Recovering Short Generators of Principal Ideals in Cyclotomic Rings

Recovering Short Generators of Principal Ideals in Cyclotomic Rings

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Recovering Short Generator: Proof Plan Folklore strategy Bernstein 2014 Campbell et al. 2014 to recover a short generator

10 of 13

10 of 13

Recovering Short Generator: Proof Plan Folklore strategy Bernstein 2014 Campbell et al. 2014 to recover a short generator

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Classroom Contents

Recovering Short Generators of Principal Ideals in Cyclotomic Rings

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  1. 1 Intro
  2. 2 Principal ideals in cryptography
  3. 3 Short generator recovery
  4. 4 Cost of those two steps
  5. 5 The Problem
  6. 6 The Unit Group and the log-unit lattice
  7. 7 Example: Logarithmic Embedding Log Z[V2]
  8. 8 Reduction modulo 1 - Log Z[V2]
  9. 9 Round-Off Decoding
  10. 10 Recovering Short Generator: Proof Plan Folklore strategy Bernstein 2014 Campbell et al. 2014 to recover a short generator
  11. 11 Geometric statement from Analytic Number Theory
  12. 12 What about the worst case?
  13. 13 Open questions

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