# Theory

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**From Computation to SNARKs: A Step-by-Step Journey**

In this tutorial, we aim to provide a comprehensive understanding of Zero-Knowledge Proofs (ZKPs), especially focusing on SNARKs. The journey from basic computation to the implementation of SNARKs can be viewed as a series of transformations, each building upon the last to achieve our final objective.

1. **Computation:** Here, we begin with basic algorithms and the problems they solve.
2. **Algebraic Circuit:** We transition from computation to an algebraic representation, which is more suitable for cryptographic contexts.
3. **R1CS (Rank-1 Constraint System):** At this juncture, we convert our computations into a system of constraints. This format is pivotal for the next stages.
4. **QAP (Quadratic Arithmetic Programs):** We further refine our representation into QAPs, setting the stage for cryptographic applications.
5. **LIP (Linear Interactive Proof):** Introducing cryptographic elements, LIPs allow for verification of statements without revealing the specifics.
6. **SNARK (Succinct Non-Interactive Argument of Knowledge):** The final stage, where we achieve a concise proof system that ensures privacy and does not require interaction.

Throughout this tutorial, we will delve into each stage, providing technical insights and clear explanations. Our goal is to elucidate the transition from pure computation to the advanced realm of SNARKs.

<figure><img src="https://2435636835-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F5BID0P7sbZpVTEKkwMbp%2Fuploads%2FfIgRG9oQEipWqtFkcGh7%2FOverveiw.png?alt=media&#x26;token=8476f866-1b93-46f4-a320-ffc128b98c1d" alt=""><figcaption><p>Credit: <a href="https://docs.google.com/presentation/d/17QQm8zYoYYc3r6sRajBgE9hkKIvmr_ECJQDm9fB4YBA/edit#slide=id.g251e15f475e_0_189">YAcedmy</a></p></figcaption></figure>


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