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"