23-08-2026, 03:54 PM
While studying Roman numeral systems and ciphers, I found two features. that could greatly help with learning the VMS cipher (but I still don’t know how
). These are the general statistical features characteristic of Roman numerals as a whole.
1). The asymmetry of character distribution: Due to the constant ratio of 14:5 in Roman numerals, the density of symbols of the first rank (I, X) in the ciphertext is significantly higher than that of the fifth‑rank symbols (V, L). Well, essentially, it’s the same as the 14:5 law: in each decimal place from 1 to 9, the symbols of the unit type sum up to 14 occurrences, while those of the quinary type sum up to 5 occurrences (for example: I - 14 times, V - 5 times). This results in a constant frequency asymmetry of 14:5
Simply put: in a ciphertext, regardless of which letter is the most frequent and which number corresponds to it, the most frequent element will be I.
2). Since the cipher alphabet is based only on basic Roman numerals and does not encode any digrams such as IV/VI, the Shannon entropy will be very low compared to the plaintext (I learned this from Gemini!):
Given that the encoding principle in VMS differs from simple digit encoding, there is still a match. Its entropy is quite close to 2.3!
So far, this is the most amazing thing for me.
). These are the general statistical features characteristic of Roman numerals as a whole.1). The asymmetry of character distribution: Due to the constant ratio of 14:5 in Roman numerals, the density of symbols of the first rank (I, X) in the ciphertext is significantly higher than that of the fifth‑rank symbols (V, L). Well, essentially, it’s the same as the 14:5 law: in each decimal place from 1 to 9, the symbols of the unit type sum up to 14 occurrences, while those of the quinary type sum up to 5 occurrences (for example: I - 14 times, V - 5 times). This results in a constant frequency asymmetry of 14:5
Simply put: in a ciphertext, regardless of which letter is the most frequent and which number corresponds to it, the most frequent element will be I.
2). Since the cipher alphabet is based only on basic Roman numerals and does not encode any digrams such as IV/VI, the Shannon entropy will be very low compared to the plaintext (I learned this from Gemini!):
Given that the encoding principle in VMS differs from simple digit encoding, there is still a match. Its entropy is quite close to 2.3!
So far, this is the most amazing thing for me.

