For common multi-block encryption schemes (CBC, CTR, CFB, stream ciphers, etc), if they are forced to be deterministic, a change in the plaintext will change only the current block and maybe future blocks, but the past blocks are unchanged.
Using DES-CBC as an example, I've fixed the IV as to force it to be deterministic. (DES is used here for the small block size, for convenience)
Input: 0001020304050607 08090a0b0c0d0e0f 1011121314151617 18191a1b1c1d1e1f 2021222324252627 28292a2b2c2d2e2f Output: 4c72f896d0b5c010 96cafa256bd7bf8c 7f3dfa17eb0721d6 2db73b14cfa32977 e87a8caf18ace662 298640486525ca14
Now to change one bit in the third block.
Input: 0001020304050607 08090a0b0c0d0e0f 1011321314151617 18191a1b1c1d1e1f 2021222324252627 28292a2b2c2d2e2f ^ Change Output: 4c72f896d0b5c010 96cafa256bd7bf8c 123ea45b2bc1d45b 876ee075d04e5c61 ea59edd03137781b 57cd1fafa7849fe2 Change ^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^
You'll notice that the first two ciphertext blocks are the same.
Are there any deterministic constructions that allow for any change of any bit in the plaintext to affect every bit of the ciphertext?