Blind signature

In cryptography, a blind signature is a form of digital signature in which the content of a message is disguised (blinded) before it is signed. The resulting blind signature can be publically verified against the original, unblinded message in the manner of a regular digital signature. Blind signatures are typically employed in privacy-related protocols where the signer and message author are different parties. Examples include cryptographic election systems and digital cash schemes.

An oft-used analogy to the cryptographic blind signature is the physical act of enclosing a message in an envelope, which is then sealed and signed by a signing agent. Thus, the signer does not view the message content, but a third party can later verify the signature and know that the signature is valid within the limitations of the underlying signature scheme.

Blind signatures can also be used to provide unlinkability, which prevents the signer from linking the blinded message it signs to a later un-blinded version that it may be called upon to verify. In this case, the signer's response is first "un-blinded" prior to verification in such a way that the signature remains valid for the un-blinded message. This can be useful in schemes where anonymity is required.

Blind signature schemes can be implemented using a number of common public key signing schemes, for instance RSA and DSA. To perform such a signature, the message is first "blinded", typically by combining it in some way with a random "blinding factor". The blinded message is passed to a signer, who then signs it using a standard signing algorithm. The resulting message, along with the blinding factor, can be later verified against the signer's public key. In some blind signature schemes, such as RSA, it is even possible to remove the blinding factor from the signature before it is verified. In these schemes, the final output (message/signature) of the blind signature scheme is identical to that of the normal signing protocol.

Uses

Blind signature schemes see a great deal of use in applications where sender privacy is important. This includes various "digital cash" schemes and voting protocols.

For example, the integrity of some electronic voting system may require that each ballot be certified by an election authority before it can be accepted for counting; this allows the authority to check the credentials of the voter to ensure that they are allowed to vote, and that they are not submitting more than one ballot. Simultaneously, it is important that this authority not learn the voter's selections. An unlinkable blind signature provides this guarantee, as the authority will not see the contents of any ballot it signs, and will be unable to link the blinded ballots it signs back to the un-blinded ballots it receives for counting.

Signature blinding also offers some protections against side channel attacks, and is used by many web servers implementing the Secure Socket Layer (SSL) to prevent timing attacks.

Blind Signature Schemes

Blind signature schemes exist for many public key signing protocols. Some examples are provided below. In each example, the message to be signed is contained in the value m. m is considered to be some legitimate input to the signature function.

Blind RSA Signatures

One of the simplest blind signature schemes is based on RSA signing. A traditional RSA signature is computed by exponentiating the message m with the secret exponent d, all mod a public modulus N. The blind version adds a random value r, such that gcd(r, N) = 1. r is exponentiated with the public exponent e (mod N), and the value <math>r^e<math> is used as a blinding factor. The signing authority receives the product of the message and blinding factor <math>m(r^e)<math> <math>\mathrm{mod}\ N <math>, which obscures the message. The blinded signature s' is then calculated as:

<math> s' \equiv (m(r^e))^d\ (\mathrm{mod}\ N) <math>

The author of the message can then remove the blinding factor to reveal s, the valid RSA signature of m:

<math> s \equiv s' * r^{-1}\ (\mathrm{mod}\ N) <math>