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18.783 Elliptic Curves (MIT) 18.783 Elliptic Curves (MIT)

Description

This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | elliptic curves | number theory | number theory | cryptography | cryptography | point-counting | point-counting | isogenies | isogenies | pairings | pairings | theory of complex multiplication | theory of complex multiplication | integer factorization | integer factorization | primality proving | primality proving | elliptic curve cryptography | elliptic curve cryptography | modular curves | modular curves | Fermat's Last Theorem | Fermat's Last TheoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power. This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.Subjects

finite automata | finite automata | Turing machine | Turing machine | halting problem | halting problem | computability | computability | computational complexity | computational complexity | polynomial time | polynomial time | P | P | NP | NP | NP complete | NP complete | probabilistic algorithms | probabilistic algorithms | private-key cryptography | private-key cryptography | public-key cryptography | public-key cryptography | randomness | randomnessLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity—with Euclid's algorithm and other ancient examples of computational thinking—the course will progress rapidly through propositional logic, Turing machines and computability, finite automata, Gödel's theorems, efficient algorithms and reducibility, NP-completeness, the P versus NP problem, decision trees and other concrete computational models, the power of randomness, cryptography and one-way functions, computational theories of learning, interactive proofs, and q This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity—with Euclid's algorithm and other ancient examples of computational thinking—the course will progress rapidly through propositional logic, Turing machines and computability, finite automata, Gödel's theorems, efficient algorithms and reducibility, NP-completeness, the P versus NP problem, decision trees and other concrete computational models, the power of randomness, cryptography and one-way functions, computational theories of learning, interactive proofs, and qSubjects

computer science | computer science | theoretical computer science | theoretical computer science | logic | logic | turing machines | turing machines | computability | computability | finite automata | finite automata | godel | godel | complexity | complexity | polynomial time | polynomial time | efficient algorithms | efficient algorithms | reducibility | reducibility | p and np | p and np | np completeness | np completeness | private key cryptography | private key cryptography | public key cryptography | public key cryptography | pac learning | pac learning | quantum computing | quantum computing | quantum algorithms | quantum algorithmsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.783 Elliptic Curves (MIT) 18.783 Elliptic Curves (MIT)

Description

This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | elliptic curves | number theory | number theory | cryptography | cryptography | point-counting | point-counting | isogenies | isogenies | pairings | pairings | theory of complex multiplication | theory of complex multiplication | integer factorization | integer factorization | primality proving | primality proving | elliptic curve cryptography | elliptic curve cryptography | modular curves | modular curves | Fermat's Last Theorem | Fermat's Last TheoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.857 Network and Computer Security (MIT) 6.857 Network and Computer Security (MIT)

Description

6.857 is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the department's Computer Systems and Architecture Engineering concentration. Topics covered include (but are not limited to) the following: Techniques for achieving security in multi-user computer systems and distributed computer systems; Cryptography: secret-key, public-key, digital signatures; Authentication and identification schemes; Intrusion detection: viruses; Formal models of computer security; Secure operating systems; Software protection; Security of electronic mail and the World Wide Web; Electronic commerce: payment protocols, electronic cash; Firewalls; and Risk assessment. 6.857 is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the department's Computer Systems and Architecture Engineering concentration. Topics covered include (but are not limited to) the following: Techniques for achieving security in multi-user computer systems and distributed computer systems; Cryptography: secret-key, public-key, digital signatures; Authentication and identification schemes; Intrusion detection: viruses; Formal models of computer security; Secure operating systems; Software protection; Security of electronic mail and the World Wide Web; Electronic commerce: payment protocols, electronic cash; Firewalls; and Risk assessment.Subjects

