Department of Complexity Science and Engineering Graduate School of Frontier Sciences The University of Tokyo

Hirosuke Yamamoto

Scripta Technica, Inc.,Electronics and Communications in Japn,Part 1, Vol.69, No.9, pp.46-54, 1986.

• 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 proposed 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 $(1\leq t\leq L-1)$ , 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.
  
  
• PDF (936Kbytes)　DOI:10.1002/ecja.4410690906