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https://github.com/lambdaclass/sparkling_water_bootcamp

Public repository for excersices, challenges and all the needs of the Sparkling Water Bootcamp
https://github.com/lambdaclass/sparkling_water_bootcamp

Last synced: 8 months ago
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Public repository for excersices, challenges and all the needs of the Sparkling Water Bootcamp

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# Lambda's Sparkling Water Bootcamp - Repo for challenges and learning path



Public repository for exercises, challenges and all the needs of the Sparkling Water Bootcamp.



## Week 1 - Forging your tools: Finite Fields



This first week will be focused on the development of one of the building blocks of Cryptography: Finite Fields. 



### Recommended material:



- [An introduction to mathematical cryptography](https://books.google.com.ar/books/about/An_Introduction_to_Mathematical_Cryptogr.html?id=BHuTQgAACAAJ&source=kp_book_description&redir_esc=y) - Chapter 1.

- [Finite Fields](https://www.youtube.com/watch?v=MAhmV_omOwA&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=8)

- [Constructing finite fields](https://www.youtube.com/watch?v=JPiXFn9WA5Y&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=6)

- [Cyclic groups](https://www.youtube.com/watch?v=UIhhs38IAGM&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=3)

- [Summary on Montgomery arithmetic](https://eprint.iacr.org/2017/1057.pdf)

- [Mersenne primes](https://eprint.iacr.org/2023/824.pdf)



### Challenges:



- [Implement Montgomery backend for 32 bit fields](https://github.com/lambdaclass/lambdaworks/issues/538).

- [Implement efficient Mersenne prime backend](https://github.com/lambdaclass/lambdaworks/issues/540).

- [Implement efficient backend for pseudo-Mersenne primes](https://github.com/lambdaclass/lambdaworks/issues/393).

- Compare specific field implementations with ordinary Montgomery arithmetic.



### Cryptography content:



- [Serious Cryptography](https://books.google.com.ar/books/about/Serious_Cryptography.html?id=1D-QEAAAQBAJ&source=kp_book_description&redir_esc=y), Chapters 9 & 10.



### Exercises

- Implement naïve version of RSA.

- $7$ is a generator of the multiplicative group of $Z_p^\star$, where $p = 2^{64} - 2^{32} +1$. Find the generators for the $2^{32}$ roots of unity. Find generators for subgroups of order $2^{16} + 1$ and $257$.

- Define in your own words what is a group, a subgroup, a ring and a field.

- What are the applications of the Chinese Remainder Theorem in Cryptography?

- Find all the subgroups of the multiplicative group of $Z_{29}^\star$



## Supplementary Material

- [Polynomial Secret Sharing](https://decentralizedthoughts.github.io/2020-07-17-polynomial-secret-sharing-and-the-lagrange-basis/)

- [Polynomials over a Field](https://decentralizedthoughts.github.io/2020-07-17-the-marvels-of-polynomials-over-a-field/)

- [Fourier Transform](https://www.youtube.com/watch?v=spUNpyF58BY)

- [Fast Fourier Transform](https://www.youtube.com/watch?v=h7apO7q16V0)



## Week 2 - Enter Elliptic Curves



During the second week we'll continue with Finite Fields and begin with Elliptic Curves and dive deeper into Rust



### Recommended material



- [Moonmath Manual](https://leastauthority.com/community-matters/moonmath-manual/) - Chapter 5, until 5.3

- [Programming Bitcoin](https://books.google.fr/books/about/Programming_Bitcoin.html?id=O2aHDwAAQBAJ&source=kp_book_description&redir_esc=y) - Chapters 2 & 3.

- [Introduction to Mathematical Cryptography](https://books.google.com.ar/books/about/An_Introduction_to_Mathematical_Cryptogr.html?id=BHuTQgAACAAJ&source=kp_book_description&redir_esc=y) - Chapter 5 until 5.5

- [Serious Cryptography](https://books.google.com.ar/books/about/Serious_Cryptography.html?id=1D-QEAAAQBAJ&source=kp_book_description&redir_esc=y) - Chapters 11 & 12.

- [Pairings for Beginners](https://static1.squarespace.com/static/5fdbb09f31d71c1227082339/t/5ff394720493bd28278889c6/1609798774687/PairingsForBeginners.pdf) - Chapters 1 & 2



### Exercises



- Define an elliptic curve element type.

- Implement the basic operations: addition and doubling.

- Implement scalar multiplication.

- Check that the point belongs to the correct subgroup.

- The BLS12-381 elliptic curve is given by the equation $y^2 = x^3 + 4$ and defined over $\mathbb{F}_p$ with p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab. The group generator is given by the point p1 = (0x04, 0x0a989badd40d6212b33cffc3f3763e9bc760f988c9926b26da9dd85e928483446346b8ed00e1de5d5ea93e354abe706c) and the cofactor is $h_1 = 0x396c8c005555e1568c00aaab0000aaab$. Find the generator $g$ of the subgroup of order 

r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001.

