Blind Signatures

Cryptography · Axiom Academy

Signing messages without seeing their content In a blind signature scheme, a user wants to get a document signed by an authority without revealing the document's contents. It's like getting something notarized while it's sealed in an envelope. Imagine placing a document inside an envelope lined with carbon paper. When someone signs the outside of the envelope, the signature transfers through to the document inside. You can then remove the document with the signature, but the signer never saw what they signed. David Chaum invented blind signatures in 1983, revolutionizing cryptographic privacy. The signer sees only a "blinded" version of the message, signs it, and returns the blind signature. The recipient can then "unblind" it to get a valid signature on the original message. 2. RSA Blind Signatures: Blinding Phase RSA blind signatures work by exploiting RSA's homomorphic properties. The user wants to get message m signed without revealing it to the signer. The user chooses a random blinding factor r and computes: where e is the signer's public exponent and n is the modulus. The blinded message m' is sent to the signer instead of the original message m . The signer applies their private key d to the blinded message: The signer returns the blind signature σ' to the user. The user removes the blinding factor by multiplying by the modular inverse of r : This yields σ = m d mod n, which is a valid RSA signature on the original message m ! 4. Applications & Privacy Properties

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