Distance Bounding Protocol with Adjustable False Acceptance Rate

At Eurocrypt 1993, Brands and Chaum introduced distance bounding protocols to defend against mafia fraud attack and distance fraud attack. A distance bounding protocol usually consists of n rounds of a single-bit challenge and a single-bit response, which determines the distance between communicating entities by measuring the round-trip time of signals. Let FAR_M and FAR_D be the false acceptance rate against the mafia fraud attack and the distance fraud attack, respectively. The state-of-the-art distance bounding protocols in terms of the false acceptance rate have either (FAR_M,FAR_D) = ((1/2)ⁿ, (1/2)ⁿ) or (FAR_M,FAR_D) = (4(3/8)ⁿ, (7/8)ⁿ). We introduce a flexible distance bounding protocol whose false acceptance rate (FAR_M,FAR_D) can be chosen from ((1/2)ⁿ, (1/2)ⁿ) to ((1/4)ⁿ, (3/4)ⁿ).