We present attribute-based encryption (ABE) schemes for Boolean formulas that are adaptively secure under simple assumptions. Notably, our KP-ABE scheme enjoys a ciphertext size that is linear in the attribute vector length and independent of the formula size (even when attributes can be used multiple times), and we achieve an analogous result for CP-ABE. This resolves the central open problem in attribute-based encryption posed by Lewko and Waters. Along the way, we develop a theory of modular design for unbounded ABE schemes and answer an open question regarding the adaptive security of Yao’s Secret Sharing scheme for NC1 circuits.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-212y-yy33 |
| Date | January 2019 |
| Creators | Kowalczyk, Lucas |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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