Arithmetic Cryptography
summary
Explains arithmetic cryptography, focusing on cryptographic constructions that use arithmetic operations and number-theoretic structures. Covers specific technologies and approaches such as homomorphic encryption, secure multiparty computation, and tools from lattice-based and number-theoretic cryptography that enable computation on encrypted or distributed data.
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chapters (21)
- 0:00Intro
- 0:48Motivating Example
- 9:08Arithmetic Cryptography
- 18:21Previous Works
- 23:34Our Results
- 30:56Private Simultaneous Messages [FKN]
- 33:03Lower Bound for Affine Functions
- 37:36Key Observation
- 39:26Coping with Is-Zero gates
- 41:25Extension I: Shortening Bob's Input
- 42:48Extension II: Multiple Players
- 43:18Multiplicative Homomorphic Encryption
- 45:10Observations Given a challenge ce Enc(O), Enc(1) define
- 47:05Abstraction: Arithmetic Predictability
- 48:51Efficient Algorithm for Polynomials over large Fields inspired by [DGW]
- 52:16The General Case
- 53:33Positive Results: Three Approaches
- 57:02Conclusion
- 57:27Future Works: Negative
- 58:16Future Works: Positive
- 59:13Future Works: RLC vs LWE
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