Table 2.

Bluetooth privacy game for the LESSP-type protocols.

Untraceability on Bluetooth Device
Bluetooth Privacy Game 𝒫𝒢𝒜,Π[n, k]
Phase 1. System setup
Select a polynomial number of the Bluetooth devices named as 1, 2, …, and n. Determine the bit length of DHKey denoted as k1 and the bit length of MacKey denoted as k2. Let k = min( k1, k2) be the security parameter. (Optional) Set the available storage capacity for the pairing information table in the Bluetooth device.
Phase 2. Learning
3.For any Bluetooth device in {1, 2, …, n}, the adversary 𝒜 can call the oracles defined in Section 5.2.1. The following oracles are polynomially invoked with interleaved order. 3.1.𝒜 calls the oracles OPA = {Execute, Result} to act as the PA. 3.2.𝒜 calls the oracles OAA = {Init, Send, Reveal, Corrupt} to act as the AA.
Phase 3. Challenge
4.𝒜 selects a challenge Bluetooth device A ∈ {1, 2, …, n} and any other Bluetooth device B ∈ {1, 2, …, n}. Here, the oracle Corrupt (ΠA,B) or the oracle Corrupt (ΠB,A) is not allowed during the learning phase, if the compromised DHKey exists in both devices’ pairing information tables. 5.𝒜 calls the oracle Test (A, B). 6.𝒜 outputs his guessing bit b′.
𝒜 wins if b = b′.