AES decryption with random keys gives unique entropy for each key (over 90% unique in test case)

aesentropy.py

#!/usr/bin/env python3
from collections import Counter
import math
from Crypto.Cipher import AES
from Crypto import Random

def multlog2(x):
    if x == 0:
        return 0
    return x*math.log2(x)

def entropy(bstr):
    #entropy of BYTES! Because plaintext is probably ascii or utf8.
    #bstr must be bytes
    cnt = Counter(bstr)

    entr = 0
    for c in range(256):
        p = cnt[c]/len(bstr)
        entr += multlog2(p)

    return -entr


def newaes(k):
    return AES.new(k, IV=b'0'*16, mode=AES.MODE_CBC)
aes = newaes(b'k'*16)
c = aes.encrypt(b'\x00'*16*42)

def dec(k, c):
    return newaes(k).decrypt(c)

es = []

for i in range(256):
    k = bytes((i for _ in range(16)))
    es.append(entropy(dec(k, c)))

for _ in range(100000):
    k = Random.new().read(16)
    es.append(entropy(dec(k, c)))

print(sorted(es))

numdups = len(es) - len(set(es))
print(numdups)
print("unique entropy: {}%".format((len(set(es))/len(es))*100))

For 100000 random keys, entropy is about 92%.
For 1000000 random keys, unique entropy drops to 60%. Textlength probably needs to be increased.