Secret sharing system using (k, L, n) threshold scheme

Abstract

Abstract In the ( k, n ) threshold scheme, the information X is partitioned and coded into subinformation. If any k subinformation is obtained among n subinformation, the original information X can be recovered completely. However, no information can be obtained at all concerning X from any ( k – 1) subinformation. Thus, the ( k, n ) threshold scheme is suited to the distributed storage or transmission of information. On the other hand, each subinformation requires the same number of bits as the original information X , which is very inefficient from the viewpoint of the coding efficiency. This paper extends the ( k, n ) threshold scheme and proposes the ( k, L, n ) threshold scheme. In the proposed scheme, the original information can be recovered completely from any k subinformation, but no information concerning X is obtained at all from any ( k – L ) subinformation. From any ( k – t ) subinformation (1 ≤ t ≤ L – 1), the information obtained for X contains the ambiguity of ( t/L ) H ( X ). In ( k, L, n ) scheme, the bit‐length of each subinformation is 1/ L of the information X , which is a coding with very high efficiency. This paper presents a construction method for ( k, L, n ) threshold scheme, together with the discussion of its characteristics.