Lectures:
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Topic 00: Course Policy and Outline (Week 01)
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Topic 01: Mathematical Basics (Probability) (Week 01)
A recommended reference:
Section 5.3 of An Introduction to Mathematical Cryptography, Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman
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Homework 1 [Source Files: file1 file2] (Due Date: 07 September, 2025)
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Topic 02: One-time Pad for Bit-strings (Week 01)
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Topic 03: Groups and Fields (Week 02)
A recommended reference:
Sections 2.5 and 1.5 of An Introduction to Mathematical Cryptography, Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman
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Homework 2 [Source Files: file1 file2] (Due Date: 21 September, 2025)
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Topic 05: Repeated Squaring (Week 03)
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Topic 06a: Private-key Encryption (Definition and Security of One-time Pad) (Week 03)
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Topic 06b: Graph Representation (Week 03)
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Topic 07: Shamir Secret-sharing Scheme (Introduction) (Week 04)
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Topic 08: Shamir Secret-sharing Scheme (Lagrange Interpolation) (Week 04)
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Homework 3 [Source Files: file1 file2] (Due Date: 05 October, 2025)
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Topic 10: Shamir Secret-sharing Scheme (Security) (Week 05)
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Topic 11: Efficient Algorithms (Week 06)
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Topic 12: Generating Large Primes (Week 06)
A recommended reference:
Sections 3.4 of An Introduction to Mathematical Cryptography, Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman
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Topic 13: Extended GCD Algorithm (Week 07)
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Topic 14: One-way Functions (Week 07)
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Homework 4 [Source Files: file1 file2] (Due Date: 26 October, 2025)
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Fall Break (Week 08)
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Topic 15: Pseudo-random Generators (Week 08)
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Topic 16: Encrypting Long Messages (Week 09)
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Topic 17: Random Functions and Encrypting Long Messages (Week 09)
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Topic 18: Pseudorandom Functions (Week 10)
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Homework 5 [Source Files: file1 file2] (Due Date: 08 November, 2025)
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Topic 19: Message Authentication Codes (Week 10)
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Topic 20: Message Authentication Codes from PRF (Week 11)
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Topic 21: Collision-Resistant Hash Function (Week 11)
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Topic 22: RSA Assumption (Week 12)
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Homework 6 [Source Files: file1 file2] (Due Date: 23 November, 2025)
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Topic 23: RSA Encryption (Week 12)
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Topic 24a: Digital Signatures using RSA Assumption (Week 13)
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Topic 24b: Digital Signatures for Arbitrary-length Messages (Week 13)
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Topic 25: DDH Assumption, Key Agreement, and ElGamal Encryption (Week 13)
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Research Topics: Secret-sharing Schemes and Side Channel Attacks (Week 14)
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Thanksgiving break
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Research Topics: Secure Computation: GMW and Yao's protocols (Week 15)
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Research Topics: Lattices, Learning with Errors, and Post-Quantum Cryptography (Week 15) file
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Research Topics: Zero-knowledge Proofs (Week 16)
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Research Topics: Blockchain and Crypto-currencies (Week 16)
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