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RSA Encryption

受众: Software Engineer类别: Computer Science

简介

Walks through the RSA public-key cryptosystem: key generation from two primes, encryption using the public key, and decryption using the private key. Alice and Bob exchange an encrypted message, demonstrating the one-way trapdoor function. The security relies on the hardness of integer factorization.

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RSA Encryption

Description

Walks through the RSA public-key cryptosystem: key generation from two primes, encryption using the public key, and decryption using the private key. Alice and Bob exchange an encrypted message, demonstrating the one-way trapdoor function. The security relies on the hardness of integer factorization.

Phases

# Phase Name Duration Description
1 Intro 3s Title displayed
2 Key Generation 14s Show p, q primes → n=pq, φ(n)=(p-1)(q-1), choose e, compute d
3 Public/Private Keys 5s Display public key (e,n) and private key (d,n)
4 Encryption 8s c = m^e mod n animated with small numbers
5 Decryption 8s m = c^d mod n animated, original message recovered
6 Alice-Bob Exchange 8s Show Alice encrypting with Bob's public key, Bob decrypting
7 Security Note 6s Show that factoring n is hard; security relies on this
8 Outro 4s Summary displayed

Layout

+--------------------------------------------------+
|  Title: RSA Encryption                           |
+--------------------------------------------------+
|                                                  |
|  Key Generation:                                 |
|  p=5, q=11  →  n=55, φ(n)=40                    |
|  Choose e=3 (gcd(3,40)=1)                        |
|  Compute d=27 (3×27 ≡ 1 mod 40)                  |
|                                                  |
|  Public key: (e=3, n=55)                         |
|  Private key: (d=27, n=55)                       |
|                                                  |
|  Encrypt: c = m^e mod n                          |
|  Decrypt: m = c^d mod n                          |
|                                                  |
|  Alice ──[c]──> Bob                              |
|  (encrypted with Bob's public key)               |
+--------------------------------------------------+

Area Descriptions

  • Center: Step-by-step key generation with formula annotations
  • Bottom left: Alice/Bob exchange diagram
  • Bottom right: Security hardness note

Assets & Dependencies

  • Fonts: LaTeX / sans-serif
  • Manim version: ManimCE 0.19.1

Notes

  • Use small concrete numbers (p=5, q=11, m=7) to make math visible
  • Each formula step animated with Write/Transform
  • One-way function shown as a locked padlock metaphor
  • Factoring difficulty shown: "Given n=55, find p,q — easy here, impossible for 2048-bit n"