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 Boyens 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 whats included and structure
• Included techniques
• KEM, IBE, signature, signcryption
• Computational methods (millers 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