Granted Patent
B2
US 12,250,310 · App. 18/094,747 · Granted Mar 11, 2025
Use of irrational numbers in elliptic curve cryptography
View Patent ↗
Loading inventors, assignments & file history…
Abstract
Elliptical curve cryptography (ECC) utilizes an elliptic curve consistent with the formula px mod q=r, where x is a private key having an irrational number component. The irrational component is employed to provide much greater entropy than would be achieved where x is a prime number.
Claims (15)
1. A method of decrypting encrypted data using elliptical curve cryptography, comprising:
initializing one or more memory locations to instantiate an elliptical curve algorithm consistent with the formula, p x mod q=r, where x is an irrational component, wherein the irrational component comprises one of: (a) a portion of a root of a non-perfect square or (b) a portion of a square root of 2 or a square root of 5;
operating digital logic circuitry to apply a series of one or more mathematical operations to the elliptic curve to produce a private key from a public key;
using the private key to de-crypt the encrypted data.
2. The method of claim 1 , wherein p is 3, 5, or 7 . . . .
3. A method of encrypting data using elliptical curve cryptography, comprising:
initializing one or more memory locations to instantiate an elliptical curve algorithm consistent with the formula, p x mod q=r, where x is an irrational component, wherein the irrational component comprises one of: (a) a portion of a root of a non-perfect square or (b) a portion of a square root of 2 or a square root of 5;
using a public key to encrypt the data;
operating digital logic circuitry to apply a series of one or more mathematical operations to the elliptic curve to produce a private key from the public key; and
providing the private key to an entity for use in decrypting the data.
4. A method of increasing entropy in elliptical curve cryptography, comprising:
initializing one or more memory locations to instantiate an elliptical curve algorithm consistent with the formula, p x mod q=r, where x is an irrational component instead of a prime number, wherein the irrational component comprises one of: (a) a portion of a root of a non-perfect square or (b) a portion of a square root of 2 or a square root of 5;
using a public key to encrypt the data;
operating digital logic circuitry to apply a series of one or more mathematical operations to the elliptic curve to produce a private key from the public key; and
providing the private key to an entity for us in decrypting the data.
Assignments (1)
ASSIGNMENT OF ASSIGNOR'S INTEREST
Recorded Jan 30, 2023
From: GRANRT, ROBERT EDWARD
To: CROWN STERLING LIMITED, LLC
Reel/Frame 062536/0079 →
Continuity (1)
References Cited (180)
US 4166405A
· Hiyoshi et al.
· 1979
[cited by applicant]
US 4613901A
· Gilhousen et al.
· 1986
[cited by applicant]
US 4860624A
· Dinnan et al.
· 1989
[cited by applicant]
US 4868624A
· Grung et al.
· 1989
[cited by applicant]
US 5033352A
· Kellogg
· 1991
[cited by applicant]
US 5516981A
· Nagai
· 1996
[cited by applicant]
US 5764772A
· Kaufman
· 1998
[cited by applicant]
US 5966445A
· Park
· 1999
[cited by applicant]
US 5987483A
· Edelkind et al.
· 1999
[cited by applicant]
US 6072876A
· Obata
· 2000
[cited by applicant]
US 6154541A
· Zhang
· 2000
[cited by applicant]
US 6154542A
· Crandall
· 2000
[cited by applicant]
US 6349319B1
· Shankar et al.
· 2002
[cited by applicant]
US 6396928B1
· Zheng
· 2002
[cited by applicant]
US 6448487B1
· Smith
· 2002
[cited by applicant]
US 6480605B1
· Uchiyama
· 2002
[cited by applicant]
US 6636968B1
· Rosner
· 2003
[cited by applicant]
US 6751736B1
· Bowman
· 2004
[cited by applicant]
US 6763364B1
· Wilber
· 2004
[cited by applicant]
US 6778666B1
· Kuzmich
· 2004
[cited by examiner]
US 6924426B2
· Clynes
· 2005
[cited by applicant]
US 6990200B1
· Kasahara
· 2006
[cited by applicant]
US 7062044B1
· Solinas
· 2006
[cited by examiner]
US 7502754B2
· Campbell
· 2009
[cited by applicant]
US 8468244B2
· Redlich
· 2013
[cited by applicant]
US 8516244B2
· Waters
· 2013
[cited by applicant]
US 8885820B1
· Lambert et al.
