If conjugate search problem of permutation is difficult , then there are next cryptosystem will appear.
A=XYX−1,B=XZX−1,Y and Z are public key.And X is secret permutation. then encryption is C=YZZYZYYZY... at random,and D=ABBABAABA follow to C. c=H(C)+m. Bob send D and c as cipher text.
decode Alice calculate XDX−1=C,and m=H(C)+c,m is plain text.
Is this cryptography insecure?