Positional Mimic Cipher (PM-Cipher)

[quimqu]

Is it possible to compute the entropy with the residuals? Just to have a better understanding.

OK, here are the entropies and helpful calculations for Culpepper ciphered with PM_cipher in single character mode (no bigrams):

Symbols at ambiguous slots (bucket>1): 164,731 / 169,710 (97.07%): positions where the glyph’s bucket has more than one possible token (ambiguity exists), regardless of which residual was chosen.

Symbols that actually required residual (residual>0): 96,425 / 169,710 (56.82%): cases where the default index (0) was not used, so a side note had to be written to disambiguate.

Residual bits/symbol E[H(R | pos,g)]: 1.762 expected residual info per glyph if you always transmit the residual index (including 0).

=== Glyph entropies (bits/symbol): word-reset model ===
H1(G) = 3.387
H2(G) = 2.326
H3(G) = 2.002
H4(G) = 1.603

Approximate joint bits/symbol (glyph + residual side info):
H1(G) + residuals ≈ 5.149
H2(G) + residuals ≈ 4.088
H3(G) + residuals ≈ 3.765
H4(G) + residuals ≈ 3.365

(I am not sure if this can be calculated so directly with a simple addition. I think entropy does not have this property. I mean, we calculate entropy of the ciphered text (chains of characters) and entropy of the residuals (chains of numbers) and I am not sure we should make the addition.)

I treated residuals as a side channel depending only on (position, glyph), so their expected cost is a constant add-on to every Hn(G).