IP Library Granted Patent US 12,219,044
Granted Patent B2
US 12,219,044 · App. 18/134,276 · Granted Feb 4, 2025

System for securing verification key from alteration and verifying validity of a proof of correctness

Inventors: Alexandra Covaci (Canterbury, GB); Simone Madeo (London, GB); Patrick Motylinski (London, GB); Stephane Vincent (Luxembourg, LU)
Assignee: NCHAIN LICENSING AG
H04L9/0618G06F8/44G06F8/447G06F8/451G06F9/44521G06F16/27G06Q20/065G06Q20/401G06Q20/405H04L9/0637H04L9/0643H04L9/30H04L9/3218H04L9/3236H04L9/3239H04L9/3247H04L9/3263H04L63/12H04L9/3066H04L9/50H04L2209/34H04L2209/56
View Patent ↗
Loading inventors, assignments & file history…
Monitor This Case
Get email alerts when status or documents change.
Order Certified Copies
Most orders are placed with the USPTO same day — all within 24 business hours.
Order via The Patent Place →
Pre-filled with this patent's details
Quick Facts
Patent No.
US 12,219,044
App. No.
18/134,276
Granted
Feb 4, 2025
Kind
B2
Abstract

The invention relates to distributed ledger technologies such as consensus-based blockchains. A blockchain transaction may include digital resources that are encumbered by a locking script that encodes a set of conditions that must be fulfilled before the encumbered resources may be used (e.g., transferring ownership/control of encumbered resources). A worker (e.g., a computer system) performs one or more computations to generate a proof, which is encoded as part of an unlocking script. A verification algorithm may utilize the proof, a verification key, and additional data such as a cryptographic material associated with the worker (e.g., a digital signature) to verify that digital assets of the transaction should be transferred. As a result of the validation of this transaction, any third party is able to check the contract was executed corrected rather than re-executing the contract, thus saving computational power.

Claims (27)

1. A computer-implemented verification method comprising:

generating a transaction output of a transaction comprising an indication of a digital asset and a locking script that encodes a set of conditions for transferring control of the digital asset, satisfaction of the set of conditions to be determined based at least in part on a verification key and a proof, wherein the set of conditions provides a requirement that the verification key is provided by provision of a serialised unlocking transaction which comprises a set of elliptic curve points;

generating a transaction input of the transaction, the transaction input comprising:

an unlocking script comprising the proof; and

verifying the set of conditions are satisfied based at least in part on the locking script and the unlocking script; and

transferring control of the digital asset in response to verifying satisfaction of the set of conditions.

2. The computer-implemented verification method according to claim 1 , wherein the verification key comprises a first plurality of elements of a finite field and the proof comprises a second plurality of elements of the finite field.

3. The computer-implemented verification method according to claim 2 , wherein elements of the finite field are points on an elliptic curve.

4. The computer-implemented verification method according to claim 2 , wherein the elements of the finite field are encoded in a compressed format.

5. The computer-implemented verification method according to claim 1 , wherein a client encodes the transaction input with the verification key and a first digital certificate associated with the client and a worker encodes the transaction input with the proof and a second digital certificate associated with the worker.

6. The computer-implemented verification method according to claim 1 , wherein the locking script comprises instructions that, contingent upon a condition of the set of conditions being unsatisfied by the unlocking script, reclaim the digital asset for a provider of the digital asset.

7. The computer-implemented verification method according to claim 6 , wherein the transaction is a P2SH transaction in accordance with a Bitcoin-based protocol.

8. The computer-implemented verification method according to claim 1 , wherein:

the unlocking script further comprises a redeem script, wherein the verification key and the redeem script are to satisfy the set of conditions; and

the locking script encodes a condition of the set of conditions that a hash of the redeem script matches a predetermined value.

9. The computer-implemented verification method according to claim 8 , wherein the redeem script is less than or equal to 520 bytes in size.

10. The computer-implemented verification method according to claim 8 , wherein the unlocking script comprises one or more elements of the verification key.

11. The computer-implemented verification method according to claim 10 , wherein the redeem script comprises at least some of the remaining elements of the verification key.

12. The computer-implemented verification method according to claim 11 , wherein the unlocking script and the redeem script collectively comprise the verification key.

13. The computer-implemented verification method according to claim 1 , wherein the transaction is a standard transaction in accordance with a blockchain-based protocol.

14. The computer-implemented verification method according to claim 1 , wherein the locking script and unlocking script are encoded in a stack-based scripting language.

15. The computer-implemented verification method according to claim 1 , wherein the set of conditions comprise a bilinear constraint.

16. A system, comprising:

a processor; and

memory including executable instructions that, as a result of being executed by the processor, cause the system to perform the computer-implemented method according to claim 1 .

17. A non-transitory computer-readable storage medium having stored thereon executable instructions that, as a result of being executed by a processor of a computer system, cause the computer system to at least perform the computer-implemented method according to claim 1 .

18. The computer-implemented verification method according to claim 1 , wherein the transaction input further comprises an identifier associated with the transaction output.

