Reversal Cipher
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see math notation
given two bijective ‹functions f and g with identical function › domain and function › range, the compositions e = `fg and `e = `gf are inverses of each other, forming the encipher-decipher pair of a reversal cipher
both the function › domain and function › range of e and `e are identical to the function › domain of f and g. consequently, reversal ciphers are most useful when the function › range of the bijections is awkward to work with
example
the function › domain of touch-typing is a set of characters and its function › range is key positions on a keyboard. within this model, a keyboard layout setting is the inverse of touch-typing that keyboard layout, which is obvious given that
a`b = {*} == a = `b#todo id. therefore, let us define:
fto be qwerty layout touch-typinggto be dvorak layout touch-typing`fto be qwerty layout setting`gto be dvorak layout settingfrom the above we may deduce:
e = `fgto be dvorak layout touch-typing on qwerty layout setting`e = `gfto be qwerty layout touch-typing on dvorak layout settingthat is, dvorak layout touch-typing on qwerty layout setting and qwerty layout touch-typing on dvorak layout setting are inverses of each other, forming the encipher-decipher pair of a reversal cipher