Related Work

This chapter organises the literature relevant to the work into seven thematic groups and closes with a comparative synthesis that situates this investigation in relation to the existing alternatives. The review favours directly comparable works, that is, those dealing with sealed-bid auctions in adversarial environments or constituting cryptographic foundations explicitly used here. Works whose background has already been covered in Chapter 2 are revisited here in summary form, with a pointer to the appropriate section, avoiding unnecessary repetition.

3.1 FHE and post-quantum cryptography

The theoretical lineage that sustains the cryptographic part of the work is set out in Chapter 2 and is only positioned here. Gentry (2009) established the first viable FHE construction; the later constructions (BGV, BFV, CKKS, TFHE) consolidated families of schemes optimised for different workloads, described in Brakerski, Gentry and Vaikuntanathan (2014), Fan and Vercauteren (2012), Cheon, Kim, Kim and Song (2017), and Chillotti et al. (2020a). The CONCRETE library, by Chillotti et al. (2020b), is the reference implementation of TFHE maintained by Zama and the basis on which on-chain FHE platforms such as Zama's own fhEVM (ZAMA, 2024; HINDI, 2024) and Fhenix CoFHE (FHENIX, 2026a) operate.

The discussion of resistance to quantum attacks was addressed in §2.4. The works of Mallick et al. (2025) and Ipsen (2026) cover the impact of post-quantum attacks on blockchain and the challenges of migrating decentralised protocols, providing the context that gives practical relevance to TFHE's quantum-resistant property. This property is inherited by the present work through the adoption of Fhenix CoFHE as its platform (FHENIX, 2026a), without that constituting an original contribution; what is argued in §4.1 and in Chapter 5 is that the property becomes especially valuable in auctions whose records are immutable and public, as is the case on a blockchain.

3.2 FHE in smart contracts

The application of FHE to smart contracts is a recent field, sitting somewhere between the classical FHE literature and smart contract engineering. Four works make up the core of that intersection and are reviewed below.

Solomon, Weber and Almashaqbeh (2021) proposed, in what became known as smartFHE, an academic architecture for privacy-preserving smart contracts by means of FHE. The work precedes and, in several respects, prefigures the practical realisation that would come with the fhEVM. The authors discuss gas trade-offs and computation-delegation strategies at a time when the ecosystem still had no platform on which to test those ideas at scale. In contrast with the present study, smartFHE is a generic framework with no real deployment; here a concrete platform is adopted and the focus is on a specific mechanism (Vickrey).

Zyskind et al. (2024), in FHE-Rollups, addressed the question of scalability for FHE-based confidential contracts, proposing rollup¹ architectures specialised in moving encrypted computation off the base layer without compromising verifiability. The focus of the work is architectural and independent of the application mechanism being executed. The present study operates at the level immediately below, that is, on a specific contract over Fhenix CoFHE, without entering into rollup design. The gas findings reported in FHE-Rollups are relevant as an order-of-magnitude reference for the discussion in Chapter 5.

Aronoff et al. (2025), in a systematization of knowledge², organise the state of the art of the field, compare platforms (including the fhEVM), discuss threats, and propose taxonomies for future contributions. The article is the most complete and recent reference for situating work within the scope of this investigation. In particular, the category "specific applications over on-chain FHE platforms with empirical evaluation" is where this research is inscribed, and the SoK explicitly identifies that category as sparsely populated in the literature, justifying the type of contribution proposed here.

The official documentation of the on-chain FHE platforms, aggregated in the fhEVM whitepaper published by Zama (2024), in complementary pieces such as the post by Hindi (2024) on the coprocessor and, in the case of the Fhenix CoFHE adopted in this work, in the architectural description published by Fhenix (2026b), completes the picture. These materials are not academic literature in the strict sense, but they constitute a primary source on the architectures involved and are cited throughout the work whenever it is necessary to ground design decisions.

3.3 Auction theory and mechanism design

The theoretical background of the mechanism was addressed in §2.5. Vickrey (1961) established the sealed-bid second-price auction and its truthfulness property; Krishna (2009) is the canonical reference for the modern treatment of mechanism design and auction theory. These two works form the basis on which any discussion of private auctions must rest. There is no significant controversy in the literature about the definition or the properties of the Vickrey auction; what is discussed is how to run it in environments where the assumptions of bid secrecy are challenged.