network | network | computer security | computer security | security | security | cryptography | cryptography | secret-key | secret-key | public-key | public-key | digital signature | digital signature | authentication | authentication | identification | identification | intrusion detection | intrusion detection | virus | virus | operating system | operating system | software | software | protection | protection | electronic mail | electronic mail | email | email | electronic commerce | electronic commerce | electronic cash | electronic cash | firewall | firewall | computer | computer | digital | digital | signature | signature | electronic | electronic | cash | cash | commerce | commerce | mail | mail | operating | operating | system | system | intrustion | intrustion | detection | detection | distributed | distributed | physical | physical | discretionary | discretionary | mandatory | mandatory | access | access | control | control | biometrics | biometrics | information | information | flow | flow | models | models | covert | covert | channels | channels | integrity | integrity | logic | logic | voting | voting | risk | risk | assessment | assessment | secure | secure | web | web | browsers | browsers | architecture | architecture | engineering | engineering | certificates | certificates | multi-user computer systems | multi-user computer systems | distributed computer systems | distributed computer systems | physical security | physical security | discretionary access control | discretionary access control | mandatory access control | mandatory access control | information-flow models | information-flow models | covert channels | covert channels | integrity models | integrity models | elementary cryptography | elementary cryptography | authentication logic;electronic cash | authentication logic;electronic cash | viruses | viruses | firewalls | firewalls | electronic voting | electronic voting | risk assessment | risk assessment | secure web browsers | secure web browsers | network security | network security | architecture engineering | architecture engineering | digital signatures | digital signatures | authentication schemes | authentication schemes | identification schemes | identification schemes | formal models | formal models | secure operating systems | secure operating systems | software protection | software protection | electronic mail security | electronic mail security | World Wide Web | World Wide Web | ecommerce | ecommerce | email security | email security | www | www | payment protocols | payment protocols | authentication logic | authentication logicLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.783 Elliptic Curves (MIT) 18.783 Elliptic Curves (MIT)

Description

This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | elliptic curves | number theory | number theory | cryptography | cryptography | point-counting | point-counting | isogenies | isogenies | pairings | pairings | theory of complex multiplication | theory of complex multiplication | integer factorization | integer factorization | primality proving | primality proving | elliptic curve cryptography | elliptic curve cryptography | modular curves | modular curves | Fermat's Last Theorem | Fermat's Last TheoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.033 Computer System Engineering (MIT) 6.033 Computer System Engineering (MIT)

Description

Includes audio/video content: AV lectures. This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Two design projects are required, and students engage in extensive written communication exercises. Includes audio/video content: AV lectures. This course covers topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, virtual memory, and threads; networks; atomicity and coordination of parallel activities; recovery and reliability; privacy, security, and encryption; and impact of computer systems on society. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Two design projects are required, and students engage in extensive written communication exercises.Subjects

computer systems | computer systems | systems design | systems design | complexity | complexity | abstractions | abstractions | modularity | modularity | client server | client server | operating system | operating system | performance | performance | networks | networks | layering | layering | routing | routing | congestion control | congestion control | reliability | reliability | atomicity | atomicity | isolation | isolation | security | security | authentication | authentication | cryptography | cryptography | therac 25 | therac 25 | unix | unix | mapreduce | mapreduce | architecture of complexity | architecture of complexity | trusting trust | trusting trust | computer system design | computer system designLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.857 Network and Computer Security (MIT)

Description

6.857 is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the department's Computer Systems and Architecture Engineering concentration. Topics covered include (but are not limited to) the following: Techniques for achieving security in multi-user computer systems and distributed computer systems; Cryptography: secret-key, public-key, digital signatures; Authentication and identification schemes; Intrusion detection: viruses; Formal models of computer security; Secure operating systems; Software protection; Security of electronic mail and the World Wide Web; Electronic commerce: payment protocols, electronic cash; Firewalls; and Risk assessment.Subjects

