality and suggest weakened versions for public scrutiny. We also announce bounties on certain research directions in cryptanalysis

CryptoWills: How to Bequeath Cryptoassets

In this paper, we put forth the problem of bequeathing cryptoassets. In this problem, a testator wishes to bequeath cryptoassets - e.g. secrets, static keys or cryptocurrency - to their heirs. Crucially, the testator should retain control of their assets before their passing. Additionally testator needs to maintain privacy, i.e. beneficiaries must not learn the bequest, moreover, beneficiaries must not be able to determine whether they will inherit at all before testator\u27s decease. We formally define the security goals of a cryptographic will (cryptowill) protocol and subsequently present schemes fulfilling the required security properties

On Soundness Notions for Interactive Oracle Proofs

Interactive oracle proofs (IOPs) (Ben-Sasson et al., TCC 2016) have emerged as a powerful model for proof systems which generalizes both Interactive Proofs (IPs) and Probabilistically Checkable Proofs (PCPs). While IOPs are not any more powerful than PCPs from a complexity theory perspective, their potential to create succinct proofs and arguments has been demonstrated by many recent constructions achieving better parameters such as total proof length, alphabet size, and query complexity. In this work, we establish new results on the relationship between various notions of soundness for IOPs. First, we formally generalize the notion of round-by-round soundness (Canetti et al., STOC 2019) and round-by-round knowledge soundness (Chiesa et al., TCC 2019). Given this generalization, we then examine its relationship to the notions of generalized special soundness (Attema et al., CRYPTO 2021) and generalized special unsoundness (Attema et al., TCC 2022). We show that: 1. generalized special soundness implies generalized round-by-round soundness; 2. generalized round-by-round knowledge soundness implies generalized special soundness; 3. generalized special soundness does not imply generalized round-by-round knowledge soundness; 4. generalized round-by-round soundness (resp., special unsoundness) is an upper bound (resp., a lower bound) on standard soundness, and that this relationship is tight when the round-by-round soundness and special unsoundness errors are equal; and 5. any special sound IOP can be transformed via (a variant of) the Fiat-Shamir transformation into a non-interactive proof that is adaptively sound in the Quantum Random Oracle Model

Fiat-Shamir Security of FRI and Related SNARKs

We establish new results on the Fiat-Shamir (FS) security of several protocols that are widely used in practice, and we provide general tools for establishing similar results for others. More precisely, we: (1) prove the FS security of the FRI and batched FRI protocols; (2) analyze a general class of protocols, which we call $\delta$-correlated, that use low-degree proximity testing as a subroutine (this includes many Plonk-like protocols (e.g., Plonky2 and Redshift), ethSTARK, RISC Zero, etc.); and (3) prove FS security of the aforementioned Plonk-like protocols, and sketch how to prove the same for the others. We obtain our first result by analyzing the round-by-round (RBR) soundness and RBR knowledge soundness of FRI. For the second result, we prove that if a $\delta$-correlated protocol is RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials, then it is RBR (knowledge) sound in general. Equipped with this tool, we prove our third result by formally showing that Plonk-like protocols are RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials. We then outline analogous arguments for the remainder of the aforementioned protocols. To the best of our knowledge, ours is the first formal analysis of the Fiat-Shamir security of FRI and widely deployed protocols that invoke it

India’s “Aadhaar” Biometric ID: Structure, Security, and Vulnerabilities

India\u27s Aadhaar is the largest biometric identity system in history, designed to help deliver subsidies, benefits, and services to India\u27s 1.4 billion residents. The Unique Identification Authority of India (UIDAI) is responsible for providing each resident (not each citizen) with a distinct identity - a 12-digit Aadhaar number - using their biometric and demographic details. We provide the first comprehensive description of the Aadhaar infrastructure, collating information across thousands of pages of public documents and releases, as well as direct discussions with Aadhaar developers. Critically, we describe the first known cryptographic issue within the system, and discuss how a workaround prevents it from being exploitable at scale. Further, we categorize and rate various security and privacy limitations and the corresponding threat actors, examine the legitimacy of alleged security breaches, and discuss improvements and mitigation strategies

Time-Deniable Signatures

In this work we propose time-deniable signatures (TDS), a new primitive that facilitates deniable authentication in protocols such as DKIM-signed email. As with traditional signatures, TDS provide strong authenticity for message content, at least for a sender-chosen period of time. Once this time period has elapsed, however, time-deniable signatures can be forged by any party who obtains a signature. This forgery property ensures that signatures serve a useful authentication purpose for a bounded time period, while also allowing signers to plausibly disavow the creation of older signed content. Most critically, and unlike many past proposals for deniable authentication, TDS do not require interaction with the receiver or the deployment of any persistent cryptographic infrastructure or services beyond the signing process (e.g., APIs to publish secrets or author timestamp certificates.) We first investigate the security definitions for time-deniability, demonstrating that past definitional attempts are insufficient (and indeed, allow for broken signature schemes.) We then propose an efficient construction of TDS based on well-studied assumptions