Secret Key Generation Over Multi-Mode Fiber: Channel Measurements, Key Rate Analysis, and System Implementation

Abstract

Secret keys are critical for many security mechanisms including secure data transmission. An efficient secret key generation and sharing scheme enhances the secure transmission rate. Meanwhile, secret keys are scarce resources for classical encryption schemes like the Rivest-Shamir-Adleman (RSA) cryptosystem and its post-quantum security counterparts in quantum applications. Therefore, harnessing every available random source for secret key extraction is crucial for maximizing the key rate across a range of potential applications. In this paper, we investigate the achievable rate of the secret key generation (SKG)-channel-model based on an actual measured multi-mode fiber (MMF) channel, where there is an additional public discussion channel between the legitimate parties, which the adversary can perfectly overhear. In particular, we first measure the MMF transmission matrix using digital holography, then design power allocation schemes among the modes. Our schemes can achieve a positive secret key rate at 51.3 bit per channel use, under a mode-dependent loss of 1 dB and a transmit power of 20 dBm. In addition, we implement an SKG system via MMF by explicitly designing the wiretap codes and discussion protocol. More specifically, we design the hash function and point-to-point channel encoder/decoder for each mode in the MMF based on Hayashi’s wiretap coding. The designed system can achieve a secret key rate-leakage trade-off at $R_{SK} = 23.6$ bits per channel use and an average leakage rate at $ 4.22 \cdot 10^{-3}$ bits per channel use per mode, at the transmit power $\textsf {P}_{T}$ at 50 dBm and mode-dependent loss at 1 dB with the error probability constraint at Bob as $10^{-5}$ . This demonstrates the feasibility and effectiveness of generating SKG via MMF, aligning with the common approaches of post-quantum cryptography and quantum key distribution in addressing the challenges posed by emerging quantum computers.

Keywords

• Multi-mode fiber
• MIMO
• secret key generation
• physical layer security