· 2014
[cited by applicant]
US 9325499B1
· Juels et al.
· 2016
[cited by applicant]
US 9425954B1
· Chalker
· 2016
[cited by applicant]
US 9450749B2
· Hammersmith
· 2016
[cited by applicant]
US 9674162B1
· Miller et al.
· 2017
[cited by applicant]
US 9917699B2
· Booth et al.
· 2018
[cited by applicant]
US 20030016823A1
· Chung
· 2003
[cited by applicant]
US 20030081785A1
· Boneh et al.
· 2003
[cited by applicant]
US 20030112972A1
· Hattick et al.
· 2003
[cited by applicant]
US 20030115449A1
· Yochim
· 2003
[cited by applicant]
US 20040096056A1
· Boren
· 2004
[cited by applicant]
US 20040200335A1
· Phillips
· 2004
[cited by applicant]
US 20050271207A1
· Frey
· 2005
[cited by applicant]
US 20060045262A1
· Orlando
· 2006
[cited by examiner]
US 20060072745A1
· Fukaya
· 2006
[cited by applicant]
US 20060177065A1
· Halbert
· 2006
[cited by applicant]
US 20060262957A1
· Asano
· 2006
[cited by applicant]
US 20070064930A1
· Fischer
· 2007
[cited by applicant]
US 20070211893A1
· Frosik
· 2007
[cited by applicant]
US 20080107274A1
· Worthy
· 2008
[cited by applicant]
US 20080006140A1
· Adams
· 2008
[cited by applicant]
US 20080130873A1
· Bolotov
· 2008
[cited by examiner]
US 20080184872A1
· Hunt et al.
· 2008
[cited by applicant]
US 20080208560A1
· Johnson
· 2008
[cited by applicant]
US 20080257136A1
· Meeks
· 2008
[cited by applicant]
US 20090146851A1
· Lablans
· 2009
[cited by applicant]
US 20090094464A1
· Futa et al.
· 2009
[cited by applicant]
US 20090207999A1
· Yonemura et al.
· 2009
[cited by applicant]
US 20090216910A1
· Duchesneau
· 2009
[cited by applicant]
US 20100119061A1
· Kawale
· 2010
[cited by applicant]
US 20120134495A1
· Liu
· 2012
[cited by applicant]
US 20120213358A1
· Dror et al.
· 2012
[cited by applicant]
US 20130142323A1
· Chiarella
· 2013
[cited by applicant]
US 20130297937A1
· Fransen
· 2013
[cited by applicant]
US 20130315388A1
· Chiarella
· 2013
[cited by applicant]
US 20140112469A1
· Layne
· 2014
[cited by applicant]
US 20140369492A1
· Lambert
· 2014
[cited by examiner]
US 20160012252A1
· Deleeuw
· 2016
[cited by applicant]
US 20160014110A1
· Kurspahic
· 2016
[cited by applicant]
US 20160042657A1
· Granger et al.
· 2016
[cited by applicant]
US 20160323736A1
· Donahue et al.
· 2016
[cited by applicant]
US 20170078087A1
· Chalker
· 2017
[cited by applicant]
US 20170222804A1
· Dewitt
· 2017
[cited by applicant]
US 20170302446A1
· Thorwirth
· 2017
[cited by applicant]
US 20170310650A1
· McMullen
· 2017
[cited by applicant]
US 20170315212A1
· Monferrer
· 2017
[cited by applicant]
US 20180039667A1
· Pierce et al.
· 2018
[cited by applicant]
US 20180101322A1
· Cheriton
· 2018
[cited by applicant]
US 20180131526A1
· Ellingson
· 2018
[cited by applicant]
US 20180241548A1
· Dolev et al.
· 2018
[cited by applicant]
US 20180332010A1
· Graber et al.
· 2018
[cited by applicant]
US 20190036678A1
· Ahmed
· 2019
[cited by applicant]
US 20190051276A1
· Lathrop et al.
