Novo protocolo de reconciliação de chaves secretas geradas quanticamente utilizando códigos LDPC no sentido Slepian-Wolf

Abstract

Resumo-Este artigo apresenta uma solução alternativa ao uso das funções Slice para reconciliação de variáveis aleatórias contínuas em um contexto de geração de chaves secretas para fins de criptografia. O protocolo de reconciliação proposto baseia-se na função distribuição de probabilidade das variáveis aleatórias e se mostra um método competitivo por sua capacidade de gerar a mesma quantidade de bits que o esquema atualmente em uso, com uma vantagem de menor iteratividade. O processo de correção de errosé feito com base no uso de códigos LDPC a partir de uma compressão da sequência de bits a ser utilizada como chave, fundamentado no teorema de Slepian-Wolf, minimizando a informação vazada pelo canal clássico-assumido perfeitopara um possível espião que observa o canal.

CASCADE as Correlation Enhancer for CVQKD Protocols

“…A much easier solution is proposed in [15] where it is performed a binary expansion of continuous values that acts as a quantizer method, ensuring expansion bits interdependence based on the following well known Lemma [20]: Fig. 2.…”

“…The complexity of extracting bits from the continuous variable is also high. Recently, a Binary Expansion Protocol has been proposed, relying on information theory arguments of probability distributions [15] presenting itself as a strong option over SEC reconciliation due to its random variable optimal compression rate.…”

Distributional Transform Based Information Reconciliation

“…Both SEC and MD reconciliation procedures present a way to extract bit sequences from continuous valued data so that an error correcting code could be applied, typically an LDPC code [10], [13], [15], [16]. A relatively recent alternative, proposed by Araújo and Assis [14] leverages a property of random variables with continuous distribution function widely used in Copula Theory [17], [18,Theorem 1.2.6].…”

“…As the bits in the expansion are independent of each other, it is also possible that both Alice and Bob perform the DTE on their sequences and treat the errors between D i (X) and D i (Y ) as a transmission over a binary symmetric channel BSC(p i ), where p i is the transition probability. This approach were used in [14] were they showed that reconciliation can be obtained in the first two sub-channels with 4 • 10 4 sized LDPC codes in at most 40 decoding iterations with 4.5 dB SNR. Although, the analysis was restricted to CVQKD protocols with homodyne detection and reconciliation efficiency was not addressed.…”

“…Here we present an alternative method for extracting binary sequences from continuous valued raw keys based on arguments of copula and information theories. More specifically, we extend the method presented in [14], that uses the distributional transform of continuous random variables (which is the principle of arithmetic source coding) to map the raw keys into the unit interval with uniform distribution. The bit sequences are then extracted with a simple binary expansion.…”