The Research Of Some Combinatorial Designs In Information Security

Since Blakley and Shamir proposed secret sharing in 1979 independently, secret sharing schemes becomes an important issue in cryptography. A model of authentication and secrecy theory was introduced by Stinson, in which unconditionally secure secrecy and authentication codes are studied. In this paper, we investigate the combination structure in key management and authentication-secrecy system including the combinatorial constructions of perfect(t, w, v; λt-1)-threshold schemes, t-fold perfect csplitting authentication codes with equal deception probabilities,(t, t- 1)-fold optimal authentication-secrecy codes with c-splitting and(t, t- 1)-fold perfect authenticationsecrecy codes with c-splitting.In chapter 2, we prove that the existence of partitionable partially balanced t-designs PPBD t-(v, b, w; λt-1, 1, 0)s implies the existence of perfect(t, w, v; λt-1)-threshold schemes, moreover, the existence of optimal partitionable partially balanced t-designs OPPBD(t, w, v)s is equivalent to the existence of optimal(t, w, v)-threshold schemes in certain circumstances. We investigate the constructions and existence of partitionable partially balanced t-designs and then obtain some new infinity classes of optimal(t, w, v)-threshold schemes.In chapter 3, we prove that t-fold perfect splitting authentication codes with equal deception probabilities can be characterized in terms of orthogonal multi-arrays.Moreover, We investigate the constructions and existence of orthogonal multi-arrays,and show that the existence of orthogonal multi-arrays OMA(t, k × c, n)s is equivalent to the existence of transversal splitting t-designs splitting TD(t, k × c, n)s. Then we obtain some new infinite classes of t-fold perfect splitting authentication codes with equal deception probabilities.In chapter 4, we prove that(t, t-1)-fold optimal authentication-secrecy codes with c-splitting can be constructed by authentication perpendicular multi-arrays APMA(t, k×c, v). Moreover, we investigate the constructions and existence of authentication perpendicular multi-arrays, and show that authentication perpendicular multi-arrays can be constructed by splitting designs, then we obtain some new infinite classes of(t, t-1)-fold optimal authentication-secrecy codes with c-splitting.In chapter 5, we prove that(t, t- 1)-fold perfect authentication-secrecy codes with c-splitting can be constructed by authentication strong partially perpendicular multiarrays ASPPMA(t, k × c, v, b; λ1, λ2, · · ·, λt-1, 1). Moreover, we investigate the constructions and existence of authentication strong partially perpendicular multi-arrays,and show that authentication strong partially perpendicular multi-arrays can be constructed by holey authentication perpendicular multi-arrays, then we obtain some new infinite classes of(t, t- 1)-fold perfect authentication-secrecy codes with c-splitting.