Classical and Quantum Algorithms for Isogeny Problems

Classical and Quantum Algorithms for Isogeny Problems

Institute for Pure & Applied Mathematics (IPAM) via YouTube Direct link

Intro

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1 of 18

Intro

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Classical and Quantum Algorithms for Isogeny Problems

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  1. 1 Intro
  2. 2 POST-QUANTUM
  3. 3 ELLIPTIC CURVES AND
  4. 4 TRADITIONAL ELLIPTIC CURVE CRYPTOGRAPHY VERSUS ISOGENIES
  5. 5 WHY SUPERSINGULAR ISOGENY CRYPTO?
  6. 6 HARDNESS ASSUMPTIONS IN PUBLIC-KEY CRYPTOGRAPHY
  7. 7 ISOGENY-BASED SYSTEMS
  8. 8 STATUS OF SECURITY OF ISOGENY-BASED CRYPTO
  9. 9 COMPUTATIONAL CHALLENGES
  10. 10 PATH FINDING IN ISOGENY GRAPHS
  11. 11 COMPUTING WITH ISOGENIES
  12. 12 REDUCTIONS TO OTHER PROBLEMS
  13. 13 COMMUTATIVE ISOGENY SCHEMES
  14. 14 REDUCTIONS-COMMUTATIVE CASE
  15. 15 COMMUTATIVE VERSUS NON- COMMUTATIVE ISOGENY CRYPTO
  16. 16 REDUCTIONS TO ENDOMORPHISM RING PROBLEM
  17. 17 CONCLUSION
  18. 18 SUMMARY

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