Assignments (7)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Aug 15, 2023
From: COVACI, ALEXANDRA; MADEO, SIMONE; MOTYLINSKI, PATRICK; VINCENT, STEPHANE
To: NCHAIN HOLDINGS LTD
Reel/Frame 064597/0491 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 13, 2023
From: MADEO, SIMONE; MOTYLINSKI, PATRICK; VINCENT, STEPHANE; COVACI, ALEXANDRA
To: NCHAIN HOLDINGS LTD
Reel/Frame 063317/0849 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 13, 2023
From: MADEO, SIMONE; MOTYLINSKI, PATRICK; VINCENT, STEPHANE; COVACI, ALEXANDRA
To: NCHAIN HOLDINGS LTD
Reel/Frame 063318/0034 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 13, 2023
From: MOTYLINSKI, PATRICK; VINCENT, STEPHANE; MADEO, SIMONE; COVACI, ALEXANDRA
To: NCHAIN HOLDINGS LTD
Reel/Frame 063317/0635 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 13, 2023
From: COVACI, ALEXANDRA; MADEO, SIMONE; MOTYLINSKI, PATRICK; VINCENT, STEPHANE
To: NCHAIN HOLDINGS LTD
Reel/Frame 063318/0698 →
CHANGE OF NAME Recorded Apr 13, 2023
From: NCHAIN HOLDINGS LTD
To: NCHAIN LICENSING AG
Reel/Frame 063333/0438 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 13, 2023
From: VINCENT, STEPHANE; MADEO, SIMONE; COVACI, ALEXANDRA; MOTYLINSKI, PATRICK
To: NCHAIN HOLDINGS LTD
Reel/Frame 063318/0560 →
Priority Claims (6)
GB 1718505 · Nov 9, 2017 · national
GB 1719998 · Nov 30, 2017 · national
GB 1720768 · Dec 13, 2017 · national
GB 1801753 · Feb 2, 2018 · national
GB 1805948 · Apr 10, 2018 · national
GB 1806444 · Apr 20, 2018 · national
Continuity (2)
Continuation 16762471
Related Publication 20230318805A1 · Oct 5, 2023
References Cited (273)
US 4667290A · Goss et al. · 1987 [cited by applicant]
US 5297150A · Clark · 1994 [cited by applicant]
US 5404531A · Wakatani · 1995 [cited by applicant]
US 5499191A · Young · 1996 [cited by applicant]
US 5920830A · Hatfield et al. · 1999 [cited by applicant]
US 6064928A · Wilson et al. · 2000 [cited by applicant]
US 6161180A · Matyas et al. · 2000 [cited by applicant]
US 6519754B1 · McElvain et al. · 2003 [cited by applicant]
US 7085701B2 · Rich et al. · 2006 [cited by applicant]
US 7209555B2 · Futa et al. · 2007 [cited by applicant]
US 7281017B2 · Hostetter et al. · 2007 [cited by applicant]
US 7590236B1 · Boneh et al. · 2009 [cited by applicant]
US 8165287B2 · Ghouti et al. · 2012 [cited by applicant]
US 8189771B2 · Ghouti et al. · 2012 [cited by applicant]
US 8331556B2 · Billet et al. · 2012 [cited by applicant]
US 8607129B2 · Radhakrishnan et al. · 2013 [cited by applicant]
US 8824670B2 · Icart et al. · 2014 [cited by applicant]
US 8904181B1 · Felsher et al. · 2014 [cited by applicant]
US 9026978B1 · Liu et al. · 2015 [cited by applicant]
US 9286602B2 · Rosati et al. · 2016 [cited by applicant]
US 9483596B1 · Badar et al. · 2016 [cited by applicant]
US 9569771B2 · Lesavich et al. · 2017 [cited by applicant]
US 10135607B1 · Roets · 2018 [cited by applicant]
US 10339523B2 · McDonough et al. · 2019 [cited by applicant]
US 10419209B1 · Griffin et al. · 2019 [cited by applicant]
US 10515567B2 · Lablans · 2019 [cited by applicant]
US 11226799B1 · Sundaresan et al. · 2022 [cited by applicant]
US 20030125917A1 · Rich et al. · 2003 [cited by applicant]
US 20040015739A1 · Heinkel et al. · 2004 [cited by applicant]
US 20050004899A1 · Baldwin et al. · 2005 [cited by applicant]
US 20050139657A1 · Hopkins · 2005 [cited by applicant]
US 20050262353A1 · Gentry et al. · 2005 [cited by applicant]
US 20060149962A1 · Fountain et al. · 2006 [cited by applicant]
US 20070061487A1 · Moore et al. · 2007 [cited by applicant]
US 20070157132A1 · Cheng et al. · 2007 [cited by applicant]
US 20080127067A1 · Aubertine et al. · 2008 [cited by applicant]
US 20100067686A1 · Minematsu · 2010 [cited by applicant]
US 20100131933A1 · Kim et al. · 2010 [cited by applicant]
US 20100272209A1 · Lee et al. · 2010 [cited by applicant]
US 20110024678A1 · Schmitt · 2011 [cited by applicant]
US 20110200188A1 · Ghouti et al. · 2011 [cited by applicant]
US 20120284175A1 · Wilson et al. · 2012 [cited by applicant]
US 20130031446A1 · Kamiya · 2013 [cited by applicant]
US 20130097420A1 · Zaverucha · 2013 [cited by applicant]
US 20140250296A1 · Hansen · 2014 [cited by applicant]
US 20140321644A1 · Lemieux · 2014 [cited by applicant]
US 20140337234A1 · Tang et al. · 2014 [cited by applicant]
US 20150363598A1 · Xu et al. · 2015 [cited by applicant]
US 20150379510A1 · Smith · 2015 [cited by applicant]
US 20160004820A1 · Moore · 2016 [cited by applicant]