· 2019
[cited by applicant]
US 20190089532A1
· Lambert
· 2019
[cited by applicant]
US 20190120929A1
· Meadow
· 2019
[cited by applicant]
US 20190238323A1
· Bunch
· 2019
[cited by applicant]
US 20200084024A1
· Myers
· 2020
[cited by applicant]
US 20200084037A1
· Zhang
· 2020
[cited by applicant]
US 20200136819A1
· Bae et al.
· 2020
[cited by applicant]
US 20200153458A1
· Strobel et al.
· 2020
[cited by applicant]
US 20200177579A1
· Allen
· 2020
[cited by applicant]
US 20200228507A1
· Anderson et al.
· 2020
[cited by applicant]
US 20200241841A1
· Tamiya
· 2020
[cited by applicant]
US 20200293212A1
· Narayanamurthy
· 2020
[cited by applicant]
US 20200366652A1
· Koyun
· 2020
[cited by applicant]
US 20200396059A1
· Micali
· 2020
[cited by applicant]
US 20210028935A1
· Wu et al.
· 2021
[cited by applicant]
US 20210065664A1
· Ryyanen et al.
· 2021
[cited by applicant]
US 20210312055A1
· Kloth
· 2021
[cited by applicant]
US 20210336766A1
· Kim et al.
· 2021
[cited by applicant]
US 20210382695A1
· Chang et al.
· 2021
[cited by applicant]
US 20220198034A1
· Rodriguez
· 2022
[cited by applicant]
DE 102018005247A1
· 2020
[cited by applicant]
EP 1220174A1
· 2000
[cited by applicant]
EP 1220174
· 2002
[cited by applicant]
EP 2680488
· 2019
[cited by applicant]
FR 2679365A1
· 1993
[cited by applicant]
JP 2002529774A
· 2002
[cited by applicant]
JP 2007157288
· 2007
[cited by applicant]
JP 2007157288A
· 2007
[cited by applicant]
JP 2007336556A
· 2007
[cited by applicant]
JP 2014026213A
· 2014
[cited by applicant]
JP 2019526201A
· 2019
[cited by applicant]
KR 20010008976A
· 2001
[cited by applicant]
KR 20130051386A
· 2013
[cited by applicant]
KR 101605496B1
· 2016
[cited by applicant]
WO 199720306A1
· 1996
[cited by applicant]
WO 0065768
· 2000
[cited by applicant]
WO 2000065768A1
· 2000
[cited by applicant]
WO 2005085992
· 2005
[cited by applicant]
WO 2005085992A1
· 2005
[cited by applicant]
WO 2010111320A2
· 2010
[cited by applicant]
WO 2016135726A1
· 2016
[cited by applicant]
WO 2016203762
· 2016
[cited by applicant]
WO 2016203762A1
· 2016
[cited by applicant]
WO 2019110955
· 2019
[cited by applicant]
WO 2019110955A1
· 2019
[cited by applicant]
Bhaumik, et al. “Safely Doubling your Block Ciphers for a Post-Quantum World,” Inria, Paris. 2020. 49 pages.
[cited by applicant]
“Elliptic Curve Cryptography (Ecc).” 1 page.
[cited by applicant]
“Elliptic Curve Over Finite Non-Prime Fields,” Mathematics. 2 pages.
[cited by applicant]
“Golden Ratio Calculator,” Good Calculators. 2 pages.
[cited by applicant]
Grant, et al. “Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical Methodology.” 8 pages.
[cited by applicant]
Grant, Robert E. “Prime Number Pattern Discovery,” Discoveries, Publications, Unified Math/Physics. Jul. 2018. 6 pages.
[cited by applicant]
Kumar, et al. “A Symmetric Mecial Image Encryption Scheme Based on Irrational Numbers,” Biomed Res 2018 Special Issue. S494-S498. 5 pages.
[cited by applicant]
Grant, et al. “Reciprocal Wave Factorization,” Strathspey Crown Holdings. Jun. 2020. 19 pages.
[cited by applicant]
Barker, et al. “Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography,” NIST. Apr. 2018. 2 pages.
[cited by applicant]
Weisstein, Eric W. “Taniyama-Shimura Conjecture,” Mathworld—A Wolfram Web Resource. 3 pages.
[cited by applicant]
Wang, et al. “A Decentralized Electricity Transaction Mode of Microgrid Based on Blockchain and Continuous Double Action,” IEEE. 2018. 5 pages.
[cited by applicant]
“Why Are Elliptic Curves Constructed Using Prime Fields and Not Composite Fields?” https://crypto.stackexchange.com. 3 pages.
[cited by applicant]
Wu, et al. “Forensic Analysis of Bitcoin Transactions,” IEEE. 2019. 3 pages.
[cited by applicant]
Burd, Barry. “A New Approach to Condensing Data Leads to a 99% Compression Rate,” TechTarget. May 2015. 9 pages.
[cited by applicant]
Zhang, et al. “A Blockchain-Based Authentication Method with One-Time Password,” IEEE, 2019. 9 pages.
[cited by applicant]
“Elliptic Curve Cryptography (ECC).” 1 pages.
[cited by applicant]
“Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography,” NIST. 2 pages.
[cited by applicant]
“Taniyama-Shimura Conjecture,” Wolfram Mathworld. 3 pages.
[cited by applicant]
“Why are elliptic curves constructed using prime fields and not composite fields?” www.crypto.stackexchange.com. 3 pages.
[cited by applicant]
“Why is a prime number used in ECDSA?” www.crypto.stackexchange.com. 3 pages.
[cited by applicant]
Overmars, et al. “An Efficient Golden Ratio Method for Secure Cryptographic Applications,” School of Engineering, Construction & Design, Melbourne Polytechnic, Preston, Australia. Sep. 17, 2018. 12 pages.
[cited by applicant]
“Prime Number Pattern Discovery,” Discoveries, Publications, Unified Math/Physics. Jul. 7, 2018, 6 pages.
[cited by applicant]
Ritam Bhaumik et al., “Safely Doubling your Block Ciphers for a Post-Quantum World”, Inria and Orange Labs, 49 pages.
[cited by applicant]
International Search Report and Written Opinion for International Patent Application No. PCT/US2021/064739, dated Apr. 4, 2022, 14 pages.
[cited by applicant]
Gabriela Ahmadi-Assalemi et al., “Federated Blockchain-based Tracking and Liability Attribution Framework for Employees and Cyber-Physical Objects in a Smart Workplace”, IEEE, 9 pages.
[cited by applicant]
Wattana Viriyasitavat et al., “Blockchain Technology for Applications in Internet of Things-Mapping From System Design Perspective”, IEEE, dated Oct. 2019, 14 pages.
[cited by applicant]
“Why is a Prime Number Used in ECDSA?”, https://crypto.stackexchange.com/, 3 pages.
[cited by applicant]
International Search Report and Written Opinion for International Patent Application No. PCT/US2022/043866, dated Jan. 18, 2023, 9 pages.
[cited by applicant]
Murat Kantarcioglu et al., “A Cryptographic Approach to Securely Share and Query Genomic Sequences”, IEEE, Sep. 2008, 12 pages.
[cited by applicant]
Luka Milinkovic et al., “Pseudo-Random Number Generator Based on Irrational Numbers”, Telsiks, dated Oct. 8, 2011, 4 pages.
[cited by applicant]
Ryutarou Ohbuchi et al., “Watermarking Three-Dimensional Polygonal Models”, IBM Tokyo Research Laboratory, dated 1997, 12 pages.
[cited by applicant]
Guangfu Wu et al, “The security and privacy of blockchain-enabled EMR storage management scheme”, IEEE, dated 2020, 5 pages.
[cited by applicant]
Devika K. N. et al., “Parameterizable FPGA Implemetation of SHA-256 using Blockchain Concept”, IEEE, dated Apr. 6, 2019, 5 pages.
[cited by applicant]
Bong-Ju Jang et al., “A New Digital Watermarking for Architectural Design Drawing using LINEs and ARCs Based on Vertex”, Department of Electronic Computer Engineer, Pusan University of Foreign Studies, dated 2004, 14 pa…
[cited by applicant]
International Search Report and Written Opinion for International Patent Application No. PCT/US2022/046045, dated Jan. 27, 2023, 11 pages.
[cited by applicant]