network | computer security | security | cryptography | secret-key | public-key | digital signature | authentication | identification | intrusion detection | virus | operating system | software | protection | electronic mail | email | electronic commerce | electronic cash | firewall | computer | digital | signature | electronic | cash | commerce | mail | operating | system | intrustion | detection | distributed | physical | discretionary | mandatory | access | control | biometrics | information | flow | models | covert | channels | integrity | logic | voting | risk | assessment | secure | web | browsers | architecture | engineering | certificates | multi-user computer systems | distributed computer systems | physical security | discretionary access control | mandatory access control | information-flow models | covert channels | integrity models | elementary cryptography | authentication logic;electronic cash | viruses | firewalls | electronic voting | risk assessment | secure web browsers | network security | architecture engineering | digital signatures | authentication schemes | identification schemes | formal models | secure operating systems | software protection | electronic mail security | World Wide Web | ecommerce | email security | www | payment protocols | authentication logicLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | number theory | cryptography | point-counting | isogenies | pairings | theory of complex multiplication | integer factorization | primality proving | elliptic curve cryptography | modular curves | Fermat's Last TheoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component. This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.Subjects

probability | probability | probability theory counting | probability theory counting | pigeonhole principle | pigeonhole principle | Van der Waerden's theorem | Van der Waerden's theorem | Chernoff bounds | Chernoff bounds | counting | counting | coding | coding | sampling | sampling | random sampling | random sampling | Catalan families | Catalan families | generating functions | generating functions | chord diagrams | chord diagrams | linear programming | linear programming | simplex method | simplex method | Zero-Sum matrix | Zero-Sum matrix | network flows | network flows | maximum flow problem | maximum flow problem | sorting algorithms | sorting algorithms | QUICKSORT | QUICKSORT | median finding | median finding | sorting networks | sorting networks | Batcher's algorithm | Batcher's algorithm | Euclid's algorithm | Euclid's algorithm | Chinese Remainder Theorem | Chinese Remainder Theorem | cryptography | cryptography | RSA code | RSA code | primaility testing | primaility testing | FFT | FFT | Fast Fourier Transform | Fast Fourier Transform | Shannon's coding theorems | Shannon's coding theorems | Lempel-Ziv codes | Lempel-Ziv codes | linear codes | linear codes | hamming code | hamming codeLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and polaSubjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following. Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following. Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&aSubjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | coherent states | and squeezed states | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | quantum teleportation | quantum teleportationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | number theory | cryptography | point-counting | isogenies | pairings | theory of complex multiplication | integer factorization | primality proving | elliptic curve cryptography | modular curves | Fermat's Last TheoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.435J Quantum Computation (MIT) 18.435J Quantum Computation (MIT)

Description

This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography. This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography.Subjects

quantum computation | quantum computation | physics of information processing | physics of information processing | quantum logic | quantum logic | quantum algorithms including Shor's factoring algorithm and Grover's search algorithm | quantum algorithms including Shor's factoring algorithm and Grover's search algorithm | quantum error correction | quantum error correction | quantum communication | quantum communication | cryptography | cryptography | 18.345 | 18.345 | 2.111 | 2.111 | ESD.79 | ESD.79License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataLecture 18: Puzzles Lecture 18: Puzzles

Description

Description: Puzzles are a popular type of game, characterized by a strict ruleset and (ideally) a single solution. They may appear on their own or embedded into a larger narrative, sometimes representing a similar real-life mechanism (e.g. unlocking a door). Instructors/speakers: Philip Tan, Jason BegyKeywords: puzzle, algorithm, mathematics, learning curve, Sudoku, crosswords, tangrams, Mystery Hunt, Portal, Rubik's Cube, rebus, logic, riddles, determinism, combinatorics, permutations, cryptographyTranscript: PDFSubtitles: SRTAudio - download: Internet Archive (MP3)Audio - download: iTunes U (MP3)(CC BY-NC-SA) Description: Puzzles are a popular type of game, characterized by a strict ruleset and (ideally) a single solution. They may appear on their own or embedded into a larger narrative, sometimes representing a similar real-life mechanism (e.g. unlocking a door). Instructors/speakers: Philip Tan, Jason BegyKeywords: puzzle, algorithm, mathematics, learning curve, Sudoku, crosswords, tangrams, Mystery Hunt, Portal, Rubik's Cube, rebus, logic, riddles, determinism, combinatorics, permutations, cryptographyTranscript: PDFSubtitles: SRTAudio - download: Internet Archive (MP3)Audio - download: iTunes U (MP3)(CC BY-NC-SA)Subjects

