Can Base64 be seen as a way of encryption if we use different index table?

As we know, the index table (which maps bytes in [0, 63] to characters) of Base64 encoding is public, so everyone can decode Base64 strings from others.

But what if we use a shuffled index table and keep it secret? Can we see Base64 with this new table as some sort of safe encryption, and the shuffled table as cipher?

• Did you see permutation cipher? Some sort of frequency attack will be possible. But there is no security against known plaintext attack. – kelalaka Dec 2 '18 at 17:04
• @kelalaka actually this is a substitution cipher as the ciphertext is not an anagram of the plaintext. – SEJPM Dec 2 '18 at 19:13
• @SEJPM yes, the correct term, thanks. Modulo 24-bit, the conversion bits (6 vs 8) fits. If we arrange the ciphertext column-wise, the frequency attack must be still working. – kelalaka Dec 2 '18 at 19:19
• – Ilmari Karonen Dec 4 '18 at 15:15

NO! This is essentially a monoalphabetic substitution cipher applied on the Base64 encoded data. This can be seen as you can always take your table $$T$$ and then find a new $$T'$$ that undoes the base64 table encoding first and then applied after standard Base64 encoding.
Now while the key size is (theoretically) respectable with $$\log_2 (64!)\approx 296$$ bit, this cipher suffers from all the usual problems such ciphers have, including: