Defining The Security of Commitment Schemes
Formal definitions of commitment schemes vary strongly in notation and in flavour. The first such flavour is whether the commitment scheme provides perfect or computational security with respect to the hiding or binding properties. Another such flavour is whether the commitment is interactive, i.e. whether both the commit phase and the reveal phase can be seen as being executed by a Cryptographic protocol or whether they are non-interactive, consisting of two algorithms Commit and CheckReveal. In the latter case CheckReveal can often be seen as a derandomised version of Commit, with the randomness used by Commit constituting the opening information.
If the commitment C to a value x is computed as C:=Commit(x,open) with open the randomness used for computing the commitment, then CheckReveal(C,x,open) simply consists in verifying the equation C=Commit(x,open).
Using this notation and some knowledge about mathematical functions and probability theory we formalise different versions of the binding and hiding properties of commitments. The two most important combinations of these properties are perfectly binding and computationally hiding commitment schemes and computationally binding and perfectly hiding commitment schemes. Note that no commitment scheme can be at the same time perfectly binding and perfectly hiding.
Read more about this topic: Commitment Scheme
Famous quotes containing the words defining the, defining, security, commitment and/or schemes:
“Art, if one employs this term in the broad sense that includes poetry within its realm, is an art of creation laden with ideals, located at the very core of the life of a people, defining the spiritual and moral shape of that life.”
—Ivan Sergeevich Turgenev (1818–1883)
“The U.S. is becoming an increasingly fatherless society. A generation ago, an American child could reasonably expect to grow up with his or her father. Today an American child can reasonably expect not to. Fatherlessness is now approaching a rough parity with fatherhood as a defining feature of American childhood.”
—David Blankenhorn (20th century)
“Learned institutions ought to be favorite objects with every free people. They throw light over the public mind which is the best security against crafty and dangerous encroachments on the public liberty.”
—James Madison (1751–1836)
“Commitment, by its nature, frees us from ourselves and, while it stands us in opposition to some, it joins us with others similarly committed. Commitment moves us from the mirror trap of the self absorbed with the self to the freedom of a community of shared values.”
—Michael Lewis (late 20th century)
“Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and observations and fruitful of further experiments and observations.”
—James Conant (1893–1978)