puzzle | puzzle | algorithm | algorithm | mathematics | mathematics | learning curve | learning curve | Sudoku | Sudoku | crosswords | crosswords | tangrams | tangrams | Mystery Hunt | Mystery Hunt | Portal | Portal | Rubik's Cube | Rubik's Cube | rebus | rebus | logic | logic | riddles | riddles | determinism | determinism | combinatorics | combinatorics | permutations | permutations | cryptography | cryptographyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and polaSubjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.080 Great Ideas in Theoretical Computer Science (MIT)

Description

This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity—with Euclid's algorithm and other ancient examples of computational thinking—the course will progress rapidly through propositional logic, Turing machines and computability, finite automata, Gödel's theorems, efficient algorithms and reducibility, NP-completeness, the P versus NP problem, decision trees and other concrete computational models, the power of randomness, cryptography and one-way functions, computational theories of learning, interactive proofs, and qSubjects

computer science | theoretical computer science | logic | turing machines | computability | finite automata | godel | complexity | polynomial time | efficient algorithms | reducibility | p and np | np completeness | private key cryptography | public key cryptography | pac learning | quantum computing | quantum algorithmsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.857 Network and Computer Security (MIT)

Description

6.857 is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the department's Computer Systems and Architecture Engineering concentration. Topics covered include (but are not limited to) the following: Techniques for achieving security in multi-user computer systems and distributed computer systems; Cryptography: secret-key, public-key, digital signatures; Authentication and identification schemes; Intrusion detection: viruses; Formal models of computer security; Secure operating systems; Software protection; Security of electronic mail and the World Wide Web; Electronic commerce: payment protocols, electronic cash; Firewalls; and Risk assessment.Subjects

network | computer security | security | cryptography | secret-key | public-key | digital signature | authentication | identification | intrusion detection | virus | operating system | software | protection | electronic mail | email | electronic commerce | electronic cash | firewall | computer | digital | signature | electronic | cash | commerce | mail | operating | system | intrustion | detection | distributed | physical | discretionary | mandatory | access | control | biometrics | information | flow | models | covert | channels | integrity | logic | voting | risk | assessment | secure | web | browsers | architecture | engineering | certificates | multi-user computer systems | distributed computer systems | physical security | discretionary access control | mandatory access control | information-flow models | covert channels | integrity models | elementary cryptography | authentication logic;electronic cash | viruses | firewalls | electronic voting | risk assessment | secure web browsers | network security | architecture engineering | digital signatures | authentication schemes | identification schemes | formal models | secure operating systems | software protection | electronic mail security | World Wide Web | ecommerce | email security | www | payment protocols | authentication logicLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.561 Information Technology Essentials (MIT) 15.561 Information Technology Essentials (MIT)

Description

This class offers a broad coverage of technology concepts and trends underlying current and future developments in information technology, and fundamental principles for the effective use of computer-based information systems. There will be a special emphasis on networks and distributed computing, including the World Wide Web. Other topics include: hardware and operating systems, software development tools and processes, relational databases, security and cryptography, enterprise applications, and electronic commerce. Hands-on exposure to Web, database, and graphical user interface (GUI) tools. This course is intended for students with little or no background in computer technology. Students with extensive education or work experience in computer technology should consider taking a more a This class offers a broad coverage of technology concepts and trends underlying current and future developments in information technology, and fundamental principles for the effective use of computer-based information systems. There will be a special emphasis on networks and distributed computing, including the World Wide Web. Other topics include: hardware and operating systems, software development tools and processes, relational databases, security and cryptography, enterprise applications, and electronic commerce. Hands-on exposure to Web, database, and graphical user interface (GUI) tools. This course is intended for students with little or no background in computer technology. Students with extensive education or work experience in computer technology should consider taking a more aSubjects

