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Project: Math 582b
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Math 582: computational number theory

Homework 3 -- due by Wednesday at 9am (that's when I'll grade it)

︠fcaf67de-0ff6-4544-b9f2-d6d494060f6bi︠ %md **Problem 1:** Make several mathematical objects over a finite fields of your choosing and do at least one thing with them: - a univariate polynomial - a matrix - a vector space - a multivariate polynomial - an elliptic curve - an algebraic curve of genus bigger than 1

Problem 1: Make several mathematical objects over a finite fields of your choosing and do at least one thing with them:

  • a univariate polynomial

  • a matrix

  • a vector space

  • a multivariate polynomial

  • an elliptic curve

  • an algebraic curve of genus bigger than 1

︠51e5bf3c-1170-4f9e-ae0c-3a6f0f0a0e5e︠ ︠3245e23c-8b44-4d6c-81f0-455d792c7547︠ ︠fd00381e-10ad-454a-aefb-3bb40d7a131f︠ ︠d8b26975-ea3e-4b5d-8626-cb24fe336e60︠ ︠81f969b4-b3ab-4008-a2ad-004aa6f0aa23︠ ︠b7d0ad95-db24-4d1f-8eb5-af5f7ede042a︠ ︠679c8d56-85fd-4034-bd07-3af1eefd70e3︠ ︠56f2221a-e6a2-4dca-bd56-bae196a60aa2i︠ %md **Problem 2:** Benchmark basic arithmetic in $\FF_p$ for $p$ a prime with the following bit sizes: 4, 8, 16, 32, 64, 128, 512.

Problem 2: Benchmark basic arithmetic in Fp\FF_p for pp a prime with the following bit sizes: 4, 8, 16, 32, 64, 128, 512.

︠ec5618f6-0d55-4685-89d6-69e278247066 ︠5471e54b-406b-4d16-9f8b-b688049c2426︠ ︠b2932bc2-7ef2-4eff-b629-790eb5a14a95︠ ︠4e7023f2-ad00-4d1e-8c16-4a68dc912409︠ ︠41df3af1-5c81-40b2-9fce-a3d0cbb53e32︠ ︠7e5e4644-eeca-4a55-8ac8-1f16de53cbdci︠ %md **Problem 3:** Benchmark basic arithmetic in $\FF_{p^2}$ for $p$ a prime with the following bit sizes: 4, 8, 16, 32, 64, 128, 512.

Problem 3: Benchmark basic arithmetic in Fp2\FF_{p^2} for pp a prime with the following bit sizes: 4, 8, 16, 32, 64, 128, 512.

︠538abfb8-27c3-4336-91dc-2476925320a6︠ ︠ee1e4474-8413-42d7-9b50-1d5482cb6db2︠ ︠706970bc-3997-404d-a300-82d455cf4b81︠ ︠6293159f-22be-4675-b607-5ff1160e2668︠ ︠6a517ed1-19c5-43f6-8b06-a6359f979c5f︠ ︠537fa1a1-325f-4988-a744-34fef7f59ff3︠