3.4 Pre-blockchain private auctions

Before the emergence of blockchains, the cryptographic literature had already developed protocols for running sealed-bid auctions without any individual bid being revealed to any party. The dominant approach was based on Secure Multiparty Computation (MPC), in which multiple parties jointly compute a function over their private inputs without revealing those inputs to one another. Three works summarise the development and maturing of that tradition.

Naor, Pinkas and Sumner (1999), in a seminal article presented at the first ACM Conference on Electronic Commerce, proposed a private auction protocol in a two-party model involving an auctioneer and a third party called the auction issuer. The protocol guarantees that the auctioneer learns only the winner and the closing price, without learning the losing bids, provided that the third party and the auctioneer do not cooperate with each other in order to defraud the process. The model is historically important as a precursor to much of what came later, but the assumption that these two parties operate in a genuinely independent way is strong, and the protocol does not scale directly to the fully decentralised scenario of a public blockchain.

Brandt (2006), in How to obtain full privacy in auctions, formalised the concept of full privacy in auctions, defined as the property that no information beyond what is strictly necessary (winner and price) is revealed to any participant, including the auctioneer. The author presents protocols based on MPC distributed among the auction participants themselves, eliminating the need for a trusted third party. The construction has a high communication cost: the number of messages exchanged grows significantly with the number of participants.

Bogetoft et al. (2009), in Secure Multiparty Computation Goes Live, describe the first deployment of MPC in production outside an academic setting. It concerns Denmark's annual double auction of sugar-beet production contracts, held between farmers' cooperatives and the processing industry. The case is a mandatory historical reference: it demonstrates that private auction protocols can operate at real scale, with non-technical participants and at high financial value, albeit at the cost of a coordinated infrastructure and dependence on computing parties designated in advance.

The fundamental architectural difference between that lineage and the approach adopted here is that MPC generally requires active communication among computing parties during the execution of the protocol, whereas the FHE approach allows each participant to send a single ciphertext and all subsequent computation to occur without the submitter's participation. On a public blockchain, that difference changes what is practicable: genuine MPC protocols would require each bid to be accompanied by multi-round communication with external servers, a pattern that does not fit Ethereum's model of independent transactions.

3.5 On-chain auctions

The literature specific to auctions on a blockchain is the one most directly comparable to this investigation. Five works make up the core of that category.

Galal and Youssef (2018), in Verifiable Sealed-Bid Auction on the Ethereum Blockchain, presented the first formal protocol for a verifiable sealed-bid auction on Ethereum. The construction uses the commit-reveal scheme and adds a layer of zero-knowledge proofs (proofs that demonstrate a statement is true without revealing the information that sustains it) to guarantee the correctness of the finalisation without trusting the auctioneer. The limitations of the commit-reveal scheme were discussed in §1.2.3 and are inherited by that construction: a double transaction per participant, complete exposure of the bids at the end, vulnerability to non-reveal griefing. The work nevertheless remains a methodological reference for the formal specification of what constitutes a "verifiable auction" in the context of smart contracts.

Galal and Youssef (2019), in Trustee: Full Privacy Preserving Vickrey Auction on top of Ethereum, is the closest reference to this research in terms of its ultimate goal. The authors propose an on-chain Vickrey auction with full privacy, resorting to a Trusted Execution Environment (TEE, an isolated environment within the processor itself in which code runs protected from the operating system and even from a hostile administrator), specifically Intel SGX, to run the logic that computes the winner and the second price over the encrypted bids. The architecture follows a different line from the one proposed here. Whereas Trustee delegates trust to a hardware property³, the FHE approach delegates trust to mathematical properties (the hardness of the LWE problem, as per §2.3 and §2.4). The practical consequences of that difference are significant. TEEs such as SGX have been the target of a succession of side-channel attacks⁴ in recent years, leading to questioning of the robustness of their guarantees in sophisticated adversarial scenarios; FHE, in return, pays in performance the cost of not depending on hardware assumptions. Trustee and the approach of this study can be seen as two distinct answers to the same research question, and the direct comparison between the two architectures is taken up in the discussion in Chapter 5.

Zhang et al. (2023), in Trustworthy sealed-bid auction with low communication cost atop blockchain, focus on a specific axis: minimising the communication cost among participants during the auction. The construction is based on combined cryptographic primitives and offers guarantees of non-repudiation (the impossibility of a participant later denying that they submitted a given bid) and auditability. The focus on communication cost is complementary to the focus on gas and latency adopted in this study, and the results are not directly comparable along every axis.

