The Set Partitions: Solution for sharing secret keys
Sadek BOUROUBI and Fella CHARCHALI
Faculty of Mathematics
University of Sciences and Technology Houari Boumediene, USTHB Algiers, Algeria
Cette adresse e-mail est protégée contre les robots spammeurs. Vous devez activer le JavaScript pour la visualiser.;';document.getElementById('cloak7c08912ba4af0bbecf1707bcc9d6ade4').innerHTML += ''+addy_text7c08912ba4af0bbecf1707bcc9d6ade4+'<\/a>';
Nesrine BENYAHIA TANI
Faculty of Economics and Management Sciences
2 Ahmed Waked Street, Dely Brahim Algiers, AlgeriaCette adresse e-mail est protégée contre les robots spammeurs. Vous devez activer le JavaScript pour la visualiser.';document.getElementById('cloak07775d05ec455d942739c1d06437593b').innerHTML += ''+addy_text07775d05ec455d942739c1d06437593b+'<\/a>';
Abstract—Confidentiality was and will always remain a critical need in the exchanges either between persons or the official parties. Recently, cryptology has made a jump, from classical form to the quantum one, we talk about quantum cryptography. This theory, although is perfectly safe, there are still binding limits of implementation. In this paper, we developed a new cryptographic protocol, called BCB12 protocol, which will be used to provide random keys shared via a classical channel, using the set partitions. Each key can be long enough that the plain text in question, in purpose, for instance, to hide then to transmit the secret information using the Vernam cipher.
Cryptography, Vernam Cipher, BCB12 Protocol, Set partitions
I. INTRODUCTION
Issues such as confidentiality and integrity of information have been solved by cryptography. The certificate that the Vernam cipher is unconditionally secure, has transformed the problem to ensure the confidentiality of information to a problem of distribution of the secret key used in the encryption process between two parties. Until the eighties, one way to distribute the secret key, apart from hand to hand, was to use algorithms whose security is based on the computational complexity. The keys generated by such algorithms are reasonably secret but not unconditionally secret.
In the early seventies, Stephen Wiesner wrote conjugate coding [3], describing the basis for a new concept that will be known to the world in the early eighty by quantum cryptography. Cryptography was attached to a quantum concept by the fact it relies on photons to transmit secret information instead of bits. Security is guaranteed not by mathematical theorems, but by the fundamental laws of physics as the Heisenberg uncertainty principle which asserts that certain quantities cannot be measured simultaneously.
Charles H. Bennett (who knew about Wiesner's idea) and Gilles Brassard took the subject in 1984 [4], where they show up to the world the first protocol of quantum key distribution whose security is unconditional because confidentiality is based on impossibilities imposed by the laws of physics [5]. This protocol was implemented in 1989 over a distance of 32 cm by calling efforts of F. Bessette, L. Salvail and J. Smolin, a full description of the prototype was published two years later [6]. All Quantum Key Distribution protocols consist of two phases [7]:
1. Initially one of the two parties sends to the other party
"quantum" signals then performs certain measurements.
2. In a second time the two parties engage in classical treatment of measurement results.
télécharger l'article