Blind Signature - Dangers of Blind Signing

Dangers of Blind Signing

RSA is subject to the RSA blinding attack through which it is possible to be tricked into decrypting a message by blind signing another message. Since the signing process is equivalent to decrypting with the signers secret key, an attacker can provide a blinded version of a message encrypted with the signers public key, for them to sign. The encrypted message would usually be some secret information which the attacker observed being sent encrypted under the signers public key which the attacker wants to learn. When the attacker unblinds the signed version they will have the clear text:

$\begin{align} m'' & = m' r^e\pmod n \\ & = (m^e\pmod n \cdot r^e)\pmod n \\ & = (mr)^e \pmod n \\ \end{align}$

where is the encrypted version of the message. When the message is signed, the cleartext is easily extracted:

$\begin{align} s' & = m''^d\pmod n \\ & = ((mr)^e\pmod n)^d\pmod n \\ & = (mr)^{ed} \pmod n \\ & = m \cdot r \pmod n \mbox{, since } ed \equiv 1 \pmod{\phi(n)}\\ \end{align}$

Note that refers to Euler's totient function. The message is now easily obtained.

$\begin{align} m = s' \cdot r^{-1} \pmod{n} \end{align}$

This attack works because in this blind signature scheme the signer signs the message directly. By contrast, in an unblinded signature scheme the signer would typically use a padding scheme (e.g. by instead signing the result of a Cryptographic hash function applied to the message, instead of signing the message itself), however since the signer does not know the actual message, any padding scheme would produce an incorrect value when unblinded. Due to this multiplicative property of RSA, the same key should never be used for both encryption and signing purposes.

Read more about this topic: Blind Signature

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