arXiv subjects

Iharantsoa Vero Raharinirina

Publications and source records attributed to Iharantsoa Vero Raharinirina.

2 recordsLinked to original sources

arXiv2017

Use of Signed Permutations in Cryptography

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm. The fact that the group of signed permutations has rich properties provides fast and easy implementation and makes these systems resistant to attacks like the Pohlig-Hellman algorithm. The only negative point is that storing and transmitting permutations need large memory. Using together the hyperoctahedral enumeration system and what is called subexceedant functions, we define a one-to-one correspondance between natural numbers and signed permutations with which we label the message units.

cs.CR↗

arXiv2016

On Hyperoctahedral Enumeration System, Application to Signed Permutations

In this paper, we start by giving the definitions and basic facts about hyperoctahedral number system. There is a natural correspondence between the integers expressed in the latter and the elements of the hyperoctahedral group when we use the inversion statistic on this group to code the signed permutations. We use this correspondence to define a way with which the signed permutations group can be ordered. With this classification scheme, we can find the r-th signed permutation from a given number r and vice versa without consulting the list in lexicographical order of the elements of the signed permutations group.

math.CO↗