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Exploring Quantum Cryptography: Unveiling Secure Transmissions

Delve into the fascinating realm of Quantum Mechanics and its implications for cryptography, including Peter Shor's algorithm for factoring large numbers. Learn how quantum computers revolutionize encryption methods. Discover the intricacies of qubits, bases selection, and quantum Fourier transforms for enhanced security. Explore the potential of quantum cryptography in real-world applications and the race against classical algorithms. References to key works by experts like Michael A. Nielsen and P. W. Shor offer valuable insights into this cutting-edge technology.

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Exploring Quantum Cryptography: Unveiling Secure Transmissions

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  1. Quantum Cryptography Shawn Fanning 4/25/03

  2. Introduction • The study of Quantum Mechanics has opened up new areas of research in cryptographic transmissions, as well as new ideas for classical problems like factoring large numbers.

  3. Topics of Discussion • Quantum Mechanics • Quantum Cryptography (an application) • Peter Shor’s factoring algorithm

  4. 2 minute intro to Quantum Mechanics • Polarized light experiment • Bit vs. Qubit • Picture a Qubit as a sphere • Measurement becomes a problem

  5. Quantum Cryptography (an application) • [2] Page 357 (our book) • 2 Channels • Quantum (Fiber optic) • Physical (Normal Wire Comm.) • 2 Bases: B1 and B2 • Alice and Bob each randomly choose Bases • A and B will agree on roughly half of the bits that she sent • Eve ‘forces’ states in action

  6. Factoring on a Quantum Computer • Peter Shor • Church’s Thesis • 2 escape clauses • 1)Physical • 2)Resources • A 3rd resource: precision • IE) 011101101… • Latitude: • 01 deg, 11 min, 01.101 sec

  7. Factoring on a Quantum Computer • L bit number N • Best Classical algorithm (number field sieve) • Quantum Computer [3]

  8. Factoring on a Quantum Computer • 300 digit number [1]: • Best Classical algorithm • (150,000 years at terahertz) • Quantum Computer • (less than a second at terahertz)

  9. Factoring on a Quantum Computer • Recall to factor n: • we want a and r with-- • Quantum Fourier transform • Find the period of a sequence • Repeated squaring until

  10. Real Life • Quantum Cryptography is possible • This has been done (34km) • Quantum Computers/Factoring (??) • Heuristics for skillful play at chess in relation to the game’s basic rules.

  11. References • [1] “Simple Rules for a Complex Quantum World”, Michael A. Nielsoen, Scientific American, May 31,2003 • [2] Introduction to Cryptography, W. Trappe and L.C. Washington, Prentice Hall, 2002 • [3] P. W. Shor, Quantum Computing, IEEE Computer Society Press (1998) • [4] P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Computing 26 (1997) • (The above two papers, as well as much more material by Shor can be found at: www.research.att.com/~shor)

  12. Questions • Comments/Suggestions

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