Creating Digital Signatures

Cryptography · Axiom Academy

EXAMPLE Creating Digital Signatures Step-by-step walkthrough of signing a message with RSA Excellent work! You've completed the digital signature creation process. Here's what we learned: RSA Key Setup: The modulus n = p × q = 143 serves as the foundation for both encryption and signing operations. Hash Function: Messages are hashed before signing to ensure fixed-size inputs and provide cryptographic integrity. Our simplified hash demonstrates the concept. Private Key Operation: The signature is created by raising the padded hash to the private exponent d modulo n , which only the signer can compute. Verification: Anyone with the public key (e, n) can verify the signature by computing σ e mod n and comparing it to the hash. Security Foundation: The difficulty of factoring large numbers makes it infeasible for attackers to derive the private key from the public key. In real-world systems, we use much larger primes (2048+ bits), standardized hash functions like SHA-256, and proper padding schemes like PSS. This simplified example demonstrates the core mathematical principles!

This is the written version of the interactive lesson above. See the full Cryptography course.