McEliece Encryption

About McEliece

The McEliece cryptosystem is one of the oldest public-key cryptosystems, proposed by Robert McEliece in 1978. It is based on the hardness of decoding a general linear code, a problem from coding theory. Unlike RSA and ECC, McEliece is believed to be resistant to attacks using quantum computers.

Key Features:

  • Type: Code-based asymmetric encryption algorithm
  • Security Basis: Hardness of decoding general linear codes (NP-hard problem)
  • Quantum Resistance: Believed to be secure against quantum computer attacks
  • Key Sizes: Public keys are typically large (hundreds of kilobytes to several megabytes)
  • Performance: Fast encryption and decryption operations compared to other post-quantum algorithms

Advantages:

  • Resistant to quantum computer attacks
  • Fast encryption and decryption operations
  • Based on a well-studied mathematical problem
  • Has withstood cryptanalysis for over 40 years

Applications:

  • Long-term secure communications
  • Data protection against future quantum attacks
  • Hybrid encryption schemes
  • Post-quantum cryptography standards
Note: McEliece is primarily used for encryption rather than digital signatures. For post-quantum digital signatures, other algorithms like Dilithium, Falcon, or SPHINCS+ are typically used.

Generate McEliece Keys

Key generation may take several seconds due to the complexity of the algorithm.
Keep your private key secret! Never share it with anyone.

Encrypt File with McEliece

Decrypt McEliece File

How McEliece Works

McEliece is a code-based asymmetric encryption algorithm that uses error-correcting codes to provide security.

Key Generation:

  1. Choose a binary Goppa code with parameters [n,k,t] that can correct t errors
  2. Generate a k×n generator matrix G for this code
  3. Choose a random k×k invertible matrix S
  4. Choose a random n×n permutation matrix P
  5. Compute G' = SGP (the "scrambled" generator matrix)
  6. Public key: (G', t)
  7. Private key: (S, G, P)

Encryption:

  1. Convert the message to a binary vector m of length k
  2. Generate a random error vector e of length n with exactly t 1's
  3. Compute the ciphertext c = mG' + e

Decryption:

  1. Compute c' = cP^(-1)
  2. Use the decoding algorithm for the Goppa code to remove the error and recover m'
  3. Compute the original message m = m'S^(-1)

Advantages and Disadvantages:

Advantages Disadvantages
  • Resistant to quantum computer attacks
  • Fast encryption and decryption operations
  • Based on a well-studied mathematical problem
  • Very large public keys
  • Ciphertext expansion
  • Less widely implemented than RSA or ECC
Note: This is a simplified explanation. The actual implementation involves complex mathematical operations and careful parameter selection to ensure security.