# Is there a practical security difference between OTP with letters and OTP with numbers?

Is there a practical security difference between “OTP with letters” and “OTP with numbers”?

If, for example, I encrypt a letter message using Tabula Recta with a random letter key, I would get:

THISI SATES TXAAA - message
MOSSK VFXNN EJRQW - OTP key
FVAKS NFQRF XGRQW - cipher


Would such encryption be less secure when it comes to frequency analysis, compared to (let's say) Dirk Rijmenant's CT-46 OTP where the most frequent letters (AEINOR) are associated with a single digit instead of two digits, like the rest of the less frequent letters in the alphabet?

Example:

THISI SATES TXAAA
83753 82390 82183 28290 83871 11000 - message
08733 64840 36236 58407 58482 94160 - OTP key
85020 28550 56957 70893 35499 27940 - cipher

• No, OTP has perfect secrecy regardless of what encoding your message uses. – otus Aug 29 '15 at 12:10
• Hint: Can you find an OTP key(part) that maps an arbitrary cipher text to an arbitrary plain text. Or formulated differently: Can every cipher text letter be decrypted to every plain text letter if an appropriate OTP is used? – SEJPM Aug 29 '15 at 12:11

There is no security difference. Of course, purely random characters with entropy rate $\log M$ where $M$ is the size of the alphabet should be independently generated and used for the OTP, whatever the size $M$ of the alphabet.

Letters only allow you to use letters and nothing else.

So you would only be able to send a message like this:

MEETA GENTV LADAT DINER ATTWO


Where as if you use numbers you can send messages with virtually all the different characters you want:

Meet Agent Vlad at diner at 2.

• Yes; but the question asks for "a practical security difference". – fgrieu Sep 17 '15 at 15:43
• Of course. Provided that ALL of the rules regarding OTPs are followed to the letter with NO shortcuts, it matters not what you use. On that note there is a ASCII Armor scheme called Codegroup that allows you to convert binary data into 5 letter groups. So if you were to encode your data with that and then apply the Letters OTP then you could solve that problem. – WAR10CK Sep 17 '15 at 15:51
• I have to agree with @fgrieu. This doesn’t really seem answer the question. You provide an example of the difference in encoding when using both, which is nice… but what is the “practical security difference”? Or are we simply not understanding you and you are pointing to some security difference between writing two and 2? If, it would probably be constructive to help us understand your answer by describing whatever difference in security you see there. – e-sushi Sep 17 '15 at 21:26
• I am simply stating that it is much more practical to use numbers to encode OTP messages which I like to call Numbers Messages because of the fact that you have more flexibility and messages can also be shrunk by using a code book as well. So in the unlikely event that a pad is compromised there is still one more layer of security. Even if it is weaker. – WAR10CK Sep 18 '15 at 18:12