Re^2: ROT8000 implementation?

Actually, my understanding has always been that ROT-N is just a notation for a Caesar cipher with a specified N. ROT13 is the case of a Caesar cipher rotated by 13d characters, which when using the 26d (2d*13d) character Latin alphabet means that rot(rot(x, 13d), 13d)=x. For any other N, deciphering would be the case of using (26d-N), or rot(rot(x, N), (26d-N))=x. Extending this further, giving a ROT-N of an M-character alphabet, this becomes rot(rot(x, N), (M-N))=x. If N is larger than M, the encoding can be simplified to (N % M) and decoding to (M - (N % M)) (thus if M=26d, ROT-53d simplifies to ROT-1d, decoded by ROT-25d).

I have never heard of ROT-N notation being in anything but decimal (but that may also be my lack of exposure). As far as the most common encodings (UTF-8, UTF-16, and UTF-32), all support the 1_112_064d Unicode code points currently defined. Thus an N value of 556_032d (hex: 0x8_7C00) should result in the equivalent behavior for the existing defined code points to the ROT-13d with the 26d-character Latin alphabet (i.e., a self-decoding function).

Below are the encoding and decoding rotations for a 26d, 256d, and 1_112_064d character "alphabets" for various N. It should be noted using 0x8000 (32_768d) rotations on a 256-character alphabet is the equivalent of "double ROT-13d encoding" on a 26-character alphabet, and that using the current number of code points (1_112_064d) has the effect on both a 256-character and 1_112_064-character alphabet.

(If you find an error in my logic or values, please advise, so I can correct my understanding and/or data, as appropriate.)

Rotations 26d-char encoding 26d-char decoding 256d-char encoding 256d-char decoding 1_112_064d-char encoding 1_112_064d-char decoding

13d (0x0D) 13d (0x0D) 13d (0x0D) 13d (0x0D) 243d (0xF3) 13d (0x0D) 1_112_051d (0x10_F7F3)

26d (0x1A) 0d (0x00) 0d (0x00) 26d (0x1A) 230d (0xE6) 26d (0x1A) 1_112_038d (0x10_F7E6)

128d (0x80) 24d (0x18) 02d (0x02) 128d (0x80) 128d (0x80) 128d (0x80) 1_111_936d (0x10_F780)

256d (0x100) 22d (0x016) 4d (0x004) 0d (0x000) 0d (0x000) 256d (0x100) 1_111_808d (0x10_F700)

8000d (0x1F40) 18d (0x12) 8d (0x08) 64d (0x40) 192d (0xC0) 8000d (0x1F40) 1_104_064d (0x10_D8C0)

32_768d (0x8000) 8d (0x08) 18d (0x12) 0d (0x00) 0d (0x00) 32_768d (0x8000) 1_079_296d (0x10_7800)

556_032d (0x8_7C00) 22d (0x0_0016) 4d (0x0_0004) 0d (0x0_0000) 0d (0x0_0000) 556_032d (0x8_7C00) 556_032d (0x8_7C00)

1_112_064d (0x10_F800) 18d (0x00_0012) 8d (0x00_0008) 0d (0x00_0000) 0d (0x00_0000) 0d (0x00_0000) 0d (0x00_0000)

Hope that helps.

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Re^3: ROT8000 implementation?
by LanX (Saint) on Oct 16, 2021 at 08:19 UTC

it's a misnomer

There is no formula with fixed N here because it operates with a 2^16 lookup table to avoid non-printable characters in both directions.

Edit

So the actual N(X) for a mapping

Y=R(X)

N(X)= N(Y)= Y-X

will vary near approximately 2^15-20+-8 (?).*

And it ignores anything >= 2^16 like emojis, similar to ROT13 ignoring any ASCII outside the alphabet.

Cheers Rolf
_{(addicted to the Perl Programming Language :)

Wikisyntax for the Monastery}

*) Actually the description of the author was outdated and doesn't fit his code.

He's excluding 2100 characters.

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