3.º a 5.º gradoApplied MathematicsPlanificado
Secret codes
Hiding messages with simple codes: Caesar shifts on an alphabet wheel, substitution ciphers, breaking codes by counting letter frequencies, and why the alphabet 'wraps around'.
math.applied.secret-codes
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Se basa en
Requisitos previos obligatorios, hasta el fondo: 3
Aprenderás a
- Encode and decode messages with a Caesar shift using an alphabet wheel.
- Break a Caesar cipher by trying every shift, and a simple substitution cipher by counting letter frequencies.
- Explain why shifting past Z wraps around to A.
Definición
- A cipher is a rule for turning a message into a disguised form and back again.
- A Caesar shift replaces each letter by the letter a fixed number of places later in the alphabet, wrapping round from Z to A.
- The key is the secret information needed to decode a message, such as the size of the shift.
Teorema
- A 26-letter alphabet has only 25 non-trivial Caesar shifts, so the cipher can be broken by trying them all.
- A shift forward by k is undone by a shift forward by 26 − k.
- In English text some letters, such as E, are much more common than others, which helps to break substitution ciphers.
Errores frecuentes
- Thinking a code is secure because the message looks scrambled.
- Forgetting to wrap around at the end of the alphabet.
Descubrimientos opcionales
- Clock arithmetic: remainders and modular arithmetic A Caesar shift is addition modulo 26.
- Cryptography Modern cryptography gets its security from number theory and computational hardness, not from keeping the method secret.
Lecturas complementarias
- Simon Singh, The Code Book (1999)