BOREALIS: Building Block for Sealed Bid Auctions on Blockchains

Abstract

We focus on securely computing the ranks of sealed integers distributed among parties. For example, we securely compute the largest or smallest integer, the median, or in general the th-ranked integer. Such computations are a useful building block to securely implement a variety of sealed-bid auctions. Our objective is efficiency, specifically low interactivity between parties to support blockchains or other scenarios where multiple rounds are timeconsuming. Hence, we dismiss powerful, yet highly-interactive MPC frameworks and propose BOREALIS, a special-purpose protocol for secure computation of ranks among integers. BOREALIS uses additively homomorphic encryption to implement core comparisons, but computes under distinct keys, chosen by each party to optimize the number of rounds. By carefully combining cryptographic primitives, such as ECC Elgamal encryption, encrypted comparisons, ciphertext blinding, secret sharing, and shuffling, BO-REALIS sets up systems of multi-scalar equations which we efficiently prove with Groth-Sahai ZK proofs. Therewith, BOREALIS implements a multi-party computation of pairwise comparisons and rank zero-knowledge proofs secure against malicious adversaries. BOREALIS completes in at most 4 rounds which is constant in both bit length ℓ of integers and the number of parties. This is not only asymptotically optimal, but surpasses generic constantround secure multi-party computation protocols, even those based on shared-key fully homomorphic encryption. Furthermore, our implementation shows that BOREALIS is very practical. Its main bottleneck, ZK proof computations, is small in practice. Even for a large number of parties (= 200) and high-precision integers (ℓ = 32), computation time of all proofs is less than a single Bitcoin block interval. CCS CONCEPTS • Security and privacy → Cryptography.

When Blockchain Meets Auction Models: A Survey, Some Applications, and Challenges

“…Since these cryptographic techniques differ in terms of effects and application scenarios, some studies choose to integrate multiple algorithms on the blockchain to build a secure and privacy-preserving auction system. For example, ZKP, MPC, AE, and CS and their variant algorithms have been widely combined in recently proposed frameworks in [196], [197], [198], [199]. Such an integrated model can reduce the potential risk of using one single encryption algorithm, thus presenting an overall good privacy-preserving effect.…”

“…It has a slightly weaker adversary model than traditional MPC and can achieve constant latency. [197] BOREALIS is an efficient model for sealed-bid auctions on the blockchain. It performs the secure comparison of integer bids among participants using ZKP.…”

Research on Blockchain-Based E-Bidding System

“…In 2020, E.O. Blass et al proposed a system to securely implement a variety of sealed-bid auctions through building blocks [12], which can improve efficiency, achieving low interactivity between parties to support blockchains or other scenarios where multiple rounds are time-consuming. In 2020, X.C.…”

On-Chain Auctions with Deposits

“…A possible solution to disclosing deposit levels includes not having them at all, and encrypting deposit levels, for example, see Blass and Kerschbaum (2020). Exploiting auctions in the blockchain environment is studied in Daian et al (2020).…”