- Implement a naïve version of the Diffie - Hellman protocol

- Implement point compression and decompression to store elliptic curve points



### Challenges



- Special CTF challenge (will be revealed later)

- [Implement BN254](https://github.com/lambdaclass/lambdaworks/issues/548)

- Implement Secp256k1

- Implement Ed25519



### Rust Workshop



- [Aguante Rust](https://youtu.be/nYpMbjzb1t8?si=HNanyXYWcu1xDjG5)



## Week 3: Polynomials



### Recommended material



- [Polynomials](https://www.youtube.com/watch?v=HiaJa3yhHTU&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=6)

- [Lagrange interpolation](https://www.youtube.com/watch?v=REnFOKo9gXs&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=10)

- [Lagrange interpolation and secret sharing](https://www.youtube.com/watch?v=3g4wZnhl4m8&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=3)

- [Moonmath](https://leastauthority.com/community-matters/moonmath-manual/) - Chapter 3.4

- [Convolution polynomial rings - Introduction to Mathematical Cryptography](https://books.google.com.ar/books/about/An_Introduction_to_Mathematical_Cryptogr.html?id=BHuTQgAACAAJ&source=kp_book_description&redir_esc=y) - Chapter 6.9



### Supplementary



- [Roots of unity and polynomials](https://www.youtube.com/watch?v=3KK5RuAgOpA&list=PLFX2cij7c2PynTNWDBzmzaD6ij170ILbQ&index=2)

- [Fast Fourier Transform](https://www.youtube.com/watch?v=toj_IoCQE-4)

- [FFT walkthrough](https://www.youtube.com/watch?v=Ty0JcR6Dvis)



### Exercises



- Define a polynomial type.

- Implement basic operations, such as addition, multiplication and evaluation.

- Implement Lagrange polynomial interpolation.

- Implement basic version of Shamir's secret sharing.



### Issue



- [Implement Stockham FFT](http://wwwa.pikara.ne.jp/okojisan/otfft-en/stockham1.html)



## Week 4: STARKs



### Recommended material



- [STARKs by Sparkling Water Bootcamp](https://www.youtube.com/watch?v=cDzTm3clrEo)

- [Lambdaworks Docs](https://github.com/lambdaclass/lambdaworks/tree/main/docs/src/starks)

- [Stark 101](https://github.com/starkware-industries/stark101)

- [Constraints](https://blog.lambdaclass.com/periodic-constraints-and-recursion-in-zk-starks/)

- [Stark 101 - rs](https://github.com/lambdaclass/stark101-rs/)

- [Anatomy of a STARK](https://aszepieniec.github.io/stark-anatomy/)

- [BrainSTARK](https://aszepieniec.github.io/stark-brainfuck/)

- [A summary on FRI low degree testing](https://eprint.iacr.org/2022/1216)

- [STARKs by Risc0](https://dev.risczero.com/reference-docs/about-starks)



### Exercises



- Complete STARK-101



## Week 5: Symmetric encryption



### Recommended material



- [One time pad - Dan Boneh](https://www.youtube.com/watch?v=pQkyFJp2eUg&list=PL58C6Q25sEEHXvACYxiav_lC2DqSlC7Og&index=6)

- [Stream ciphers and pseudorandom generators - Dan Boneh](https://www.youtube.com/watch?v=ZSjTMSvp-eI&list=PL58C6Q25sEEHXvACYxiav_lC2DqSlC7Og&index=7)

- [Attacks - Dan Boneh](https://www.youtube.com/watch?v=Qm8fycVt5v8&list=PL58C6Q25sEEHXvACYxiav_lC2DqSlC7Og&index=8)

- [Semantic security - Dan Boneh](https://www.youtube.com/watch?v=6LFyXO58F4A&list=PL58C6Q25sEEHXvACYxiav_lC2DqSlC7Og&index=11)

- [Block ciphers - Dan Boneh](https://www.youtube.com/watch?v=dzoqxqfpZB4&list=PL58C6Q25sEEHXvACYxiav_lC2DqSlC7Og&index=35)

- [Serious Cryptography](https://books.google.com.ar/books/about/Serious_Cryptography.html?id=1D-QEAAAQBAJ&source=kp_book_description&redir_esc=y) - Chapters 3 - 5.



### Supplementary material



- [AES - NIST](https://nvlpubs.nist.gov/nistpubs/fips/nist.fips.197.pdf)



### Exercises



- Implement AES round function



### Side project - Multilinear polynomials



- [Proofs, Args and ZK](https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf)



### Mandatory task



- Choose a project: STARKs, Sumcheck protocol or Groth16 (or propose a new project)



### Additional resources for each project



- STARKs: see week 4.

- [Groth16](https://eprint.iacr.org/2016/260.pdf)

- [DIZK - Groth 16](https://eprint.iacr.org/2018/691.pdf)

- [Multilinear polynomials and sumcheck protocol](https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf)



#### Challenges



- Implement a multilinear polynomial type with all the basic operations.