Li et al. (2024), in Sealed-bid Auctions on Blockchain with Timed Commitment Outsourcing, explore an alternative path: using timed commitments⁵ computed by off-chain nodes. The approach is interesting because it moves the cryptographic complexity outside the contract, but it introduces a dependence on designated nodes with honesty or reputation guarantees. By contrast, the FHE approach adopted in this work does not require trusted off-chain nodes in the sense of a single guarantor: the Fhenix CoFHE coprocessor distributes decryption among the nodes of the Threshold Services Network, as described in §2.3, eliminating the dependence on any individual participant.

Zhou et al. (2024), in FACT: Sealed-Bid Auction With Full Privacy via Threshold Fully Homomorphic Encryption, propose an alternative direction within the FHE family itself: using threshold FHE, in which the decryption key is split among multiple parties via secret sharing and recovering the result requires the cooperation of at least t out of N share holders. The construction eliminates the dependence on a single trusted auctioneer or coprocessor, satisfies Brandt's (2006) notion of full privacy by revealing only the winner and the closing price, and admits direct extension to the Vickrey auction, as the authors themselves observe. The article presents an experimental evaluation of the protocol in isolation, without deployment on a specific blockchain platform. In the design space, FACT occupies the quadrant of "FHE with distributed trust in decryption". The Fhenix CoFHE adopted in this work shares that architectural property through the Threshold Services Network described in §2.3, but differs from FACT in being a complete blockchain platform, with a coprocessor, live networks and client tooling, rather than an isolated protocol evaluated in the laboratory.

Taken together, these five works define the terrain in which this research is inscribed. The existing approaches either inherit the limitations of commit-reveal, or depend on specific hardware, or require trusted off-chain nodes, or treat the problem along a different axis (communication), or propose FHE with distributed trust outside a concrete blockchain platform. None of them delivers, in a single implementation empirically evaluated on a public blockchain, the combination of full privacy for the losing bids, quantum resistance, exclusive reliance on mathematical assumptions and end-to-end reproducibility with a graphical interface for real users.

3.6 MEV and practical motivation

The literature on Maximal Extractable Value was addressed in §1.2.2. Daian et al. (2020) introduced the term in the academic context and demonstrated empirically its systematic existence in decentralised exchanges. Alipanahloo et al. (2024) consolidated, in a survey, the state of the art of mitigation approaches. These works do not deal with auctions directly, but they provide the backdrop that justifies the need for privacy mechanisms in on-chain auctions. Their relation to this study is one of motivation, not of direct comparison.

3.7 Engineering references

Two pieces of grey literature are directly related to this work. Faruukku (2026), in a post about the VeilBid project, records practical aspects of implementing sealed-bid auctions on Zama's fhEVM, including gas figures observed on the platform. Fhenix itself maintains, in its poc-sealed-bid-auction repository (FHENIX, 2026c), an official proof-of-concept sealed-bid auction on CoFHE, with a Solidity contract, a Next.js frontend and the two-step flow (requestSettlement + finalizeSettlement) discussed in §2.3.5. The PoC implements a first-price auction, not a second-price one, and therefore does not deliver the truthfulness property of the Vickrey mechanism; it serves, however, as a practical starting point and a source of engineering patterns for the Vickrey implementation in this work. As neither is academic output, both references are cited here for completeness of the picture.

