Bounds on encryption using linear code ciphers

Abstract

Summary form only given. When a memoryless source of entropy H is enciphered using cipher sequences from some linear (n, nR) code of rate R, the average distortion D for unauthorized decryption is shown to be lower bounded by the expression Rr(D/R) ≤ Hmax-H, where Hmax = log2|AM| is the source entropy when the letters in its alphabet are equally likely. Using cipher codes where every nR positions form an information set, D is bounded by the tighter expression Rr(D) ≤ Hmax -H. Both bounds improve on Lu's bound r(D ≤ 2Hmax - RH - H for 1 - H/Hmax ≤ R ≤ 1 except at the boundaries, where they are equal.