technology concepts | technology concepts | information technology | information technology | IT | IT | IS | IS | computer-based systems | computer-based systems | networks | networks | distributed computing | distributed computing | WWW | WWW | hardware | hardware | software tools | software tools | relational databases | relational databases | security | security | cryptography | cryptography | enterprise applications | enterprise applicationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.875 Cryptography and Cryptanalysis (MIT) 6.875 Cryptography and Cryptanalysis (MIT)

Description

This course features a rigorous introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements. This course features a rigorous introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements.Subjects

modern cryptography | modern cryptography | fundamental cryptographic primitives | fundamental cryptographic primitives | public-key encryption | public-key encryption | digital signatures | digital signatures | pseudo-random number generation | pseudo-random number generation | basic protocols | basic protocols | computational complexity | computational complexity | two-party protocols | two-party protocols | zero-knowledge | zero-knowledgeLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.897 Selected Topics in Cryptography (MIT) 6.897 Selected Topics in Cryptography (MIT)

Description

This course covers a number of advanced "selected topics" in the field of cryptography. The first part of the course tackles the foundational question of how to define security of cryptographic protocols in a way that is appropriate for modern computer networks, and how to construct protocols that satisfy these security definitions. For this purpose, the framework of "universally composable security" is studied and used. The second part of the course concentrates on the many challenges involved in building secure electronic voting systems, from both theoretical and practical points of view. In the third part, an introduction to cryptographic constructions based on bilinear pairings is given. This course covers a number of advanced "selected topics" in the field of cryptography. The first part of the course tackles the foundational question of how to define security of cryptographic protocols in a way that is appropriate for modern computer networks, and how to construct protocols that satisfy these security definitions. For this purpose, the framework of "universally composable security" is studied and used. The second part of the course concentrates on the many challenges involved in building secure electronic voting systems, from both theoretical and practical points of view. In the third part, an introduction to cryptographic constructions based on bilinear pairings is given.Subjects

cryptography | cryptography | cryptanalysis | cryptanalysis | cryptographic protocols | cryptographic protocols | general security definitions | general security definitions | composition theorems | composition theorems | protocols | protocols | commitments | commitments | key exchange | key exchange | general multi-party computation | general multi-party computation | composable notions of security for PK encryption and signatures | composable notions of security for PK encryption and signatures | theory of extractors | theory of extractors | privacy amplification | privacy amplification | special-purpose factoring devices | special-purpose factoring devices | algorithms | algorithms | concrete security arguments | concrete security arguments | differential cryptanalysis | differential cryptanalysis | public-key infrastructures | public-key infrastructures | electronic voting | electronic votingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.857 Network and Computer Security (MIT) 6.857 Network and Computer Security (MIT)

Description

6.857 Network and Computer Security is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the Computer Systems and Architecture Engineering concentration. 6.857 Network and Computer Security is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the Computer Systems and Architecture Engineering concentration.Subjects

network | network | computer security | computer security | security | security | cryptography | cryptography | secret-key | secret-key | public-key | public-key | digital signature | digital signature | authentication | authentication | Bitcoin | Bitcoin | encryption | encryption | block ciphers | block ciphers | cryptographic hash functions | cryptographic hash functions | one-time pad | one-time pad | stream ciphers | stream ciphers | web browser security | web browser security | biometrics | biometrics | Viruses | Viruses | electronic voting | electronic votingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.045J Automata, Computability, and Complexity (MIT)

