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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Topic 02: One-time Pad for Bit-strings (Week 01)
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Homework 1 [Source Files: file1 file2] (Due Date: 26 January, 2025)
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Topic 03: Groups and Fields (Week 02)
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Additional material on basics of elliptic curves
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Homework 2 [Source Files: file1 file2] (Due Date: 09 February, 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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Topic 09: Shamir Secret-sharing Scheme (Security) (Week 05)
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Homework 3 [Source Files: file1 file2] (Due Date: 23 February, 2025)
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Topic 10: Shamir Secret-sharing Scheme (Concluding Remarks) (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:
Section 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: 11 March, 2025)
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Topic 15: Pseudo-random Generators (Week 08)
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Topic 16: Encrypting Long Messages (Week 08)
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Topic 17: Random Functions and Encrypting Long Messages (Week 09)
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Midterm
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Spring Break (Week 10)
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Topic 18: Pseudorandom Functions (Week 11)
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Homework 5 [Source Files: file1 file2] (Due Date: 06 April, 2025)
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Topic 19: Message Authentication Codes (Week 11)
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Topic 20: Message Authentication Codes from PRF (Week 12)
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Topic 21: Collision-Resistant Hash Function (Week 12)
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Topic 22: RSA Assumption (Week 13)
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Topic 23: RSA Encryption (Week 13)
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Homework 6 [Source Files: file1 file2] (Due Date: 27 April, 2025)
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Topic 24a: Digital Signatures using RSA Assumption (Week 14)
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Topic 24b: Digital Signatures for Arbitrary-length Messages (Week 14)
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Topic 25: DDH Assumption, Key Agreement, and ElGamal Encryption (Week 14)
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