CP-20200128

Cryptography Primitives Intermediate January 28, 2020

Back to All Tasks

Problem Statement

Design a simple digital signature scheme using hash functions and symmetric encryption. Your task is to create a function that takes a message, a secret key, and produces a digital signature. The digital signature should be generated by first hashing the message with SHA-256, then encrypting this hash with AES in ECB mode using the provided secret key. For verification, implement another function that checks if a given message matches its supposed digital signature when decrypted and compared to the original hash of the message. Ensure your functions are secure against common cryptographic pitfalls such as ECB mode weaknesses. Document any assumptions made during the implementation.

Concepts

  • hash functions
  • message authentication codes (MAC)
  • symmetric encryption

Constraints

  • Use SHA-256 for hashing
  • Use AES in ECB mode for encryption
  • Implement both signing and verification functions

Security Notes

  • ECB mode is not recommended for encrypting messages longer than one block size due to lack of diffusion. Consider using a more secure mode like CBC or GCM for real-world applications.
  • Ensure the secret key is kept confidential as it allows forging signatures.

Solutions

Java Solution

import java.security.MessageDigest;
import javax.crypto.Cipher;
import javax.crypto.spec.SecretKeySpec;

public class DigitalSignature {
    // Method to generate a digital signature using SHA-256 hash and AES ECB encryption.
    public static byte[] signMessage(String message, byte[] secretKey) throws Exception {
        // Hash the message using SHA-256
        MessageDigest digest = MessageDigest.getInstance("SHA-256");
        byte[] hashedMessage = digest.digest(message.getBytes());

        // Encrypt the hash with AES in ECB mode
        Cipher cipher = Cipher.getInstance("AES/ECB/PKCS5Padding");
        SecretKeySpec secretKeySpec = new SecretKeySpec(secretKey, "AES");
        cipher.init(Cipher.ENCRYPT_MODE, secretKeySpec);
        return cipher.doFinal(hashedMessage);
    }

    // Method to verify a digital signature.
    public static boolean verifySignature(String message, byte[] signature, byte[] secretKey) throws Exception {
        // Hash the original message using SHA-256
        MessageDigest digest = MessageDigest.getInstance("SHA-256");
        byte[] hashedMessage = digest.digest(message.getBytes());

        // Decrypt the signature with AES in ECB mode
        Cipher cipher = Cipher.getInstance("AES/ECB/PKCS5Padding");
        SecretKeySpec secretKeySpec = new SecretKeySpec(secretKey, "AES");
        cipher.init(Cipher.DECRYPT_MODE, secretKeySpec);
        byte[] decryptedHash = cipher.doFinal(signature);

        // Compare the decrypted hash with the original hash
        return MessageDigest.isEqual(hashedMessage, decryptedHash);
    }
}

This Java solution implements a simple digital signature scheme using SHA-256 for hashing and AES in ECB mode for encryption. The signMessage function first hashes the input message to produce a fixed-size hash value. This hash is then encrypted using the provided secret key with AES in ECB mode, resulting in the digital signature. The verifySignature function decrypts the provided digital signature back into a hash and compares it with a newly computed hash of the original message. If both hashes match, the signature is valid.

ECB mode is used here for demonstration purposes only; it is not recommended for real-world applications due to its lack of diffusion across blocks, which can reveal patterns in the encrypted data if the same plaintext block is repeated. For a secure implementation, modes like CBC or GCM are preferred as they provide better security properties.

It's crucial that the secret key used in AES encryption remains confidential, as possession of it allows anyone to forge signatures. In a real-world scenario, proper key management practices must be followed to ensure the secrecy and integrity of cryptographic keys.