1363.3 Foundations

1. 1363.3 Foundations Mike Scott Hovav Shacham Terence Spies

2. Agenda • Mathematical foundations (Mike Scott) • What fields, curves, and extensions to include • Review of definitions section (section 5) • Pairing primitives (Hovav Shacham) • Algorithm building blocks • Skeleton outline (Terence Spies) • Next Steps

3. Foundations Proposal • Fields • Characteristic p only (no 2 or 3) • Embedding degree • Even only • Curve families • Supersingular (k = 2) • Miyaji-Nakabayashi-Takano • Cocks-Pinch • Barretto-Naehrig • Brezing-Weng

4. Definitions Section • Review of included document

5. Pairing Primitives • Taxonomy of pairing based building blocks • Organization follows Boyen’s schema • Sufficient for implementing: • BF1, BB1, Waters, SK, BB2 IBE/KEM • BLS, Waters, BB2 Signatures • Description is general enough to capture any needed KEM / IBE variant, with CCA strengthening • Extensible to any id-based key agreements and id-based sigs needed

6. 1363 Outline • Top level outline • Sanity check on what’s included and structure • Included techniques • KEM, IBE, signature, signcryption • Computational methods (miller’s algorithm) • In annex A

7. Next Steps • Build a clean list of candidates for each category • Make case for inclusion for each algorithm • Cleanly write out each algorithm in terms of the primitives