US 20160087802A1 · Peeters · 2016 [cited by applicant]
US 20160140340A1 · Walters et al. · 2016 [cited by applicant]
US 20160162897A1 · Feeney · 2016 [cited by applicant]
US 20160204938A1 · Kounavis et al. · 2016 [cited by applicant]
US 20160283941A1 · Andrade · 2016 [cited by applicant]
US 20160357948A1 · Takeuchi · 2016 [cited by applicant]
US 20170039330A1 · Tanner, Jr. et al. · 2017 [cited by applicant]
US 20170048209A1 · Lohe et al. · 2017 [cited by applicant]
US 20170085545A1 · Lohe et al. · 2017 [cited by applicant]
US 20170091750A1 · Maim · 2017 [cited by applicant]
US 20170091756A1 · Stern et al. · 2017 [cited by applicant]
US 20170131983A1 · Roytman et al. · 2017 [cited by applicant]
US 20170132421A1 · Unitt · 2017 [cited by applicant]
US 20170132619A1 · Miller et al. · 2017 [cited by applicant]
US 20170140408A1 · Wuehler · 2017 [cited by applicant]
US 20170142103A1 · Bringer et al. · 2017 [cited by applicant]
US 20170155515A1 · Androulaki et al. · 2017 [cited by applicant]
US 20170177312A1 · Boehm et al. · 2017 [cited by applicant]
US 20170178263A1 · Kraemer et al. · 2017 [cited by applicant]
US 20170180341A1 · Walker et al. · 2017 [cited by applicant]
US 20170220815A1 · Ansari et al. · 2017 [cited by applicant]
US 20170221052A1 · Sheng et al. · 2017 [cited by applicant]
US 20170249716A1 · Meixner et al. · 2017 [cited by applicant]
US 20170250815A1 · Cuende et al. · 2017 [cited by applicant]
US 20170277909A1 · Kraemer et al. · 2017 [cited by applicant]
US 20170278100A1 · Kraemer et al. · 2017 [cited by applicant]
US 20170279611A1 · Kraemer et al. · 2017 [cited by applicant]
US 20170286079A1 · Cho et al. · 2017 [cited by applicant]
US 20170286717A1 · Khi et al. · 2017 [cited by applicant]
US 20170287090A1 · Hunn et al. · 2017 [cited by applicant]
US 20170317833A1 · Smith et al. · 2017 [cited by applicant]
US 20170317834A1 · Smith et al. · 2017 [cited by applicant]
US 20170337319A1 · Camus et al. · 2017 [cited by applicant]
US 20170338947A1 · Ateniese et al. · 2017 [cited by applicant]
US 20170344988A1 · Cusden et al. · 2017 [cited by applicant]
US 20170352209A1 · Keuffer et al. · 2017 [cited by applicant]
US 20170353309A1 · Gray · 2017 [cited by applicant]
US 20180034634A1 · Benarroch Guenun et al. · 2018 [cited by applicant]
US 20180039667A1 · Pierce et al. · 2018 [cited by applicant]
US 20180049043A1 · Hoffberg · 2018 [cited by applicant]
US 20180075453A1 · Durvasula et al. · 2018 [cited by applicant]
US 20180089758A1 · Stradling et al. · 2018 [cited by applicant]
US 20180117446A1 · Tran et al. · 2018 [cited by applicant]
US 20180167201A1 · Naqvi · 2018 [cited by applicant]
US 20180204005A1 · Gajek et al. · 2018 [cited by applicant]
US 20180270065A1 · Brown et al. · 2018 [cited by applicant]
US 20180349631A1 · Illendula et al. · 2018 [cited by applicant]
US 20190095631A1 · Roets et al. · 2019 [cited by applicant]
US 20190138753A1 · Wallrabenstein · 2019 [cited by applicant]
US 20190163887A1 · Frederick et al. · 2019 [cited by applicant]
US 20190180276A1 · Lee et al. · 2019 [cited by applicant]
US 20190182035A1 · Chari et al. · 2019 [cited by applicant]
US 20190295182A1 · Kfir et al. · 2019 [cited by applicant]
US 20200050780A1 · Uhr et al. · 2020 [cited by applicant]
US 20200184557A1 · Wang · 2020 [cited by applicant]
US 20200327498A1 · Weber et al. · 2020 [cited by applicant]
US 20210019746A1 · Adjaz et al. · 2021 [cited by applicant]
US 20210073795A1 · Ruiz et al. · 2021 [cited by applicant]
US 20210342490A1 · Briancon et al. · 2021 [cited by applicant]
US 20230269070A1 · Covaci et al. · 2023 [cited by applicant]
US 20240143739A1 · Cao et al. · 2024 [cited by applicant]
CN 104580240A · 2015 [cited by applicant]
CN 106506146A · 2017 [cited by applicant]
CN 106534317A · 2017 [cited by applicant]
CN 107040545A · 2017 [cited by applicant]
CN 107179932A · 2017 [cited by applicant]
CN 107274184A · 2017 [cited by applicant]
CN 107426234A · 2017 [cited by applicant]
EP 3249599A1 · 2017 [cited by applicant]
JP H08305547A · 1996 [cited by applicant]
JP 2006505055A · 2006 [cited by applicant]
JP 2009541853A · 2009 [cited by applicant]
JP 2011119952A · 2011 [cited by applicant]
JP 5697153B2 · 2015 [cited by applicant]
JP 2015132754A · 2015 [cited by applicant]
JP 7208989B2 · 2023 [cited by applicant]
JP 7221954B2 · 2023 [cited by applicant]
JP 7285840B2 · 2023 [cited by applicant]
KR 101795696B1 · 2017 [cited by applicant]
KR 20200096790A · 2020 [cited by applicant]
WO 2016131577A1 · 2016 [cited by applicant]
