Logical Analysis and Verification of Cryptographic Protocols - Loria

8 CHAPTER 1. INTRODUCTION
And, a perfect signature scheme with message recovery is represented by
the following equation
1.2.6 Blind signature
ver(sig(x, Sk(y)), P k(y)) = x
Blind signature schemes, initially introduced by D. Chaum [61], is a form of digital
signature schemes in which the content of a message is blinded (disguised) before
it is signed. The resulting blind signature can be publicly 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 electronic
voting systems [115] and digital cash schemes.
The blind signature schemes are described by the following algorithms:
• the signature generation “sig”, the verification “ver”, and the key generation
“G” algorithms which are defined as for the traditional digital signature
schemes given in Section 1.2.5.
• The blind “Bl”and unblind “Ubl” algorithms defined as follows:
Blind algorithm takes as input a message “m” and a random selected value
“r”, and returns the blinded value of “m” with respect to “r”.
Unblind algorithm takes as input a blinded message “b” and a random selected
value “r”, and outputs the original (unblinded) message provided
that “b” has been constructed using “r” as random selected
value.
The blind signature schemes have the following algebraic properties:
ver(sig(x, Sk(y)), P k(y)) = x, (or, ver(x, sig(x, Sk(y)), P k(y)) = 1)
Ubl(Bl(x, y), y) = x
Ubl(sig(Bl(x, y), Sk(z)), y) = sig(x, Sk(z))
1.2.7 Hash function
A cryptographic hash function is a deterministic procedure that takes an arbitrary
block of data and returns a fixed-size bit string. Cryptographic hash
functions have many information security applications, notably in digital signatures,
message authentication codes (MACs), and other forms of authentication.
Hash functions may have some of the following properties: