[Paper Review] Quantum Key Distribution From A Random Seed

Eduin H Serna|arXiv (Cornell University)|Nov 7, 2013

Quantum Mechanics and Applications16 citations

TL;DR

This paper proposes a novel quantum key distribution (QKD) protocol that leverages a random seed and asymmetric cryptography to generate four full-length, secure keys from a single set of transmitted qubits, achieving 100% key reconciliation efficiency—unlike BB84’s 50% expected coincidence rate—while maintaining identical quantum operations to BB84 and enabling key swapping between non-communicating parties via a central source.

ABSTRACT

It is designed a new quantum cryptography protocol that generates various secret and secure keys of the same size of the transmitted qubits, implying zero information losses between the interlocutors. Besides, generates key swapping between the two recipients of photons, without even sharing a past between them. This protocol differs from BB84 just in the classic procedures, using a random seed and asymmetric cryptography.

Motivation & Objective

• To address the practical limitation of key distribution in quantum cryptography, particularly the inefficiency and key loss inherent in traditional QKD protocols like BB84.
• To eliminate information loss during key reconciliation by introducing a random seed and asymmetric cryptographic techniques in the classical post-processing phase.
• To enable key swapping between two recipients (Alice and Bob) who have no prior shared history, using a central photon source.
• To maintain compatibility with existing quantum hardware by preserving the BB84 quantum operations while enhancing classical processing.
• To achieve 100% reconciliation efficiency, surpassing the 50% theoretical limit of BB84, through novel private reconciliation using a shared random seed.

Proposed method

• The protocol uses the same quantum state preparation and measurement as BB84, encoding two keys (i_k and j_k) in qubits using two bases, with states |0⟩, |1⟩, |+⟩, |−⟩.
• A public random seed x_k is shared between Alice and Bob to generate new basis sequences t_k = s_k ⊕ x_k and n_k = (1 ⊕ m_k) ⊕ x_k for the missing key exchange.
• Alice and Bob perform standard BB84-style quantum key exchange, measuring qubits in randomly chosen bases to obtain measurement outcomes a_k and b_k.
• A symmetric function f(z,x,y) is defined to conditionally select between x and y based on z, used to construct encrypted strings u_k and v_k for asymmetric key exchange.
• Asymmetric cryptography is applied: Bob computes u_k and v_k using f(m_k, a_k, b_k ⊕ y_k) and f(m_k, b_k, a_k ⊕ y_k), respectively, and sends them publicly.
• Alice decrypts the messages using f(s_k, (1⊕i_k)⊕u_k, j_k⊕v_k) to recover Bob’s basis string m_k, enabling full private reconciliation and key extraction.

Experimental results

Research questions

• RQ1 Can a QKD protocol achieve 100% key reconciliation efficiency, eliminating information loss, by modifying only the classical post-processing phase?
• RQ2 Can a random seed and asymmetric cryptography enable the generation of multiple secure keys from a single set of qubits without altering quantum operations?
• RQ3 Is key swapping possible between two recipients who have no prior communication, using a central source and the proposed protocol?
• RQ4 Can the proposed protocol be implemented on existing QKD hardware without modifications, given its identical quantum layer to BB84?
• RQ5 Does the use of a random seed and asymmetric cryptography enhance security and efficiency compared to standard BB84 reconciliation?

Key findings

• The protocol achieves 100% reconciliation efficiency, meaning all raw key bits are successfully reconciled into final secret keys, in contrast to BB84’s expected 50% coincidence rate.
• Four full-length secret keys—m_k, s_k, i_k, and j_k—are generated from a single set of N transmitted qubits, each of length N, with no information loss.
• Key swapping is enabled between Alice and Bob via a central source that compares their basis choices and informs them of coincidences, allowing them to extract shared keys without prior communication.
• The protocol maintains identical quantum operations to BB84, ensuring compatibility with existing quantum hardware and infrastructure.
• The use of a random seed and asymmetric cryptography in the classical layer allows for private reconciliation and secure key extraction without exposing raw key information.
• The protocol is mathematically secure under the same assumptions as BB84, with enhanced efficiency due to the elimination of information loss in reconciliation.