Of the two, Faruukku's (2026) VeilBid is the work closest in purpose to this investigation: it implements a private on-chain Vickrey auction using FHE and solves the exclusion problem by means of the same homomorphic masking technique discussed in §4.2. It is therefore worth situating what this work inherits from it and the points at which the present implementation differs. The most visible difference is the platform: VeilBid runs on Zama's fhEVM, and this work on Fhenix CoFHE. The two platforms share the same cryptographic basis (the TFHE scheme, as per §2.2.6) and expose to the developer an analogous set of encrypted types and homomorphic operations, but they diverge on three points relevant to the implementation. First, the type library is distinct: VeilBid uses TFHE.sol, whereas this implementation uses Fhenix's FHE.sol, with close but not identical APIs, especially in the access-control calls and in the conversion of encrypted inputs. Second, the decryption model differs structurally: on Zama's fhEVM, the reveal is orchestrated by an oracle callback triggered inside the contract, whereas on Fhenix the TSN is queried by the off-chain client and the result is published on-chain in a subsequent transaction, as described in §2.3.5; that difference forces a different design of the contract's state machine. Third, Fhenix operates through a modular coprocessor attachable to existing EVM chains, whereas Zama's fhEVM, in its original lineage, operates as a dedicated chain (HINDI, 2024 discusses that transition). Porting VeilBid's homomorphic masking pattern to Fhenix is not trivial: it requires rewriting the finalisation flow, adjusting the access-control calls (ACL, that is, the definition of which addresses may operate on or decrypt each piece of encrypted data) and adapting the deterministic handling of ties to the set of primitives available in FHE.sol.

Beyond the platform differences, two points distinguish the present work from VeilBid in reach. The first is the formal analysis of information leakage under an explicit adversary model, with a quantitative component of residual uncertainty about the losing bids, detailed in §4.1 and operationalised in Chapter 5; VeilBid, by its nature as engineering literature, makes only a qualitative observation about privacy. The second is the position on the spectrum between prototyping and documented academic contribution: VeilBid is an engineering record in the form of a post, without the apparatus of reproducible validation, adversary modelling and systematic measurement expected of an academic contribution. The two works are therefore complementary: VeilBid shows that the FHE pattern for Vickrey is viable on a platform of the TFHE lineage, and the validation of that fact in a real environment motivated the platform choice of this work; the present work delivers that pattern on Fhenix CoFHE, with formal analysis, end-to-end validation on a public testnet and a reproducible graphical interface, as described in Chapter 4.

3.8 Positioning and gaps

The review in the previous sections reveals three groups of answers to the problem of private auctions on a public blockchain: answers based on commit-reveal (with or without zero-knowledge), answers based on TEE (Intel SGX), and answers based on advanced cryptography (MPC or FHE). Each group pays, along some dimension, the cost of the secrecy it offers. The table below summarises the works comparable to this study along the most relevant axes.

Table 1: Comparative synthesis of related work along the most relevant axes.

Reading across the table points to two gaps that this investigation sets out to fill, together with one positioning observation.

The first gap is the absence of quantitative analysis of information leakage in a comparable format. Most works discuss privacy qualitatively, in terms of "the winner is revealed" or "the losing bids are protected", without quantifying how much information remains accessible to the adversary at the end of the auction. This research proposes an explicit adversary model and a quantitative measure based on residual uncertainty about the losing bids, as detailed in §4.1 and operationalised in Chapter 5.

The second gap is the absence of reproducible practical validation with a usable interface. The works in the table are typically presented as protocol contributions or research prototypes, without the path to third-party reproduction being preserved in usable form. This work delivers, in addition to the contract code, a web interface operable on a public testnet, as described in §4.4. That deliverable does not constitute a scientific contribution in itself, but acts as a validation artefact that makes it possible to verify, outside the author's environment, the operation of the proposed mechanism.

One positioning point about the chosen platform should be added. In the Fhenix lineage there is an earlier public implementation of a Vickrey auction (TOMOSAIGON, 2024), which computes the second-highest bid over encrypted values. It runs, however, on legacy Fhenix (the @fhenixprotocol/contracts/FHE.sol library), whose decryption model is synchronous and on-chain: the comparisons between bids are decrypted during the bidding phase itself, which exposes in real time whether each new bid exceeds the current highest, a model distinct from the threshold-distributed decryption adopted by CoFHE. It is, moreover, a prototyping artefact, with no adversary modelling, leakage analysis or systematic validation. In the literature consulted up to the date of this work, no documented academic implementation of a Vickrey (second-price) auction on Fhenix CoFHE was identified: the official proof-of-concept maintained by Fhenix itself (FHENIX, 2026c) implements only a first-price auction. This study therefore delivers the first documented academic implementation of a private Vickrey auction on Fhenix CoFHE, complementing the existing picture and solving the exclusion problem (§4.2) that distinguishes second price from first price.

This investigation closes a methodological gap: giving the community a concrete, measured and replicable exemplar of a confidential Vickrey auction on a public blockchain, with formal leakage analysis under an explicit adversary model, executed over Fhenix CoFHE (FHENIX, 2026a).