Secret Key Generation With Cross Multiplication of Two-Way Random Signals

The secret key generation rate (SKGR) of current physical layer security methods is not high enough for practical requirements. A novel SKG method based on the cross multiplication (XM) of two-way random signals is proposed for TDD-MIMO system. The principle concealed beneath the XM method is found that the XM operation not only derives the common random source for both legitimate partners, but also employs new generated cross-terms due to bilinear operation to provide more measurements of the random source and more secret keys accordingly, which is essentially superior to the existing paired multiplication (PM) method. Then, the theoretical SKGR of two-way random signals is analyzed and it is validated that SKGR is determined by the randomness of the reciprocal channel and the two-way secure transmission rates collectively. Furthermore, SKGR of XM and PM methods are derived in closed-form respectively under infinite antenna condition and the former shows a linear increase with the channel coherence interval, which are also approximately valid for finite antenna. The innovative conclusion means the slow-changing property of some channel environments can be further exploited and the proposed XM method can be applied to solve the low SKGR problem in static or quasi-static channel environment such as IoT. Finally, the simulations verify the theoretical results and show that the XM method achieves several orders of magnitude higher SKGR than the PM method.