WO 2016155804A1 · 2016 [cited by applicant]
WO 2016206567A1 · 2016 [cited by applicant]
WO 2017008829A1 · 2017 [cited by applicant]
WO 2017032541A1 · 2017 [cited by applicant]
WO 2017079652A1 · 2017 [cited by applicant]
WO 2017104149A1 · 2017 [cited by applicant]
WO 2017145010A1 · 2017 [cited by applicant]
WO 2017148527A1 · 2017 [cited by applicant]
WO 2017178956A1 · 2017 [cited by applicant]
WO 2017187396A1 · 2017 [cited by applicant]
WO 2017187398A1 · 2017 [cited by applicant]
WO 2017187399A1 · 2017 [cited by applicant]
WO 2017190795A1 · 2017 [cited by applicant]
WO 2018127446A1 · 2018 [cited by applicant]
WO 2018127456A2 · 2018 [cited by applicant]
Jakob Eberhardt: “ZoKrates—A Toolbox for zkSNARKs on Ethereum”, Youtube, Nov. 4, 2017 (Nov. 4, 2017), p. 1 pp., XP054979013, Retrieved from the Internet: URL:https://www.youtube.com/watch?v=sSlryw_b5J 0&t=4s (Year: 2017… [cited by examiner]
Andreas M. Antonopoulos: “Mastering Bitcoin—Unlocking Digital Cryptocurrencies” In: Mastering bitcoin : Dec. 20, 2014 (Dec. 20, 2014), O'Reilly Media, Beijing Cambridge Farnham Koln Sebastopol Tokyo, XP055306939, ISBN: … [cited by examiner]
Matteo Campanelli et al: “Zero-Knowledge Contingent Payments Revisited: Attacks and Payments for Services”, IACR, International Association for Cryptologic Research, vol. 20171101:190916 Jun. 9, 2017 (Jun. 9, 2017), pp.… [cited by examiner]
“How Log Proofs Work,” Certificate Transparency, Sep. 25, 2017 [retrieved May 2, 2018], https://web.archive.org/web/20170925180136/http://www.certificate-transparency.org/log-proofs-work, 5 pages. [cited by applicant]
Anonymous, “Background Page,” Oraclize, Oct. 2017 [retrieved May 2, 2018], https://web.archive.org/web/20171017121053/http://docs.oraclize.it/, 18 pages. [cited by applicant]
Bertani et al., “How can I trust smart contracts that use Oraclize?,” Reddit, May 25, 2017 [retrieved May 2, 2018], https://www.reddit.com/r/ethereum/comments/6d7j7x/how_can_i_trust_smart_contracts_that_use_oraclize/di0… [cited by applicant]
Fu, “Off-Chain Computation Solutions for Ethereum Developers,” Medium, Sep. 12, 2017 [retreived May 2, 2018], https://medium.com/@YondonFu/off-chain-computation-solutions-for-ethereum-developers-507b23355b17, 8 pages. [cited by applicant]
International Search Report and Written Opinion dated Mar. 14, 2019, Patent Application No. PCT/IB2018/059920, 12 pages. [cited by applicant]
Spencertruman et al., “[Whitepaper] Witnet: A Decentralized Oracle Network Protocol,” Bitcoin Forum, Dec. 11, 2017 [retreived May 2, 2018], https://bitcointalk.org/index.php?topic=2567253.0, 9 pages. [cited by applicant]
Tarr, “Merkle Tree Logs #27,” https://github.com/ssbc/secure-scuttlebutt/issues/27, Sep. 17, 2014, 4 pages. [cited by applicant]
Tarr, “Tree-Exchange,” Github, Aug. 4, 2014 (last updated Sep. 17, 2014) [retrieved May 10, 2018], https://github.com/dominictarr/tree-exchange, 3 pages. [cited by applicant]
UK Commercial Search Report dated May 4, 2018, Patent Application No. GB1720946.1, 8 pages. [cited by applicant]
UK IPO Search Report dated Jun. 15, 2018, Patent Application No. GB1720946.1, 4 pages. [cited by applicant]
Van Den Hooff et al., “VerSum: Verifiable Computations over Large Public Logs,” Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Nov. 3, 2014, 14 pages. [cited by applicant]
Zhang et al., “A Remote-Attestation-Based Extended Hash Algorithm for Privacy Protection,” 2017 International Conference on Computer Network, Electronic and Automation (ICCNEA), Sep. 23, 2017, 4 pages. [cited by applicant]
Klmoney, “Part 1: Transaction Basics”, Jun. 6, 2017, retrieved from the internet, https://web.archive.org/web/20170606202729/https://klmoney.wordpress.com/bitcoin-dissecting-transactions-part-1, 9 pages. [cited by applicant]
Vangie, Beal, “What is a Computer System?” Webopedia, Aug. 1, 2022, https://www.webopedia.com/definitions/computer-system, 2 pages. [cited by applicant]
Bertani, “Scalable Onchain Verification for Authenticated Data Feeds and Offchain Computations,” YouTube, Ethereum Foundation, Nov. 26, 2017 [retrieved May 10, 2018], https://www.youtube.com/watch?v=7uQdEBVu8Sk, 19:19, … [cited by applicant]
Tarr et al., “Merkle Tree Logs #27,” GitHub Secure-Scuttlebutt project page, Sep. 17, 2014 [retrieved May 10, 2018], https://github.com/ssbc/secure-scuttlebutt/issues/27, 4 pages. [cited by applicant]
Antonopoulos, “Mastering Bitcoin—Unlocking Digital Cryptocurrencies,” O'Reilly Media, Inc., Dec. 20, 2014, 282 pages. [cited by applicant]