## Week 6: Interactive proofs and SNARKs



- [Moonmath](https://leastauthority.com/community-matters/moonmath-manual/) Chapters 6 - 8.

- [Proofs, Arguments and Zero Knowledge](https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf) Chapters 1 - 5.

- [Overview of modern SNARK constructions](https://www.youtube.com/watch?v=bGEXYpt3sj0)

- [Pinocchio protocol overview](https://www.zeroknowledgeblog.com/index.php/zk-snarks)

- [Pinocchio implementation](https://github.com/lambdaclass/pinocchio_lambda_vm)

- [SNARKs and STARKs](https://zkhack.dev/whiteboard/module-four/)



### Additional material on some proof systems



- [EthSTARK](https://github.com/starkware-libs/ethSTARK/tree/master)

- [EthSTARK - paper](https://eprint.iacr.org/2021/582)

- [STARK paper](https://eprint.iacr.org/2018/046.pdf)

- [DEEP FRI](https://eprint.iacr.org/2019/336)

- [Proximity gaps](https://eprint.iacr.org/2020/654)

- [STARKs by Eli Ben-Sasson I](https://www.youtube.com/watch?v=9VuZvdxFZQo)

- [STARKs by Eli Ben-Sasson II](https://www.youtube.com/watch?v=L7tZeO8ihcQ)



## Week 7: Plonk



- [Plonk](https://eprint.iacr.org/2019/953)

- [Custom gates](https://zkhack.dev/whiteboard/module-five/)

- [Plonk by hand](https://research.metastate.dev/plonk-by-hand-part-1/)

- [Plonk docs in Lambdaworks](https://github.com/lambdaclass/lambdaworks/tree/main/docs/src/plonk)



## Week 8: Lookup arguments



- [Plookup](https://eprint.iacr.org/2020/315.pdf)

- [LogUp and GKR](https://eprint.iacr.org/2023/1284.pdf)

- [Neptune - Permutation Argument](https://neptune.cash/learn/tvm-cross-table-args/)

- [Randomized AIR with preprocessing](https://hackmd.io/@aztec-network/plonk-arithmetiization-air)

- [PlonkUp](https://eprint.iacr.org/2022/086.pdf)

- [Lookups by Ingonyama](https://medium.com/@ingonyama/a-brief-history-of-lookup-arguments-a4eeeeca2749)

- [LogUp](https://eprint.iacr.org/2022/1530.pdf)

- [Lookups - Halo2](https://zcash.github.io/halo2/design/proving-system/lookup.html)



## Week 9: Signatures



- [BLS signatures](https://www.ietf.org/archive/id/draft-irtf-cfrg-bls-signature-05.html#name-introduction-2)

- [Real World Cryptography](https://books.google.com.ar/books/about/Real_World_Cryptography.html?id=Qd5CEAAAQBAJ&source=kp_book_description&redir_esc=y) Chapter 7

- [ECDSA](https://www.rfc-editor.org/rfc/rfc6605.txt)

- [RSA Signature](https://www.ietf.org/rfc/rfc8017.html#section-5.2)



## Week 10: Folding schemes



- [Nova by Justin Drake](https://zkhack.dev/whiteboard/module-fourteen/)

- [Nova](https://eprint.iacr.org/2021/370)

- [SuperNova](https://eprint.iacr.org/2022/1758)

- [ProtoStar](https://eprint.iacr.org/2023/620)

- [ProtoGalaxy](https://eprint.iacr.org/2023/1106)



## Projects



- Implement IPA commitment scheme

- Implement Jacobian coordinates for Elliptic Curves

- Benchmark elliptic curve operations

- Add improvements to fixed base scalar multiplication in Elliptic Curves

- Add BN254 elliptic curve

- Implement Pasta curves

- Implement Lookup arguments for Plonk (Plookup)

- Sumcheck protocol

- Benchmark and optimize multilinear polynomial operations

- Import circuits from gnark or circom to use with Groth16 backend



### Links to repos with solutions to the exercises

- [Naïve ECC](https://github.com/saitunc/naive_ecc)

- [Crypto](https://github.com/irfanbozkurt/crypto)

- [Naïve RSA](https://github.com/WiseMrMusa/rsa-naive)

- [Naïve RSA](https://github.com/Elvis339/naive_rsa)

- [Exercises from weeks 1 & 2](https://github.com/ArpitxGit/sparkling_water_bootcamp/tree/main)

- [Programming bitcoin EC](https://github.com/Elvis339/rbtc)

- [Shamir secret sharing](https://github.com/cliraa/shamir_secret_sharing)

- [Several exercises](https://github.com/ArpitxGit/sparkling_water_bootcamp/tree/main)



### Intended Roadmap



- Finite Fields

- Elliptic Curves

- Polynomials

- Extension fields

- Pairings

- Public key encryption

- Symmetric encryption

- Hash functions

- Signatures

- Authenticated encryption

- SNARKs

- STARKs