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Elliptic-curve Cryptography

Elliptic-curve cryptography (ECC) ek public-key cryptography ka approach hai jo elliptic curves ki…

Overview

Elliptic-curve Cryptography — Quick Facts

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Property: Detail

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Topic: Elliptic-curve Cryptography (ECC)

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Category: Public-Key Cryptography /…

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Based On: Elliptic curve mathematics over…

Topic 1

Kya Hai Elliptic-curve Cryptography

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Public key — sab ko share kar…

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Private key — sirf tumhare paas…

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Public key se private key nikalna…

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Private key se sign kiya hua data…

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Elliptic Curves — Basic Idea

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Yeh smooth, continuous curve hoti…

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Curve par do points ko "add" kar…

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Yeh point addition operation ECC…

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Curve par do points P aur Q lo

Topic 3

ECC Kaise Kaam Karta Hai

🎯 `mermaid sequenceDiagram participant Alice participant Bob Note over Alice,Bob: ECDH Key…

Topic 4

ECC vs RSA

⭐ | Feature | ECC | RSA | |---|---|---| | Key Size (128-bit security) | 256 bits | 3072…

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Common ECC Algorithms

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ECDSA purana, widely deployed hai…

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EdDSA naya, simpler, deterministic…

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Industry EdDSA ki taraf move kar…

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Popular Curves

✨ | Curve | Key Size | Standardized By | Used In | Notes | |---|---|---|---|---| | P-256…

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Where ECC Is Used

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Website visit karte ho → TLS…

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Server ka certificate ECDSA se…

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TLS 1.3 me ECC default aur…

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Ed25519 SSH keys — modern, fast,…

Topic 8

Security Foundation

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Brute force me $2^{128}$…

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Best known classical algorithm:…

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No shortcut known (unlike RSA…

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RSA ki security integer…

Topic 9

Advantages aur Limitations

📚 | Advantages | Limitations | |---|---| | Smaller keys — 256-bit ECC ≈ 3072-bit RSA |…

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Quantum Computing Threat

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ECDLP efficiently solve kar sakta…

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Matlab: powerful quantum computer…

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RSA bhi equally vulnerable hai

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NIST ne PQC standards finalize kar…

Comparison

ECC vs RSA

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Key Size (128-bit security): 256 bits

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Key Size (256-bit security): 512 bits

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Speed (key generation): Faster

Diagram

Visual Flow

📊 Diagram visualization — details in narration

Quiz — Question 1

Elliptic-curve Cryptography ka sabse sahi definition kya hai?

Quick Quiz

Quiz — Question 2

Elliptic-curve Cryptography ka 'Topic' kya hai?

Complete! 🎉

Elliptic-curve Cryptography Complete!

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