複数の情報源出力を伴うシャノン暗号システムに対する符号化定理に関する研究
Project/Area Number  04650279 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
電子通信系統工学

Research Institution  The University of Tokyo 
Principal Investigator 
YAMAMOTO Hirosuke The University of Tokyo, Department of Mathematical Engineering and Information Physics, Associate Professor, 工学部, 助教授 (30136212)

CoInvestigator(Kenkyūbuntansha) 
KOBAYASHI Kingo The University of ElectroCommunications, Department of Information Engineering,, 電気通信学部, 教授 (20029515)

Project Fiscal Year 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1993 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1992 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Cipher / Shannon Theory / Coding Theorem / Common Information / Correlated Source Outputs / 暗号 / シャノン理論 / 符号化定理 / 共通情報量 / 相関を有する情報源 
Research Abstract 
We obtained the following results for this research. 1. We can consider new coding problems for the following cases when we transmit a correlated source outputs (X, Y) via Shannon's cipher system. The coding theorems for such cases cannot be derived from the known results. We have perfectly proved the coding theorems by using the codes that can attain the common information, which is described in 2. ・ Secret information is both X and Y, only X, or only Y. ・ Transmitted information is both X and Y, only X, or only Y. ・ Security of the system is measured by 1/H(X^KY^<K >W)or(1/H(X^KW), 1/H(Y^KW)). 2. We can define common information for correlated source outputs (X, Y). In this research, we give the following two new definitions of common information, which are different from the known ones (i.e., GacsKorner's or Wyner's common information). (a) C_1(X ; Y) : The rate of the attainable minimum core of (X^K, Y^K) by removing each private information from (X^K, Y^K) as much as possible. (b) C_2(X ; Y) : The rate of the attainable maximum core of V_C such that if we lose V_C, then each uncertainty of X^K and Y^K becomes H(V_C). We evaluate these two common information theoretically, and we show that C_1(X ; Y)=I(X ; Y) and C_2(X ; Y)=max{H(X), H(Y)} hold.

Report
(4results)
Research Output
(7results)