🔐 Zero-Knowledge Proofs Kariyer Roadmap'i

1. Matematik Temelleri

Temel Cebir

• Gruplar, halkalar, cisimler (fields)
• Sonlu cisimler (finite fields / Galois fields)
• Modüler aritmetik
• Polinomlar ve polinom aritmetiği
• Lagrange interpolation

Soyut Cebir (İleri)

• Grup homomorfizmaları
• Cyclic groups ve generators
• Quotient groups
• Field extensions
• Algebraic number theory temelleri

Eliptik Eğri Matematiği

• Eliptik eğri denklemi ve grup yapısı
• Point addition ve scalar multiplication
• Pairing-based cryptography (Weil, Tate, Ate pairings)
• BLS12-381, BN254 eğrileri
• Twist curves

Polinom Matematiği

• Polynomial commitment schemes
• Schwartz-Zippel lemma
• Reed-Solomon codes
• Fast Fourier Transform (FFT) ve Number Theoretic Transform (NTT)
• Polynomial division ve evaluation

Olasılık ve Bilgi Teorisi

• Computational vs statistical indistinguishability
• Negligible functions
• Entropy ve randomness
• Interactive proof systems

2. Kriptografi Temelleri

Temel Kriptografik Primitifler

• Hash fonksiyonları ve özellikleri (collision resistance, preimage resistance)
• Commitment schemes (Pedersen, hash-based)
• Digital signatures
• Merkle trees

Hardness Assumptions

• Discrete Logarithm Problem (DLP)
• Computational Diffie-Hellman (CDH)
• Decisional Diffie-Hellman (DDH)
• RSA assumption
• Knowledge of Exponent Assumption (KEA)
• Bilinear Diffie-Hellman

Interactive Proof Systems

• IP, AM, MA complexity classes
• Arthur-Merlin protocols
• Sumcheck protocol
• GKR protocol

Fiat-Shamir Heuristic

• Interactive to non-interactive transformation
• Random oracle model
• Security implications

3. Zero-Knowledge Proof Sistemleri

Temel ZKP Kavramları

• Completeness, soundness, zero-knowledge
• Perfect vs computational vs statistical ZK
• Proof of knowledge vs proof of statement
• Witness ve statement kavramları
• Simulator paradigm

Sigma Protocols

• Schnorr protocol (ZK proof of discrete log)
• OR-proofs ve AND-proofs
• Composition techniques
• Sigma protocol to NIZK

zk-SNARKs - Teorik Temeller

• Quadratic Arithmetic Programs (QAP)
• Rank-1 Constraint Systems (R1CS)
• Linear PCP
• Knowledge soundness

Groth16

• Trusted setup (powers of tau)
• Proving ve verification equations
• Pairing-based verification
• Circuit-specific setup

PLONK

• Universal trusted setup
• Permutation arguments
• Custom gates
• Lookup arguments (plookup)

Halo 2

• Recursive proofs
• Accumulation schemes
• Inner Product Argument (IPA)
• No trusted setup

zk-STARKs

• AIR (Algebraic Intermediate Representation)
• FRI (Fast Reed-Solomon IOP)
• Transparency (no trusted setup)
• Post-quantum security
• Blow-up factor ve proof size

Diğer Sistemler

• Bulletproofs (range proofs)
• Aurora, Ligero, Brakedown
• Spartan
• Nova (folding schemes)
• HyperNova

4. Circuit Development

Arithmetization

• Computation to circuit transformation
• R1CS constraint writing
• AIR constraint design
• Custom gate design
• Constraint optimization

Circom

• Template syntax
• Signal types (input, output, intermediate)
• Component composition
• snarkjs integration

Arkworks (Rust)

• r1cs-std library
• Gadget implementation
• Constraint system API
• Native field operations

Halo2 (Rust)

• PLONKish arithmetization
• Region ve cell management
• Selector columns
• Lookup tables
• Custom gates

Noir (Aztec)

• High-level ZK language
• Standard library
• Noir to ACIR compilation

Cairo (StarkWare)

• Memory model
• Builtins
• Hints
• Program execution trace

Optimization Techniques

• Constraint minimization
• Lookup table usage
• Batch verification
• Recursive composition
• Proof aggregation

5. ZK Applications

Zcash

• Sapling circuit (spend, output)
• Orchard circuit (Halo 2)
• Note encryption
• Nullifier sets
• Value commitments

Tornado Cash (tarihsel öğrenme için)

• Merkle tree membership
• Nullifier generation
• Deposit/withdrawal flow

Aztec

• Private transactions
• Account abstraction
• Note discovery

zk-Rollup Mimarisi

• State commitment
• Batch proving
• Data availability
• Sequencer design
• Escape hatch

zkEVM

• EVM opcode circuits
• State trie proofs
• Transaction execution proving
• Types: Polygon zkEVM, Scroll, zkSync Era, Linea

Diğer Uygulamalar

• zkBridge (cross-chain)
• Identity ve credentials (Semaphore, WorldID)
• Voting systems
• zkML (machine learning)
• Verifiable computation

6. Performans ve Optimizasyon

Prover Optimization

• Multi-scalar multiplication (MSM) optimization
• FFT/NTT optimization
• GPU acceleration (CUDA, Metal)
• Parallelization strategies
• Memory optimization

Verifier Optimization

• Batch verification
• Aggregation techniques
• On-chain verification gas optimization
• Precompile usage

Hardware Acceleration

• FPGA implementation
• ASIC design considerations
• GPU kernel optimization
• Memory bandwidth optimization

7. Güvenlik

Soundness Analysis

• Forking lemma
• Rewinding arguments
• Knowledge extraction
• Simulation proofs

Common Vulnerabilities

• Trusted setup compromise
• Weak Fiat-Shamir
• Missing constraints (underconstrained circuits)
• Frozen heart vulnerability
• Grinding attacks

Audit Practices

• Circuit review methodology
• Constraint completeness checking
• Test vector generation
• Formal verification approaches

8. Araştırma Alanları (Cutting Edge)

Folding Schemes

• Nova
• SuperNova
• HyperNova
• ProtoStar

Lookup Arguments

• Plookup
• Caulk
• Baloo
• Lasso

Post-Quantum ZK

• Lattice-based proofs
• Hash-based constructions
• Code-based systems

zkVM

• General purpose ZK virtual machines
• RISC Zero
• SP1 (Succinct)
• Valida

Proof Composition

• Recursive SNARKs
• Proof aggregation
• Incrementally verifiable computation