| AAC+17 | Hamza Abusalah, Joël Alwen, Bram Cohen, Danylo Khilko, Krzysztof Pietrzak, and Leonid Reyzin. Beyond Hellman’s time-memory trade-offs with applications to proofs of space. In Tsuyoshi Takagi and Thomas Peyrin, editors, Advances in Cryptology - ASI- ACRYPT 2017 - 23rd International Conference on the Theory and Applications of Cryptology and Information Security, Hong Kong, China, December 3-7, 2017, Proceedings, Part II, volume 10625 of Lecture Notes in Computer Science, pages 357–379. Springer, 2017. |
| BBBF18 | Dan Boneh, Joseph Bonneau, Benedikt Bu ̈nz, and Ben Fisch. Verifiable delay functions. In Hovav Shacham and Alexandra Boldyreva, editors, Advances in Cryptology - CRYPTO 2018 - 38th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2018, Proceedings, Part I, volume 10991 of Lecture Notes in Computer Science, pages 757–788. Springer, 2018. |
| BBF18 | Dan Boneh, Benedikt Bu ̈nz, and Ben Fisch. A survey of two verifi- able delay functions. IACR Cryptol. ePrint Arch., page 712, 2018. |
| BDK+19 | Vivek Bagaria, Amir Dembo, Sreeram Kannan, Sewoong Oh, David Tse, Pramod Viswanath, Xuechao Wang, and Ofer Zeitouni. Proof- of-stake longest chain protocols: Security vs predictability. 2019. |
| BGK+18 | Christian Badertscher, Peter Gazi, Aggelos Kiayias, Alexander Russell, and Vassilis Zikas. Ouroboros genesis: Composable proof-of-stake blockchains with dynamic availability. In David Lie, Mohammad Mannan, Michael Backes, and XiaoFeng Wang, editors, Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, CCS 2018, Toronto, ON, Canada, October 15-19, 2018, pages 913–930. ACM, 2018. |
| BNPW19 | Jonah Brown-Cohen, Arvind Narayanan, Alexandros Psomas, and S. Matthew Weinberg. Formal barriers to longest-chain proof-of-stake protocols. In Anna Karlin, Nicole Immorlica, and Ramesh Johari, editors, Proceedings of the 2019 ACM Conference on Economics and Computation, EC 2019, Phoenix, AZ, USA, June 24-28, 2019, pages 459–473. ACM, 2019. |
| BP22 | Mirza Ahad Baig and Krzysztof Pietrzak. On the existence of proof of space longest chain protocols (working title), 2022. 2022. Manuscript in preparation. |
| CKWN16 | Miles Carlsten, Harry A. Kalodner, S. Matthew Weinberg, and Arvind Narayanan. On the instability of bitcoin without the block reward. In Edgar R. Weippl, Stefan Katzenbeisser, Christopher Kruegel, Andrew C. Myers, and Shai Halevi, editors, Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria, October 24-28, 2016, pages 154–167. ACM, 2016. |
| CP19 | Bram Cohen and Krzysztof Pietrzak. The chia network blockchain. 2019. |
| DFKP15 | Stefan Dziembowski, Sebastian Faust, Vladimir Kolmogorov, and Krzysztof Pietrzak. Proofs of space. In Rosario Gennaro and Matthew Robshaw, editors, Advances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part II, volume 9216 of Lecture Notes in Computer Science, pages 585–605. Springer, 2015. |
| DKT21 | Soubhik Deb, Sreeram Kannan, and David Tse. Posat: Proof-of-work availability and unpredictability, without the work. In Nikita Borisov and Claudia Diaz, editors, Financial Cryptography and Data Security - 25th International Conference, FC 2021, Virtual Event, March 1-5, 2021, Revised Selected Papers, Part II, volume 12675 of Lecture Notes in Computer Science, pages 104–128. Springer, 2021. |
| DW13 | Christian Decker and Roger Wattenhofer. Information propagation in the bitcoin network. In 13th IEEE International Conference on Peer-to-Peer Computing, IEEE P2P 2013, Trento, Italy, September 9-11, 2013, Proceedings, pages 1–10. IEEE, 2013. |