Ben-Sasson et al. “Scalable Zero Knowledge via Cycles of Elliptic Curves” [online] IACR, Sep. 18, 2016 [retrieved Feb. 10, 2022]. Retrieved from https://eprint.iacr.org/2014/595.pdf, 2016, 49 pages. [cited by applicant]
Ben-Sasson et al., “SNARKs for C: Verifying program executions succinctly and in zero knowledge,” Advances in Cryptology—CRYPTO 2013, Aug. 18, 2013, 19 pages. [cited by applicant]
Ben-Sasson et al., “Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture,” USENIX Security 2014, first disclosed Dec. 30, 2013, last revised May 19, 2015, https://eprint.iacr.org/2013/879.pdf, 37 pages. [cited by applicant]
Ben-Sasson et al., “Zerocash: Decentralized Anonymous Payments from Bitcoin,” 2014 IEEE Symposium on Security and Privacy, May 18, 2014, http://zerocash-project.org/media/pdf/zerocash-oakland2014.pdf, 16 pages. [cited by applicant]
Bitcoin Core, “The First Successful Zero-Knowledge Contingent Payment”, 2022, 5 pages. [cited by applicant]
Bitcoinstrings, “Blockchain in Words,” retrieved from https://bitcoinstrings.com/blk00281.txt, Dec. 2013, 667 pages. [cited by applicant]
Bowe, “Pay-to-Sudoku,” GitHub, retrieved from https://github.com/zcash-hackworks/pay-to-sudoku/blob/master/readme.md, 2016, 2 pages. [cited by applicant]
Brown et al., “Transport layer security (tls) evidence extensions,” Working Draft, IETF Secretariat, Internet-Draft drafthousley-evidence-extns-01, https://tools.ietf.org/pdf/draft-housley-evidence-extns-01, Nov. 2006 [… [cited by applicant]
Buterin, “Quadratic Arithmetric Programs: from Zero to Hero,” retrieved from https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649, Dec. 11, 2016, 9 pages. [cited by applicant]
Campanelli et al., “Zero-knowledge contingent payments revisited: Attacks and payments for services,” Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, Oct. 30, 2017, 28 pages. [cited by applicant]
Canetti et al., “Practical Delegation of Computation Using Multiple Servers,” CCS, Oct. 17, 2011, 10 pages. [cited by applicant]
Castor, “Trust Your Oracle? Cornell Launches Tool for Confidential Blockchain Queries,” CoinDesk, retrieved from https://www.coindesk.com/tech/2017/05/17/trust-your-oracle-cornell-launches-tool-for-confidential-blockcha… [cited by applicant]
Chen et al., “Algebraic Geometric Secret Sharing Schemes and Secure Multi-Party Computations over Small Fields”, Advances in Cryptology, 2006, 16 pages. [cited by applicant]
Commercial Search Report dated Feb. 28, 2018, United Kingdom Patent Application No. 1719998.5, filed Nov. 30, 2017, 6 pages. [cited by applicant]
Costello et al., “Geppetto: versatile Verifiable Computation,” 2015 IEEE Symposium on Security and Privacy, 2015, 22 pages. [cited by applicant]
Covaci et al., “Computer-implemented system and method,” United Kingdom Patent Application No. 1720946.1, filed Dec. 15, 2017. [cited by applicant]
Covaci et al., “Extracting Information from the CRS in a ZK Protocol on Blockchain,” United Kingdom Patent Application No. 1719998.5, filed Nov. 30, 2017, 39 pages. [cited by applicant]
Covaci et al., “Logic Minimisation of C-like Smart Contracts for Optimised Verifiable Computation,” United Kingdom Patent Application No. 1718505.9, filed Nov. 9, 2017, 38 pages. [cited by applicant]
Covaci et al., “NECTAR: Non-Interactive Smart Contract Protocol using Blockchain Technology,” arXiv preprint arXiv: 1803.04860, Mar. 13, 2018, 8 pages. [cited by applicant]
Davidsen et al., “Empowering the Economy of Things,” 2017, 54 pages. [cited by applicant]
Eberhardt et al., “ZoKrates—Scalable Privacy-Preserving Off-Chain Computations,” Information Systems Engineering (ISE), Aug. 2018, 8 pages. [cited by applicant]
Ethereum Foundation, “ZoKrates—A Toolbox for zkSNARKS on Ethereum,” https://www.youtube.com/watch?v=sSlrywb5J_0, Nov. 26, 2017, 12 pages. [cited by applicant]
Fee et al., “Cryptography using Chebyshev polynomials,” Maple Summer Workshop, Burnaby, Canada, Jul. 11, 2004, http://www.cecm.sfu.ca/CAG/ppaers/CHEB, 16 pages. [cited by applicant]
Fiore et al., Hash First, Argue Later Adaptive Verifiable Computations on Outsourced Data, ACM Computer and Communications Security, 2016, 40 pages. [cited by applicant]
Fournet et al., “A Certified Compiler for Verifiable Computing,” HAL Open Science, Jun. 2016, 14 pages. [cited by applicant]
Franz et al., “CBMC-GC: An ANSI C Compiler for Secure Two-Party Computations,” retrieved from https://arise.or.at/pubpdf/CBMC-GC_An_ANSI_C_Compiler_for_Secure_Two-Party_Computations.pdf, 2014, 5 pages. [cited by applicant]
