RareSkills

ZK-SNARKs from First Principles

Master zero-knowledge proofs from the ground up

Chunk 1

Basic Set Theory

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Chunk 2

Introduction to Zero Knowledge Proofs

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Chunk 3

Boolean Expressions and Indicator Functions for Zero Knowledge Proofs

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Chunk 4

Böhm-Jacopini Theorem and Its Implication for Zero Knowledge Proofs

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Chunk 5

Congruence and Addition in Modular Arithmetic

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Chunk 6

Additive Inverses in Modular Arithmetic

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Chunk 7

Multiplicative Inverses and Fractions in Modular Arithmetic

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Chunk 8

Fractions and Solving Linear Equations in Modular Arithmetic

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Chunk 9

Matrices and Vectors in Modular Arithmetic

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Chunk 10

Modular Exponents and the Discrete Logarithm

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Chunk 11

Diffie-Hellman Algorithm

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Chunk 12

Precursors to Group Theory

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Chunk 13

Group Theory Introduction

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Chunk 14

Introduction to Finite Fields

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Chunk 15

Cyclic Groups

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Chunk 16

Lines Through Elliptic Curves

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Chunk 17

Points on an Elliptic Curve as a Magma

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Chunk 18

Points on an Elliptic Curve as an Abelian Group

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Chunk 19

Homomorphisms

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Chunk 20

Exponent Properties of Homomorphisms

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Chunk 21

More Properties of Homomorphisms

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Chunk 22

Homomorphic Encryption

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Chunk 23

Quadratic Residues

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Chunk 24

Polynomial Arithmetic in Finite Fields

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Chunk 25

Polynomial Roots and Degree in a Finite Field

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Chunk 26

Introduction to Subgroups

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Chunk 27

Elliptic Curve Point Algebra

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Chunk 28

Elliptic Curves in Finite Fields

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Chunk 29

Subgroups and Homomorphisms in Elliptic Curves

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Chunk 30

BN128 Elliptic Curve in Python

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Chunk 31

Introduction to Bilinear Pairings

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Chunk 32

Lagrange Interpolation

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Chunk 33

A Homomorphism from Vectors Under Addition to Polynomial Under Addition

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Chunk 34

Schwartz-Zippel Lemma and Polynomial Equality Testing

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Chunk 35

Multiparty Computation for Vector Equality Tests

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Chunk 36

Rank 1 Constraint Systems

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Chunk 37

Span Proofs

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Chunk 38

Span Proofs and Consistent Coefficient Checks

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Chunk 39

Polynomial Division in Fq

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Chunk 40

Powers of Tau and Proof of Polynomial Divisibility

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Chunk 41

Succinct Proofs That a Polynomial Vanishes

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Chunk 42

Quadratic Arithmetic Programs

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Chunk 43

Converting R1CS to QAP

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Chunk 44

Succinct Interactive Proof of Knowledge of a Satisfying Witness for an R1CS

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Chunk 45

Trusted Setups

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Chunk 46

Pinocchio Protocol

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Chunk 47

A Smaller QAP Verification Check

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Chunk 48

Removing H From the QAP Verification

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Chunk 49

Public Inputs and the Smaller QAP Check

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Chunk 50

Groth16

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Chunk 1

Basic Set Theory

Learn →

Chunk 2

Introduction to Zero Knowledge Proofs

Complete the previous chunk to unlock

Chunk 3

Boolean Expressions and Indicator Functions for Zero Knowledge Proofs

Complete the previous chunk to unlock

Chunk 4

Böhm-Jacopini Theorem and Its Implication for Zero Knowledge Proofs

Complete the previous chunk to unlock

Chunk 5

Congruence and Addition in Modular Arithmetic

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Chunk 6

Additive Inverses in Modular Arithmetic

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Chunk 7

Multiplicative Inverses and Fractions in Modular Arithmetic

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Chunk 8

Fractions and Solving Linear Equations in Modular Arithmetic

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Chunk 9

Matrices and Vectors in Modular Arithmetic

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Chunk 10

Modular Exponents and the Discrete Logarithm

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Chunk 11

Diffie-Hellman Algorithm

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Chunk 12

Precursors to Group Theory

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Chunk 13

Group Theory Introduction

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Chunk 14

Introduction to Finite Fields

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Chunk 15

Cyclic Groups

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Chunk 16

Lines Through Elliptic Curves

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Chunk 17

Points on an Elliptic Curve as a Magma

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Chunk 18

Points on an Elliptic Curve as an Abelian Group

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Chunk 19

Homomorphisms

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Chunk 20

Exponent Properties of Homomorphisms

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Chunk 21

More Properties of Homomorphisms

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Chunk 22

Homomorphic Encryption

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Chunk 23

Quadratic Residues

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Chunk 24

Polynomial Arithmetic in Finite Fields

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Chunk 25

Polynomial Roots and Degree in a Finite Field

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Chunk 26

Introduction to Subgroups

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Chunk 27

Elliptic Curve Point Algebra

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Chunk 28

Elliptic Curves in Finite Fields

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Chunk 29

Subgroups and Homomorphisms in Elliptic Curves

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Chunk 30

BN128 Elliptic Curve in Python

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Chunk 31

Introduction to Bilinear Pairings

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Chunk 32

Lagrange Interpolation

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Chunk 33

A Homomorphism from Vectors Under Addition to Polynomial Under Addition

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Chunk 34

Schwartz-Zippel Lemma and Polynomial Equality Testing

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Chunk 35

Multiparty Computation for Vector Equality Tests

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Chunk 36

Rank 1 Constraint Systems

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Chunk 37

Span Proofs

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Chunk 38

Span Proofs and Consistent Coefficient Checks

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Chunk 39

Polynomial Division in Fq

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Chunk 40

Powers of Tau and Proof of Polynomial Divisibility

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Chunk 41

Succinct Proofs That a Polynomial Vanishes

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Chunk 42

Quadratic Arithmetic Programs

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Chunk 43

Converting R1CS to QAP

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Chunk 44

Succinct Interactive Proof of Knowledge of a Satisfying Witness for an R1CS

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Chunk 45

Trusted Setups

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Chunk 46

Pinocchio Protocol

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Chunk 47

A Smaller QAP Verification Check

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Chunk 48

Removing H From the QAP Verification

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Chunk 49

Public Inputs and the Smaller QAP Check

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Chunk 50

Groth16

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