The Set Partitions: Solution for sharing secret keys






Faculty of Mathematics

University of Sciences and Technology Houari Boumediene, USTHB Algiers, Algeria

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Faculty of Economics and Management Sciences

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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



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.



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