| EFKP20 | Naomi Ephraim, Cody Freitag, Ilan Komargodski, and Rafael Pass. Continuous verifiable delay functions. Naomi Ephraim, Cody Freitag, Ilan Komargodski, and Rafael Pass. Continuous verifiable delay functions. In Anne Canteaut and Yuval Ishai, editors, Advances in Cryptology - EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10-14, 2020, Proceedings, Part III, volume 12107 of Lecture Notes in Computer Science, pages 125–154. Springer, 2020. Springer, 2020. |
| ES18 | Ittay Eyal and Emin Gu ̈n Sirer. Majority is not enough: bitcoin mining is vulnerable. Commun. ACM, 61(7):95–102, 2018. |
| FZ17 | Lei Fan and Hong-Sheng Zhou. iching: A scalable proof-of-stake blockchain in the open setting (or, how to mimic nakamoto’s design via proof-of-stake). IACR Cryptol. ePrint Arch., page 656, 2017. |
| GKL15 | Juan A. Garay, Aggelos Kiayias, and Nikos Leonardos. The bitcoin backbone protocol: Analysis and applications. In Elisabeth Oswald and Marc Fischlin, editors, Advances in Cryptology - EUROCRYPT 2015 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26-30, 2015, Proceedings, Part II, volume 9057 of Lecture Notes in Computer Science, pages 281–310. Springer, 2015. |
| GKR18 | Peter Gazi, Aggelos Kiayias, and Alexander Russell. Stake-bleeding attacks on proof-of-stake blockchains. In Crypto Valley Conference on Blockchain Technology, CVCBT 2018, Zug, Switzerland, June 20-22, 2018, pages 85–92. IEEE, 2018. |
| Hel80 | Martin E. Hellman. A cryptanalytic time-memory trade-off. IEEE Trans. Inf. Theory, 26(4):401–406, 1980. |
| Lew21 | Andrew Lewis-Pye. Byzantine generals in the permissionless setting. CoRR, abs/2101.07095, 2021. |
| LR21 | Andrew Lewis-Pye and Tim Roughgarden. How does blockchain security dictate blockchain implementation? In Yongdae Kim, Jong Kim, Giovanni Vigna, and Elaine Shi, editors, CCS ’21: 2021 ACM SIGSAC Conference on Computer and Communications Security, Virtual Event, Republic of Korea, November 15 - 19, 2021, pages 1006–1019. ACM, 2021. |
| Pie19a | Krzysztof Pietrzak. Proofs of catalytic space. In Avrim Blum, editor, 10th Innovations in Theoretical Computer Science Conference, ITCS 2019, January 10-12, 2019, San Diego, California, USA, volume 124 of LIPIcs, pages 59:1–59:25. Schloss Dagstuhl - Leibniz- Zentrum für Informatik, 2019. |
| Pie19b | Krzysztof Pietrzak. Simple verifiable delay functions. In Avrim Blum, editor, 10th Innovations in Theoretical Computer Science Conference, ITCS 2019, January 10-12, 2019, San Diego, California, USA, volume 124 of LIPIcs, pages 60:1–60:15. Schloss Dagstuhl - Leibniz-Zentrum fu ̈r Informatik, 2019. |
| PKF+18 | Sunoo Park, Albert Kwon, Georg Fuchsbauer, Peter Gazi, Joël Alwen, and Krzysztof Pietrzak. Spacemint: A cryptocurrency based on proofs of space. In Sarah Meiklejohn and Kazue Sako, editors, Financial Cryptography and Data Security - 22nd International Conference, FC 2018, Nieuwpoort, Cura ̧cao, February 26 - March 2, 2018, Revised Selected Papers, volume 10957 of Lecture Notes in Computer Science, pages 480–499. Springer, 2018. |
| PS17 | Rafael Pass and Elaine Shi. The sleepy model of consensus. Rafael Pass and Elaine Shi. The sleepy model of consensus. In Tsuyoshi Takagi and Thomas Peyrin, editors, Advances in Cryptology - ASIACRYPT 2017 - 23rd International Conference on the Theory and Applications of Cryptology and Information Security, Hong Kong, China, December 3-7, 2017, Proceedings, Part II, volume 10625 of Lecture Notes in Computer Science, pages 380–409. Springer, 2017. Springer, 2017. |
| SNM+21 | Caspar Schwarz-Schilling, Joachim Neu, Barnab ́e Monnot, Aditya Asgaonkar, Ertem Nusret Tas, and David Tse. Three attacks on proof-of-stake ethereum. IACR Cryptol. ePrint Arch., page 1413, 2021. |
| SSZ15 | Ayelet Sapirshtein, Yonatan Sompolinsky, and Aviv Zohar. Optimal selfish mining strategies in bitcoin. CoRR, abs/1507.06183, 2015. |
| Wes20 | Benjamin Wesolowski. Efficient verifiable delay functions. J. Cryptol., 33(4):2113–2147, 2020. |