RSA Key Pair Generator

The ElGamal Asymmetric Encryption Tool 🧩✨ brings one of the most elegant and influential public-key encryption systems to life — the ElGamal Cryptosystem, invented by Taher ElGamal in 1985.

Built on the mathematical foundation of modular exponentiation and the Discrete Logarithm Problem, the ElGamal algorithm provides a secure and flexible method for encrypting, decrypting, and signing data using a pair of asymmetric keys.

This interactive tool allows users to generate key pairs, encrypt and decrypt messages, and visualize the mathematical process that keeps modern communication secure. It’s a perfect learning platform for students, researchers, developers, and cybersecurity enthusiasts who want to understand how asymmetric encryption works under the hood.

⚙️ Key Features:

• 🔑 Key Generation Made Simple:
  Instantly create public and private key pairs using safe prime numbers and generators. The tool displays all key components — p, g, x (private), and y (public).

• 📡 Asymmetric Encryption Process:
  Encrypt any message using the recipient’s public key. Watch how randomization through the ephemeral key k creates unique ciphertexts for identical messages — ensuring forward secrecy.

• 🔍 Step-by-Step Decryption:
  Decrypt ciphertexts using your private key and see exactly how modular arithmetic reconstructs the original plaintext.

• 🧮 Mathematical Breakdown:
  Understand each stage:

   

  Encryption:  c1 = g^k mod p  c2 = (m * y^k) mod p Decryption:  m = (c2 * (c1^x)^(-1)) mod p

  Every calculation is shown visually with mod exponentiation steps and intermediate results.

• 🧠 Random Ephemeral Key (k) Generator:
  Each encryption uses a fresh random number k to ensure ciphertext unpredictability — even if the same plaintext and public key are reused.

• 🔁 Re-Encrypt Function:
  Demonstrates non-determinism by showing how multiple encryptions of the same message yield different ciphertexts.

• 🔐 Digital Signature Mode:
  Learn how ElGamal can be adapted for digital signatures by generating message hashes and verifying authenticity using modular verification equations.

• 📊 Visualization Panel:
  Displays the flow of data between sender and receiver — highlighting public vs. private values to clarify asymmetric security.

• 🧩 Flexible Input Support:
  Accepts text, numbers, or hex-encoded data for encryption and decryption, supporting a range of cryptographic demonstrations.

• 💾 Export & Import Keys:
  Save generated key pairs as JSON or PEM-like files and reuse them in later sessions or educational projects.

• 🔒 Secure & Offline:
  All encryption and decryption happen entirely in your browser — no external communication, ensuring full data privacy.

💡 How It Works (Simplified):

The ElGamal Encryption Algorithm is built on three core ideas: modular arithmetic, randomization, and asymmetric key usage.

1. Key Generation:

   • Choose a large prime number (p) and a generator (g).

   • Select a private key (x) randomly.

   • Compute the public key as y = g^x mod p.

2. Encryption (Using Recipient’s Public Key):

   • Pick a random ephemeral key k.

   • Compute c1 = g^k mod p.

   • Compute c2 = (m * y^k) mod p.

   • The ciphertext is (c1, c2).

3. Decryption (Using Private Key):

   • Compute the shared secret s = c1^x mod p.

   • Compute the inverse s^-1 mod p.

   • Recover the plaintext: m = c2 * s^-1 mod p.

✅ The receiver gets back the original message without ever sharing their private key.
✅ Even if an attacker intercepts c1 and c2, they cannot compute the secret without solving the Discrete Logarithm Problem — a task computationally infeasible for large primes.

🧭 Historical & Practical Context:

Introduced by Taher ElGamal, the ElGamal system was the first to explicitly show how asymmetric encryption could be built from Diffie–Hellman key exchange principles.

It inspired many modern encryption systems, including:

• 🧩 DSA (Digital Signature Algorithm) — used for cryptographic signing.

• 🔐 PGP/GPG — for email encryption and authentication.

• 💬 Modern cryptosystems like ECC (Elliptic Curve Cryptography) variants of ElGamal for efficient encryption in mobile and IoT devices.

ElGamal remains a core asymmetric algorithm in academic and applied cryptography, valued for its simplicity, randomness, and strong security properties.

🌍 Perfect For:

• 🧑‍🏫 Educators & Students: Learning modular arithmetic and asymmetric encryption principles.

• 💻 Developers: Studying or implementing public-key cryptography in web or software applications.

• 🕵️‍♂️ Cybersecurity Enthusiasts: Experimenting with asymmetric key generation and message encryption.

• 🧮 Mathematicians: Exploring group theory, modular inverses, and exponentiation.

• 📚 Researchers & Historians: Understanding the evolution of public-key cryptography from Diffie–Hellman to ElGamal.

🔍 Why It’s Valuable:

The ElGamal Asymmetric Encryption Tool combines education, security, and interactivity — turning abstract number theory into an intuitive experience.

It helps users grasp:
✅ The mechanics of asymmetric key systems.
✅ The role of modular arithmetic and randomness in encryption.
✅ The importance of key size and randomness for cryptographic security.
✅ How public and private keys protect data even across open networks.

This tool makes encryption visual, understandable, and hands-on, giving users the power to simulate real cryptographic operations safely and clearly.

✨ In Short:

The ElGamal Asymmetric Encryption Tool 🧠🔑 transforms one of cryptography’s most important algorithms into an engaging, interactive experience. It lets you generate keys, encrypt, decrypt, and understand the math behind asymmetric encryption — all in one place.

Encrypt. Exchange. Verify.
With the ElGamal Asymmetric Encryption Tool, you’ll see how mathematics, logic, and randomness unite to secure the modern digital world. 🔐💻✨