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1. Proof-of-Useful-Randomness: Mitigating the Energy Waste in Blockchain Proof-of-Work

   https://doi.org/10.5220/0010519204120419  

   Seyitoglu, Efe; Yavuz, Attila; Hoang, Thang (January 2021, In Proceedings of the 18th International Conference on Security and Cryptography (SECRYPT 2021))

   Proof-of-Work (PoW) is one of the fundamental and widely-used consensus algorithms in blockchains. In PoW, nodes compete to receive the mining reward by trying to be the first to solve a puzzle. Despite its fairness and wide availability, traditional PoW incurs extreme computational and energy waste over the blockchain. This waste is considered to be one of the biggest problems in PoW-based blockchains and cryptocurrencies. In this work, we propose a new useful PoW called Proof-of-Useful-Randomness (PoUR) that mitigates the energy waste by incorporating pre-computed (disclosable) randomness into the PoW. The key idea is to inject special randomness into puzzles via algebraic commitments that can be stored and later disclosed. Unlike the traditional wasteful PoWs, our approach enables pre-computed commitments to be utilized by a vast array of public-key cryptography methods that require offline-online processing (e.g., digital signature, key exchange, zero-knowledge protocol). Moreover, our PoW preserves the desirable properties of the traditional PoW and therefore does not require a substantial alteration in the underlying protocol. We showed the security of our PoW, and then fully implemented it to validate its significant energy-saving capabilities. 

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2. Proof of the simplicity conjecture

   https://doi.org/10.4007/annals.2024.199.1.3  

   Cristofaro-Gardiner, Daniel; Humilière, Vincent; Seyfaddini, Sobhan (January 2024, Annals of Mathematics)
3. The SABRE Proof of Principle

   https://doi.org/10.1088/1742-6596/1468/1/012029  

   Copello, Simone; Antonello, M.; Barberio, E.; Baroncelli, T.; Benziger, J.; Bignell, L.J.; Bolognino, I.; Calaprice, F.; Copello, S.; D’Angelo, D.; et al (February 2020, Journal of Physics: Conference Series)

   Abstract SABRE is a dark matter direct detection experiment based on NaI(Tl) scintillating crystals. The primary goal of the experiment is to test the dark matter interpretation of the DAMA/LIBRA annual modulation signal. To reach its purpose, SABRE will operate an array of ultra-low background NaI(Tl) crystals within an active veto, based on liquid scintillator. Finally two twin detectors will be used, one in the northern hemisphere at Laboratori Nazionali del Gran Sasso, Italy (LNGS) and the other, first of its kind, in the southern hemisphere, in the Stawell Underground Physic Laboratory (SUPL). The collaboration has successfully developed a NaI(Tl) crystal with the impressive potassium content of about 4 ppb, according to the mass spectroscopy measurements. A value that, if confirmed, would be about 3 times lower than the DAMA/LIBRA crystals one. The first phase of the SABRE experiment, called SABRE Proof of Principle (PoP), aims to prove the achieved radiopurity by direct measurement of crystals at LNGS. This work reports the status of the PoP setup and the recent progresses on the development of low radioactivity NaI(Tl) crystals. 

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4. Investigating undergraduate students’ proof schemes and perspectives about combinatorial proof

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   Erickson, Sarah A.; Lockwood, Elise (June 2021, The Journal of Mathematical Behavior)

   null (Ed.)
5. Liquid proof macros

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   Blanchette, Henry; Vazou, Niki; Lampropoulos, Leonidas (September 2022, International Symposium on Haskell)