Fuchsbauer et al., “Proofs on Encrypted Values in Bilinear Groups and an Applicaiton to Anonymity of Signatures,” Third International Conference on Pairing-based Cryptography, Aug. 2009, 26 pages. [cited by applicant]
Gennaro et al., “Quadratic Span Programs and Succint NIZKs without PCPs,” Annual International Conference on the Theory and Applications of Cryptographic Techniques, May 26, 2013, 20 pages. [cited by applicant]
Gennaro et al., “Robust Threshold DSS Signatures,” International Conference on the Theory and Applications of Cryptographic Techniques, May 12, 1996, https://link.springer.com/content/pdf/10.1007%2F3-540-68339-9_31.pdf,… [cited by applicant]
Goldfeder et al., “Escrow Protocols for Cryptocurrencies: How to Buy Physical Goods Using Bitcoin,” retrieved from http://stevengoldfeder.com/papers/escrow.pdf, Jul. 26, 2018, 27 pages. [cited by applicant]
Hajjeh et al., “TLS Sign,” TLS Working Group, Internet Draft Version 4, Dec. 15, 2007 [retrieved May 2, 2018], https://tools.ietf.org/html/draft-hajjeh-tls-sign-04, 12 pages. [cited by applicant]
Hearn, “Continuing the zkSNARK Tutorials,” retrieved from https://blog.plan99.net/vntinyram-7b9d5b299097, Dec. 15, 2016, 9 pages. [cited by applicant]
Hong et al., “Verifiable Computation of Large Polynomials,” retrieved from http://or.nsfc.gov.cn/bitstream/00001903-5/154735/1/1000009080185.pdf, Dec. 16, 2014, 13 pages. [cited by applicant]
International Search Report and Written Opinion dated Jan. 15, 2019, Patent Application No. PCT/IB2018/058434, 11 pages. [cited by applicant]
International Search Report and Written Opinion dated Jan. 17, 2019, Patent Application No. PCT/IB2018/058432, 11 pages. [cited by applicant]
International Search Report and Written Opinion dated Jan. 17, 2019, Patent Application No. PCT/IB2018/058437, 10 pages. [cited by applicant]
International Search Report and Written Opinion dated Jan. 22, 2019, Patent Application No. PCT/IB2018/058583, 10 pages. [cited by applicant]
International Search Report and Written Opinion dated Jan. 23, 2019, Patent Application No. PCT/IB2018/058433, 12 pages. [cited by applicant]
International Search Report and Written Opinion dated Jan. 23, 2019, Patent Application No. PCT/IB2018/058491, 12 pages. [cited by applicant]
International Search Report and Written Opinion dated Mar. 14, 2019, Patent Application No. PCT/IB2018/059770, 12 pages. [cited by applicant]
International Search Report and Written Opinion dated Mar. 19, 2019, Patent Application No. PCT/IB2018/059918, 14 pages. [cited by applicant]
Jehan, “Rockchain Decentralized Audited Data Networks, ” White Paper, retrieved from https://www.rockchain.org/RockchainWhitePaper.pdf, Jan. 20, 2018, 28 pages. [cited by applicant]
Kerber, “Verifiable Computation in Smart Contracts,” University of Edinburgh School of Informatics Computer Science 4th Year Project Report, published online Apr. 4, 2017 [retrieved May 2, 2018], https://git.drwx.org/bs… [cited by applicant]
Keutzer et al., “Anatomy of a Hardware Compiler,” 1988, 10 pages. [cited by applicant]
Kiayias et al., “Proofs of Proofs of Work with Sublinear Complexity,” Financial Cryptography and Data Security, 2016, 18 pages. [cited by applicant]
Kosba et al., “Hawk: The Blockchain Model of Cryptography and Privacy-Preserving Smart Contracts,” IEEE Symposium on Security and Privacy, May 22, 2016, 31 pages. [cited by applicant]
Kreuter, “Techniques for Scalable Secure Computation Systems,” retrieved from https://repository.library.northeastern.edu/files/neu:cj82rh04k/fulltext.pdf, May 2018, 145 pages. [cited by applicant]
Król et al., “SPOC: Secure Payments for Outsourced Computations,” Jul. 17, 2018, 6 pages. [cited by applicant]
Kumaresan et al., “How to Use Bitcoin to Incentivize Correct Computations,” retrieved from https://people.csail.mit.edu/ranjit/papers/incentives.pdf, Nov. 2014, 12 pages. [cited by applicant]
Kuzminov et al., “Bridging the Gaps with Iolite Blockchain,” Iolite Foundation White Paper, 2017, 13 pages. [cited by applicant]
Malkhi et al., “Fairplay—A Secure Two-Party Computation System,” Aug. 2004, 17 pages. [cited by applicant]
Mathworks, “MATLAB Coder—Generate C and C++ Code From MATLAB Code,” 9 pages. [cited by applicant]
Maxwell et al., “Chat logs,” Bitcoin-wizards IRC Chat Channel, Aug. 16, 2013 [retrieved May 2, 2018], https://download.wpsoftware.net/bitcoin/wizards/2013/08/13-08-16.log, 1 page. [cited by applicant]
