Using Permutations to Enhance the Gain of RUQB Technique

Using Permutations to Enhance the Gain of RUQB Technique

Abdulla M. Abu-ayyash (Central Bank of Jordan, Jordan) and Naim Ajlouni (Al-Balqa University, Jordan)
DOI: 10.4018/jitwe.2012040103
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Abstract

Quantum key distribution (QKD) techniques usually suffer from a gain problem when comparing the final key to the generated pulses of quantum states. This research permutes the sets that RUQB (Abu-ayyash & Ajlouni, 2008) uses in order to increase the gain. The effect of both randomness and permutations are studied; While RUQB technique improves the gain of BB84 QKD by 5.5% it was also shown that the higher the randomness of the initial key the higher the gain that can be achieved, this work concluded that the use of around 7 permutations results in 30% gain recovery in an ideal situations.
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Introduction

Preserving confidentiality during communications is always considered a hard task; encryption is one solution for such a problem. The simplest, yet proved (Shannon, 1949) secure, encryption method is one-time pad (Vernam, 1926); which uses symmetric keys between communicating parties. The main two problems of one-time-pad is i) the need to always generate new keys, and ii) the need to securely distribute such keys between the communicating parties; while the first problem can be solved using any real random number generator, the second is harder to solve and known as Key Distribution problem (KD).

Diffie and Hellman (1976) were the first to solve the (KD) problem, utilizing a mathematical problem known as discreet log (DL) (Menezes, Oorschot, & Vanstone, 1997). Based on DL problem and utilizing another mathematical problem known as factorization problem (FP) Rivest, Shamir, and Adleman (1978) introduced the asymmetric encryption technique RSA using two correlated keys; Multiple methods were introduced to generated such keys see FIM (Abu-Ayyash & Jabbar, 2003).

Another recent solution for key distribution was achieved by utilizing a well-known scientific problem related to quantum physics known as uncertainty (Price, Chissick, & Heisenberg, 1977); were two co-related properties of a quantum particle cannot be measured with high precision at the same time, Wiesner (1983) was the first to suggest using it, followed by Bennett and Brassard (1984); Since then, lots of quantum key distribution (QKD) protocols were proposed (Nung & Kuo, 2002; Bennett, 1992; Ekert, 1991; Kak, 2006; Kanamori, Yoo, & Al-Shurman, 2005; Bostrom & Felbinger, 2002; Lucamarini & Mancini, 2004; Wang, Koh, & Han, 1997; Barrett, Hardy, & Adrian, 2005).

Some well-known protocols, in addition to implementations, suffers from big losses comparing the size of the final key to the number of quantum states (particles) used. The loss is due to the protocol implementation steps, in addition to the characteristics and implementations of physical devices and channels used (Abu-ayyash & Ajlouni, 2008; Bennett & Brassard, 1992).

Researchers have already tried to solve this problem in a multi-dimensional space: first by enhancing the physical devices, channels, parameters and implementations (Chou, Polyakov, Kuzmich, & Kimble, 2004; Santori et al, 2004; Tisa, Tosi, & Zappa, 2007); second by increasing the information content in the quantum particle states used (Groblacher, Jennewein, Vaziri, Weihs, & Zeilinger, 2005; Kuang & Zhoul, 2004); third by using other quantum phenomena such as EPR (Einstein, Pololsky, & Rosen, 1935; Ekert, 1991; Kuang & Zhoul, 2004); fourth by changing or enhancing the way the protocol works (Abu-ayyash & Ajlouni, 2008; Nung & Kuo, 2002; Kak, 2006; Kanamori, Yoo, & Al-Shurman, 2005; Barrett, Hardy, & Adrian, 2005).

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