Description

This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.Subjects

finite automata | Turing machine | halting problem | computability | computational complexity | polynomial time | P | NP | NP complete | probabilistic algorithms | private-key cryptography | public-key cryptography | randomnessLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.564 Information Technology I (MIT) 15.564 Information Technology I (MIT)

Description

Information Technology I helps students understand technical concepts underlying current and future developments in information technology. There will be a special emphasis on networks and distributed computing. Students will also gain some hands-on exposure to powerful, high-level tools for making computers do amazing things, without the need for conventional programming languages. Since 15.564 is an introductory course, no knowledge of how computers work or are programmed is assumed. Information Technology I helps students understand technical concepts underlying current and future developments in information technology. There will be a special emphasis on networks and distributed computing. Students will also gain some hands-on exposure to powerful, high-level tools for making computers do amazing things, without the need for conventional programming languages. Since 15.564 is an introductory course, no knowledge of how computers work or are programmed is assumed.Subjects

developing-country governments; international | developing-country governments; international | computers; future developments; networks;distributed computing; programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers; future developments; networks;distributed computing; programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers;future developments;networks;distributed computing;programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers;future developments;networks;distributed computing;programming languages;firewall;e-business;computerarchitecture;operating systems;software development;database;user interface;telecommunication;data transmission;localarea network;wireless network;internet;world wide web;digital security | computers | computers | future developments | future developments | networks | networks | distributed computing | distributed computing | programming languages | programming languages | firewall | firewall | e-business | e-business | computer architecture | computer architecture | operating | operating | software development | software development | database | database | user interface | user interface | telecommunication | telecommunication | data transmission | data transmission | local area network | local area network | wireless network | wireless network | internet | internet | world wide web | world wide web | digital security | digital security | architecture | architecture | data | data | transmission | transmission | wireless | wireless | interface | interface | user | user | software | software | development | development | programming | programming | languages | languages | distributed | distributed | computing | computing | LAN | LAN | local | local | area | area | future | future | digital | digital | security | security | technology | technology | information | information | management | management | systems | systems | relational | relational | graphical | graphical | interfaces | interfaces | client/server | client/server | enterprise | enterprise | applications | applications | cryptography | cryptography | services | services | Microsoft | Microsoft | Access | Access | Lotus Notes | Lotus Notes | processing | processing | memory | memory | I/O | I/O | CPU | CPU | OS | OS | hardware | hardware | compression | compression | SQL | SQL | queries | queries | design | design | WAN | WAN | wide | wide | Ethernet | Ethernet | packet-switched | packet-switched | peer-to-peer | peer-to-peer | WWW | WWW | public | public | key | key | mining | mining | warehousing | warehousing | concepts | concepts | conceptual | conceptual | modern computing | modern computing | information management | information management | operating systems | operating systems | relational database systems | relational database systems | graphical user interfaces | graphical user interfaces | client/server systems | client/server systems | enterprise applications | enterprise applications | web.internet services | web.internet services | Microsoft Access | Microsoft Access | database management systems | database management systems | information technology | information technology | telecommunications | telecommunications | eBusiness applications | eBusiness applications | client | client | servers | servers | wireless area network | wireless area networkLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataCoding Techniques Coding Techniques

Description

The objective of this course is to give an overview of different cipher and security techniques as well as their applications to computer networks and telematic services. The student will have to know both symmetric and asymmetric encryption techniques, hash functions, cryptographic checksums, authentication protocols, digital signature, digital certificates and applications of all of them. The objective of this course is to give an overview of different cipher and security techniques as well as their applications to computer networks and telematic services. The student will have to know both symmetric and asymmetric encryption techniques, hash functions, cryptographic checksums, authentication protocols, digital signature, digital certificates and applications of all of them.Subjects

network security | network security | cryptography | cryptography | ía de Telecomunicación | ía de Telecomunicación | security protocols | security protocols | security services | security services | 2010 | 2010 | ía Telemática | ía TelemáticaLicense

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