This question's explanation and your answers so far.
小文字の英字からなる文字列の暗号化を考える。次表で英字を文字番号に変換し，変換後の文字番号について1文字目分には1を，2文字目分には2を，…，n文字目分にはnを加える。それぞれの数を26で割った余りを新たに文字番号とみなし，表から対応する英字に変換する。 例 fax → 6, 1, 24 → 6+1, 1+2, 24+3 → 7, 3, 27 → 7, 3, 1 → gca この手続で暗号化した結果が“tmb”であるとき，元の文字列はどれか。
| 文字番号 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 英字 | a | b | c | d | e | f | g | h | i | j | k | l | m |
| 文字番号 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| 英字 | n | o | p | q | r | s | t | u | v | w | x | y | z |
Encrypting “she” gives s=19, h=8, e=5 → 19+1=20, 8+2=10, 5+3=8 → “tjh”, which is not “tmb”. The 2nd and 3rd characters do not match.
Encrypting “shy” gives s=19, h=8, y=25 → 20, 10, 28→2 → “tjb”. The 1st and 3rd characters match, but the 2nd character is j, not m.
Encrypting “ski” gives s=19, k=11, i=9 → 20, 13, 12 → “tml”. The 1st and 2nd characters match, but the 3rd character is l, not b. This is an easy wrong answer to pick if you make a mistake decrypting the 3rd character (b→y).
正解 The encryption rule is “add the position n to the character number, then take the remainder divided by 26 as the new character number”, so decryption is simply the reverse: “subtract the position n from the character number”. Converting the ciphertext “tmb” with the table gives t=20, m=13, b=2. For the 1st character, 20−1=19 → s; for the 2nd, 13−2=11 → k; for the 3rd, 2−3=−1, which is negative, so add 26 to get 25 → y. Put together, the original string is “sky”, so エ is correct. As a check, encrypting “sky” gives s=19, k=11, y=25 → 19+1=20, 11+2=13, 25+3=28 → the remainder of 28 divided by 26 is 2 → 20, 13, 2 → t, m, b, which is back to “tmb”. Also, as the example “27 → 1” shows, the key point is the wrap-around handling: when a number exceeds 26, subtract 26 (that is, take the remainder).