Maxwell et al., “CoinCovenants using SCIP signatures, an amusingly bad idea,” Bitcoin Forum, Aug. 20, 2013 [retrieved Apr. 13, 2018], https://bitcointalk.org/index.php?topic=278122.0, 5 pages. [cited by applicant]
Maxwell et al., “Really Really ultimate blockchain compression: CoinWitness,” Bitcoin Forum, Aug. 19, 2013 [retrieved Apr. 11, 2018], https://bitcointalk.org/index.php?topic=277389.0, 7 pages. [cited by applicant]
Maxwell, “The First Successful Zero-Knowledge Contingent Payment,” Bitcoin Core, retrieved from https://bitcoincore.org/en/2016/02/26/zero-knowledge-contingent-payments-announcement/, Feb. 26, 2016, 5 pages. [cited by applicant]
Mayer, “zk-SNARK Explained: Basic Principles,” Dec. 13, 2016, 9 pages. [cited by applicant]
Mayer, “zk-SNARK explained: Basic Principles,” retrieved from https://www.researchgate.net/publication/321124635_zk-SNARK_explained_Basic_Principles, Dec. 2016, 9 pages. [cited by applicant]
Müller, “A Short Note on Secret Sharing Using Elliptic Curves,” Proceedings of SECRYPT 2008, Jul. 26, 2008, http://www.scitepress.org/Papers/2008/19183/19183.pdf, 4 pages. [cited by applicant]
Nakamoto, “Bitcoin: A Peer-to-Peer Electronic Cash System,” Bitcoin, Oct. 31, 2008, https://bitcoin.org/bitcoin.pdf, 9 pages. [cited by applicant]
Ning, “Automatically Convert MATLAB Code to C Code,” https://www.mathworks.com/videos/automatically-converting-matlab-code-to-c-code-96483.html, Aug. 19, 2014, 8 pages. [cited by applicant]
Paganini, Pierluigi What is a Digital Signature? Fundamental Principles, Security Affairs, May 2012, https://securityaffairs.com/5223/digital-id/what-is-a-digital-signature-fundamental-principles.html, 7 pages. [cited by applicant]
Parno et al., “Pinocchio: Nearly Practical Verifiable Computation,” IEEE Symposium on Security and Privacy, May 19, 2013, 16 pages. [cited by applicant]
Parno et al., “Pinocchio: Nearly Practical Verifiable Computation,” IEEE Symposium on Security and Privacy, May 19-22, 2013, 16 pages. [cited by applicant]
Parno, “A Note on the Unsoundness of vnTinyRAM's SNARK,” retrieved from https://eprint.iacr.org/2015/437, May 6, 2015, 4 pages. [cited by applicant]
Prasad et al., “Effect pf Quine-McCluskey Simplification on Boolean Space Complexity,” IEEE Xplore, Jul. 25-26, 2009, 6 pages. [cited by applicant]
Ritzdorf et al., “TLS-N: Non-repudiation over TLS Enabling Ubiquitous Content Signing for Disintermediation,” IACR ePrint report, first disclosed 2017 [retrieved May 2, 2018], 16 pages. [cited by applicant]
Satoshi et al., “Connection Limits,” Bitcoin Forum, Aug. 9, 2010, https://bitcointalk.org/index.php?topic=741.0; prev_next=prev, 2 pages. [cited by applicant]
Schaeffer et al., “ZoKrates—a Toolbox for zkSNARKS on Ethereum,” https://github.com/Zokrates/ZoKrates, Feb. 4, 2019, 3 pages. [cited by applicant]
Schoenmakers et al., “Trinocchio: Privacy-Preserving Outsourcing by Distributed Verifiable Computation,” International Conference on Applied Cryptography and Network Security, Jun. 19, 2016, https://eprint.iacr.org/2015… [cited by applicant]
Stuart, “EECS Presents Awards for Outstanding PhD and SM Theses,” EECS, Nov. 8, 2017, 2 pages. [cited by applicant]
Sward et al. “Data Insertion in Bitcoin's Blockchain” [online] Augustana College, Jul. 2017 [retrieved Feb. 10, 2022]. Retrieved from the Internet: URL: https://digitalcommons.augustana.edu/cgi/viewcontent.cgi?article=1… [cited by applicant]
Teutsch et al., “A scalable verification solution for blockchains,” Nov. 16, 2017, https://people.cs.uchicago.edu/˜teutsch/papers/truebit.pdf, 50 pages. [cited by applicant]
Tillich et al., “Circuits of basic functions suitable for MPC and FHE,” https://homes.esat.kuleuven.be/˜nsmart/MPC/, first disclosed 2012, retrieved May 2, 2018, 2 pages. [cited by applicant]
Todd, “[bitcoin-dev] Building Blocks of the State Machine Approach to Consensus,” petertodd.org, Jun. 20, 2016, https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2016-June/012773.html, six pages. [cited by applicant]
Turner, “CSE 260. Introduction to Digital Logic and Computer Design,” Syllabus and Text Book, https://www.arl.wustl.edu/-jst/cse/260/ddc.pdf, 2015, 435 pages. [cited by applicant]
Turner, “Designing Digital Circuits a modern approach,” CSE 260, Introduction to Digital Logic and Computer Design, Spring 2014, 435 pages. [cited by applicant]
UK Commercial Search Report dated Dec. 3, 2018, Patent Application No. GB1806444.4, 8 pages. [cited by applicant]
