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Optimal Parameters for XMSS MT

Optimal Parameters for XMSS MT. Andreas Hülsing , Lea Rausch, and Johannes Buchmann. Digital Signatures are Important!. E-Commerce. … and many others. Software updates. What if….

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Optimal Parameters for XMSS MT

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  1. Optimal Parameters for XMSSMT Andreas Hülsing, Lea Rausch, and Johannes Buchmann 04.09.2013 | TU Darmstadt | Andreas Hülsing| 1

  2. Digital Signatures are Important! E-Commerce … and many others Software updates 04.09.2013 | TU Darmstadt | Andreas Hülsing| 2

  3. What if… IBM 2012: „…optimism about superconducting qubits and the possibilities for a future quantum computer are rapidely growing.“ 04.09.2013 | TU Darmstadt | Andreas Hülsing| 3

  4. Post-Quantum Signatures Based on Lattice, MQ, Coding Signature and/or key sizes Runtimes Secure parameters 04.09.2013 | TU Darmstadt | Andreas Hülsing| 4

  5. Hash-based Signature Schemes[Merkle, Crypto‘89] 04.09.2013 | TU Darmstadt | Andreas Hülsing| 5

  6. Forward Secure Signatures 04.09.2013 | TU Darmstadt | Andreas Hülsing| 6

  7. Forward Secure Signatures pk classical sk pk forward sec sk sk1 sk2 skT ski time tT ti t1 t2 Key gen. 04.09.2013 | TU Darmstadt | Andreas Hülsing| 7

  8. Construction 04.09.2013 | TU Darmstadt | Andreas Hülsing| 8

  9. Hash-based Signatures Parameter h PK SIG = (i, , , , , ) H H OTS OTS OTS OTS OTS OTS OTS OTS H H h H H H H H H H H H H H H SK 04.09.2013 | TU Darmstadt | Andreas Hülsing| 9

  10. Winternitz OTS [Merkle, Crypto‘89; Even et al., JoC‘96] Parameter h 1. = f( ) 2. Trade-off between runtime and signature size, controlled by parameter w 3. Minimal security requirements [Buchmann et al.,Africacrypt’11] 4. Uses PRFF F SIG = (i, , , , , ) H w F 04.09.2013 | TU Darmstadt | Andreas Hülsing| 10

  11. XMSS – secret key Parameter h Generated using forward secure pseudorandom generator (FSPRG), build using PRFF F: Secret key: Random SEED for pseudorandom generation of current signature key. H w F FSPRG PRG PRG PRG PRG PRG FSPRG FSPRG FSPRG FSPRG 04.09.2013 | TU Darmstadt | Andreas Hülsing| 11

  12. BDS-TreeTraversal[Buchmann et al., 2008] Parameter h • Computes authentication paths • Left nodes are cheap • Store most expensive nodes • Distribute costs • (h-k)/2 updates per round H w F k # 2h-1 k # 2h-2 h 04.09.2013 | TU Darmstadt | Andreas Hülsing| 12

  13. Accelerate key generationTree Chaining [Buchmann et al., 2006] Parameter h H wi w F j k ki d hi i Generalized distributed signature generation from [Huelsing et al., SAC’12] 04.09.2013 | TU Darmstadt | Andreas Hülsing| 13

  14. Parameter Selection 04.09.2013 | TU Darmstadt | Andreas Hülsing| 14

  15. Trade-Offs 04.09.2013 | TU Darmstadt | Andreas Hülsing| 15

  16. Linear Optimization Input: h, bmin, TF, TH Output: b, d, (h,w,k)i Obj. Minimizeweightedsumofruntimes & sizes • Linearization: Generalizedlambdamethod [Moritz, 2007] • Complexityreduction: Split into sub-problems 04.09.2013 | TU Darmstadt | Andreas Hülsing| 16

  17. Conclusion 04.09.2013 | TU Darmstadt | Andreas Hülsing| 17

  18. 04.09.2013 | TU Darmstadt | Andreas Hülsing| 18

  19. Thank you!

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