[Paper Review] Achieving Shannon Capacity in a Wiretap Channel via Previous Messages

Shahid Mehraj Shah, Vinod Sharma|arXiv (Cornell University)|Apr 23, 2014

Wireless Communication Security Techniques17 references3 citations

TL;DR

This paper proposes a wiretap channel coding scheme that achieves the main channel's capacity for secrecy by leveraging a secret key buffer to store and reuse old secret bits. By using the oldest stored keys to secure current and recent transmissions, the scheme ensures all messages from the last $N_1$ slots remain secure against the eavesdropper, with $N_1$ arbitrarily large, surpassing prior work in security strength.

ABSTRACT

In this paper we consider a wiretap channel with a secret key buffer. We use the coding scheme of [1] to enhance the secrecy rate to the capacity of the main channel, while storing each securely transmitted message in the secret key buffer. We use the oldest secret bits from the buffer to be used as a secret key to transmit a message in a slot and then remove those bits. With this scheme we are able to prove stronger results than those in [1]. i.e., not only the message which is being transmitted currently, but all the messages transmitted in last $N_1$ slots are secure with respect to all the information that the eavesdropper possesses, where $N_1$ can be chosen arbitrarily large.

Motivation & Objective

• To enhance secrecy rates in wiretap channels to match the main channel's capacity.
• To improve security guarantees beyond current transmissions by protecting messages from the last $N_1$ slots.
• To design a scheme that reuses stored secret key bits efficiently from a buffer to secure new transmissions.
• To prove stronger security results than prior work, especially for past messages.

Proposed method

• The scheme uses a secret key buffer to store each securely transmitted message's secret bits.
• It reuses the oldest secret bits from the buffer as one-time pads for current transmissions.
• After use, the secret key bits are removed from the buffer to prevent reuse.
• The coding strategy ensures that all messages from the last $N_1$ slots remain secure, regardless of the eavesdropper's observations.
• The approach builds on the framework of [1] but strengthens its security guarantees by extending the scope of protected messages.

Experimental results

Research questions

• RQ1 Can the secrecy rate be increased to match the main channel capacity using a secret key buffer?
• RQ2 Can the security of past messages, not just the current one, be guaranteed against an eavesdropper?
• RQ3 How large can the number of past messages remain secure, and can this number be made arbitrarily large?
• RQ4 Can the reuse of stored secret bits improve both efficiency and security in wiretap channels?

Key findings

• The proposed scheme achieves the secrecy capacity of the main channel, matching its capacity.
• All messages transmitted in the last $N_1$ slots are secure, where $N_1$ can be chosen arbitrarily large.
• The security of past messages is preserved even if the eavesdropper observes all past channel outputs.
• The scheme improves upon prior work by extending the scope of secrecy beyond the current transmission slot.