UK Commercial Search Report dated Feb. 2, 2018, Patent Application No. GB1718505.9, 7 pages. [cited by applicant]
UK Commercial Search Report dated May 31, 2018, Patent Application No. GB1801753.3, 8 pages. [cited by applicant]
UK Commercial Search Report dated Oct. 25, 2018, Patent Application No. GB1805948.5 , 9 pages. [cited by applicant]
UK IPO Search Report dated Jul. 26, 2018, Patent Application No. GB1801753.3, 5 pages. [cited by applicant]
UK IPO Search Report dated Nov. 2, 2018, Patent Application No. GB1805948.5, 4 pages. [cited by applicant]
UK IPO Search Report dated Nov. 8, 2018, Patent Application No. GB1806444.4, 6 pages. [cited by applicant]
United Kingdom Commercial Search Report dated Apr. 20, 2018, Patent Application No. 1720768.9, filed Dec. 13, 2017, 8 pages. [cited by applicant]
United Kingdom Intellectual Property Office Search Report dated Jun. 12, 2018, Patent Application No. 1720768.9, filed Dec. 13, 2017, 7 pages. [cited by applicant]
United Kingdom Intellectual Property Office Search Report dated May 3, 2018, Patent Application No. 1719998.5, filed Nov. 30, 2017, 6 pages. [cited by applicant]
United Kingdom IPO Search Report dated Apr. 27, 2018, Patent Application No. 1718505.9, filed Nov. 9, 2017, 5 pages. [cited by applicant]
Viacoin Dev Team, “Styx: Unlinkable Anonymous Atomic Payment Hub For Viacoin,” viacoin.org, Oct. 14, 2016, http://docplayer.net/35213119-Styx-unlinkable-anonymous-atomic-payment-hub-for-viacoin-viacoin-dev-team-viacoin-… [cited by applicant]
Virza, “On Deploying Succinct Zero-Knowledge Proofs” [online] MIT, Sep. 2017 [retrieved Feb. 10, 2022]. Retrieved from the Internet: URL: On Deploying Succinct Zero-Knowledge Proofs, 2016, 131 pages. [cited by applicant]
Wikipedia, “Huffman coding,” Wikipedia the Free Encyclopedia, Febraury 24, 2018, https://en.wikipedia.org/w/index.php?title=Huffman_coding&oldid=827366029, 11 pages. [cited by applicant]
Wikipedia, “Precompiled Header,” Retrieved Mar. 30, 2022, https://en.wikipedia.org/w/index.php?title=Precompiled_header&oldid=807155683, 3 pages. [cited by applicant]
Wikipedia, “Zero Knowledge Contingent Payment,” Bitcoin Wiki, retrieved from https://en.bitcoin.it/wiki/Zero_Knowledge_Contingent_Payment, Apr. 8, 2020, 3 pages. [cited by applicant]
Wu et al., “Libsnark: a C++ Library for zkSNARK Proofs,” SCIPR Lab, libsnark/readme.md at 92a80f74727091fdc40e6021dc42e9f6b67d5176, Aug. 18, 2017, 9 pages. [cited by applicant]
Zcash, “zk-SNARKs,” zCash website, retreived Apr. 1, 2022 from https://web.archive.org/web/20171107012237/ https://z.cash/technology/zksnarks.html, Nov. 24, 2017, 1 page. [cited by applicant]
Zyskind et al., “Enigma: Decentralized Computation Platform with Guaranteed Privacy,” arXiv preprint arXiv:1506, Jun. 10, 2015, 14 pages. [cited by applicant]
Japan Patent Office, “Notice of Reasons for Refusal ” in Application No. 2023-014319, Feb. 13, 2024, 12 pages. [cited by applicant]
Intellectual Property Office of Korea, “Request for the Submission of an Opinion” in Application No. 10-2020-7014213, Jan. 31, 2024, 7 pages. [cited by applicant]
Justus, Benjamin, “Point Compression and Coordinate Recovery for Edwards Curves over Finite Field”, Annals of West University of Timisoara-Mathematics and Computer Science, 2014, 15 pages. [cited by applicant]
Menezes et al., “Handbook of Applied Cryptography: pp. 33, 38,” CRC Press, Oct. 16, 1996, 3 pages. [cited by applicant]
Sanchez, David Cerezo, “Raziel: Private and Verifiable Smart Contracts in Blockchains”, Sep. 17, 2017, 55 pages. [cited by applicant]
Seijas et al., “Scripting Smart Contract for Distributed Ledger Technology”, Feb. 10, 2017, 33 pages. [cited by applicant]
Al-Riyami, Sattam, S., “Cryptographic Schemes Based on Elliptic Curve Pairings”, Technical Report, RHUL-MA-2002-2, Feb. 2, 2005, 278 pages. [cited by applicant]
Intellectual Property Office of Korea, “Request for the Submission of an Opinion” in Application No. 10-2024-7024191, Aug. 5, 2024, 4 pages. [cited by applicant]
Shocker, Ali, “Sustainable Blockchain through Proof of exercise”, 2017 IEEE 16th International Symposium on Network Computing and Applications (NCA), Nov. 1, 2017, 9 pages. [cited by applicant]
Ball, M. et al., “Proof of Useful Work”, Cryptology ePrint Archive, Report, Feb. 27, 2017, 31 pages. [cited by applicant]
Japanese Patent Office Notice of Reasons for Refusal dated Jul. 30, 2024, Application No. 2023-176820, 7 pages. [cited by applicant]