Post-Quantum Verifiable Random Function from Symmetric Primitives in PoS Blockchain

Buser, Maxime; Dowsley, Rafael; Esgin, Muhammed F.; Kermanshahi, Shabnam Kasra; Kuchta, Veronika; Liu, Joseph K.; Phan, Raphaël C.‐W.; Zhang, Zhenfei

doi:10.1007/978-3-031-17140-6_2

Cited by 9 publications

(2 citation statements)

References 13 publications

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“…Our proposed approach diverges from the conventional methods, by incorporating a blockchainbased VRF via Multiparty Computation (MPC) with Ring-LWE encryption and NTRU linkable ring signature. Our VRF scheme utilizes the NTRU lattice cryptography to generate the DID-based linkable ring signature with VRF proof, which differentiates from the recent post-quantum VRF instantiaions of XMSS signature-based X-VRF scheme [33] or conventional ring signature-based VRF scheme [34]. To this end, we aim to provide enhanced post-quantum security, scalability, and efficiency in random value generation for decentralized systems.…”

Section: Vrf Constructionsmentioning

confidence: 99%

Untitled

2023

IJCIS

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In this study, we present a secure smart contract-based Verifiable Random Function (VRF) model, addressing the shortcomings of existing systems. As quantum computing emerges, conventional public key cryptography faces potential vulnerabilities. To enhance our VRF's robustness, we employ post-quantum Ring-LWE encryption for generating pseudorandom sequences and a NTRU lattice-based linkable ring signature scheme. Given the computational intensity of this approach and associated on-chain gas costs, we propose a hybrid architecture of VRF system where both on-chain and off-chain can communicate in a scalable and secure way. Our decentralized VRF employs multi-party computation (MPC) with blockchain-based decentralized identifiers (DID), ensuring the collective efforts of enhanced randomness and security. We show the security and privacy advantages of our proposed VRF model with the approximated estimation of overall temporal and spatial complexities. We also evaluate our VRF MPC model's entropy and outline its Solidity smart contract integration. This research also provides a method to produce and verify the VRF output's proof, optimal for scenarios necessitating randomness and validation. Lastly, using NIST SP800-22 test suite for randomness, we demonstrate the commendable result with a 97.73% overall pass rate on 11 standard tests and 0.5459 of average 𝑝-value for the total 176 tests.

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Section: Vrf Constructionsmentioning

confidence: 99%

Untitled

2023

IJCIS

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“…Module-SIS and module-LWE ranks are denoted as k and l, respectively. |C| denotes the number of AND gates of the LowMC[7] PRF applied in[10]. Here n is the length of the Legendre symbol sequence being proved.…”

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confidence: 99%

The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications

Seres

Horváth

Burcsi

2023

AAECC

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Sequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988. Major interest has been shown towards pseudorandom functions (PRF) recently, based on the Legendre and power residue symbols, due to their efficiency in the multi-party setting. The security of these PRFs is not known to be reducible to standard cryptographic assumptions. In this work, we show that key-recovery attacks against the Legendre PRF are equivalent to solving a specific family of multivariate quadratic (MQ) equation system over a finite prime field. This new perspective sheds some light on the complexity of key-recovery attacks against the Legendre PRF. We conduct algebraic cryptanalysis on the resulting MQ instance. We show that the currently known techniques and attacks fall short in solving these sparse quadratic equation systems. Furthermore, we build novel cryptographic applications of the Legendre PRF, e.g., verifiable random function and (verifiable) oblivious (programmable) PRFs.

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The Superlinearity Problem in Post-quantum Blockchains

Park,

Spooner

2023

Lecture Notes in Computer Science

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Post-Quantum Verifiable Random Function from Symmetric Primitives in PoS Blockchain

Cited by 9 publications

References 13 publications

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The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications

The Superlinearity Problem in Post-quantum Blockchains

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