Single Secret Leader Election

In a Single Secret Leader Election (SSLE), a group of participants aim to randomly choose exactly one leader from the group with the restriction that the identity of the leader will be known to the chosen leader and nobody else. At a later time, the elected leader should be able to publicly reveal her identity and prove that she has won the election. The election process itself should work properly even if many registered users are passive and do not send any messages. Among the many applications of SSLEs, their potential for enabling more efficient proof-of-stake based cryptocurrencies have recently received increased attention. This paper formally defines SSLE schemes and presents three constructions that provide varying security and performance properties. First, as an existence argument, we show how to realize an ideal SSLE using indistinguishability obfuscation. Next, we show how to build SSLE from low-depth threshold fully homomorphic encryption (TFHE) via a construction which can be instantiated with a circuit of multiplicative depth as low as 10, for realistically-sized secret leader elections. Finally, we show a practical scheme relying on DDH that achieves a slightly relaxed notion of security but which boasts extremely lightweight computational requirements.

[1]  Satoshi Nakamoto.  Bitcoin : A Peer-to-Peer Electronic Cash System , 2009 .

[2]  Jeremy Clark,et al.  On the Use of Financial Data as a Random Beacon , 2010, EVT/WOTE.

[3]  Jens Groth,et al.  On the Size of Pairing-Based Non-interactive Arguments , 2016, EUROCRYPT.

[4]  Shafi Goldwasser,et al.  Functional Signatures and Pseudorandom Functions , 2014, Public Key Cryptography.

[5]  Silvio Micali,et al.  On the Cryptographic Applications of Random Functions , 1984, CRYPTO.

[6]  Florian Mendel,et al.  Rasta: A cipher with low ANDdepth and few ANDs per bit , 2018, IACR Cryptol. ePrint Arch..

[7]  Aggelos Kiayias,et al.  Ouroboros Genesis: Composable Proof-of-Stake Blockchains with Dynamic Availability , 2018, IACR Cryptol. ePrint Arch..

[8]  Amit Sahai,et al.  On the (im)possibility of obfuscating programs , 2001, JACM.

[9]  Alessandra Scafuro,et al.  Anonymous Lottery In The Proof-of-Stake Setting , 2020, 2020 IEEE 33rd Computer Security Foundations Symposium (CSF).

[10]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2009, JACM.

[11]  Arjen K. Lenstra,et al.  A random zoo: sloth, unicorn, and trx , 2015, IACR Cryptol. ePrint Arch..

[12]  Dan Boneh,et al.  Threshold Cryptosystems From Threshold Fully Homomorphic Encryption , 2018, IACR Cryptol. ePrint Arch..

[13]  Johan Håstad,et al.  The square lattice shuffle , 2006, Random Struct. Algorithms.

[14]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[15]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[16]  Dan Boneh,et al.  Zether: Towards Privacy in a Smart Contract World , 2020, IACR Cryptol. ePrint Arch..

[17]  Yuval Ishai,et al.  Exploring Crypto Dark Matter: - New Simple PRF Candidates and Their Applications , 2018, TCC.

[18]  Martin R. Albrecht,et al.  MiMC: Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity , 2016, ASIACRYPT.

[19]  Dan Boneh,et al.  Verifiable Delay Functions , 2018, IACR Cryptol. ePrint Arch..

[20]  Elaine Shi,et al.  Snow White: Provably Secure Proofs of Stake , 2016, IACR Cryptol. ePrint Arch..

[21]  Aggelos Kiayias,et al.  Ouroboros Crypsinous: Privacy-Preserving Proof-of-Stake , 2019, 2019 IEEE Symposium on Security and Privacy (SP).

[22]  Aggelos Kiayias,et al.  Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol , 2017, CRYPTO.

[23]  Aggelos Kiayias,et al.  Delegatable pseudorandom functions and applications , 2013, IACR Cryptol. ePrint Arch..

[24]  Hugo Krawczyk,et al.  Secure Distributed Key Generation for Discrete-Log Based Cryptosystems , 1999, Journal of Cryptology.

[25]  Stuart G. Stubblebine,et al.  Publicly Verifiable Lotteries: Applications of Delaying Functions , 1998, Financial Cryptography.

[26]  Martin R. Albrecht,et al.  Ciphers for MPC and FHE , 2015, IACR Cryptol. ePrint Arch..

[27]  Silvio Micali,et al.  Algorand: Scaling Byzantine Agreements for Cryptocurrencies , 2017, IACR Cryptol. ePrint Arch..

[28]  Johan Håstad.  The square lattice shuffle, correction , 2016, Random Struct. Algorithms.

[29]  Ariel Gabizon,et al.  Cryptocurrencies Without Proof of Work , 2014, Financial Cryptography Workshops.

[30]  Ignacio Cascudo,et al.  SCRAPE: Scalable Randomness Attested by Public Entities , 2017, IACR Cryptol. ePrint Arch..

[31]  Daniel Tschudi,et al.  Proof-of-Stake Protocols for Privacy-Aware Blockchains , 2019, IACR Cryptol. ePrint Arch..

[32]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[33]  Jeremy Clark,et al.  On Bitcoin as a public randomness source , 2015, IACR Cryptol. ePrint Arch..

[34]  Sarah Meiklejohn,et al.  Betting on Blockchain Consensus with Fantomette , 2018, ArXiv.

[35]  Brent Waters,et al.  How to use indistinguishability obfuscation: deniable encryption, and more , 2014, IACR Cryptol. ePrint Arch..

[36]  Aggelos Kiayias,et al.  Ouroboros Praos: An Adaptively-Secure, Semi-synchronous Proof-of-Stake Blockchain , 2018, EUROCRYPT.

[37]  Brent Waters,et al.  Constrained Pseudorandom Functions and Their Applications , 2013, ASIACRYPT.

[38]  Adam O'Neill,et al.  Definitional Issues in Functional Encryption , 2010, IACR Cryptol. ePrint Arch..

[39]  Michael J. Fischer,et al.  Scalable Bias-Resistant Distributed Randomness , 2017, 2017 IEEE Symposium on Security and Privacy (SP).

[40]  Brent Waters,et al.  Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[41]  Brent Waters,et al.  Functional Encryption: Definitions and Challenges , 2011, TCC.

[42]  Anne Canteaut,et al.  Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression , 2016, Journal of Cryptology.

[43]  Claude Carlet,et al.  Towards Stream Ciphers for Efficient FHE with Low-Noise Ciphertexts , 2016, EUROCRYPT.