Digital Signatures

Number Theory · Axiom Academy

Authenticating messages using public key cryptography 1. RSA Signatures: Sign with Private, Verify with Public RSA signatures reverse the typical encryption pattern. Instead of encrypting with the public key , we "encrypt" (sign) with the private key . Anyone with the public key can verify, but only the private key holder can create the signature. 2. Hash-Then-Sign: The Practical Approach In practice, we don't sign the message directly. Why? Messages can be arbitrarily long, but RSA requires the input to be smaller than the modulus n . The solution: hash the message first , then sign the hash. A cryptographic hash function like SHA-256 converts any message into a fixed-size digest (e.g., 256 bits). This digest acts as a unique "fingerprint" of the message. 3. Key Properties: Authentication, Integrity, and Non-Repudiation Digital signatures provide three critical security properties that make them invaluable for secure communication:

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