How to Use Lattice Trapdoors: IBE, ABE and More
summary
Shows how to get IBE/ABE from lattice trapdoors by combining Regev encryption with explicit trapdoor sampling: sample fat matrix A with trapdoor and extend it to identity-specific matrices, compress identities using set A1 = A0 R − ID·G so the trapdoor vanishes for the challenge ID, and embed LWE samples to simulate selective security. Ciphertexts encode inputs as encode x as (A_i + x_i G)^T s + e, support linear and multiplicative evaluation to build circuit-based ABE, but noise grows exponentially with depth.
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chapters (10)
- 0:00Intro
- 0:20Broad structure IBE
- 2:32Identity Based Encryption (CHKP10)
- 10:15IBE Security
- 15:41Security Model: Key Points
- 21:07Efficient Identity Based Encryption [ABB10]
- 34:36Generalizing to Inner Product (AFV11)
- 45:08Recall Ciphertext Structure
- 47:51Handling Multiplication BGG+14
- 57:46Security Definition
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