Eve Does Some Magic with Nothing Up Her Sleeve

Right. Eve The Magician asks the audience for a value of G, and Carol shouts out “5”. Eve then asks Alice to think of a number (a) and multiply the two values together to give y:

y = aG

“Don’t tell me the result”, says Eve. She now asks for another number from the audience, and they shout out “7”. Eve writes something on a piece of paper, and shouts out that her answer is “38”. She turns to Alice and asks her for the result of her calculation, and she says that y is “10”. The audience are worried that Eve has failed in her trick.

“But”, she says, “my card says a value of ‘4’”, and she shows this to the audience, “Now please calculate z, and which is aG + bH”. What is the value that you get?”. Alice calculates and shows her calculation:

“38”

“And that is the answer that I showed you before I knew Alice’s value”, says Eve to great applause. This the Pedersen Commitment in action, and where Eve committed to a value, and then blinding her guess. She then revealed her blinding factor, and showed that she knew the answer all along.

In this case Alice’s secret was “2” and Eve’s blinding factor was “4”, so Eve got:

z = aG + bH = 2*5 + 4 * 7 = 38