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In OTP you have $C=K\oplus{M}$. If the key is the same $C1=K\oplus M1$ and $C2=K\oplus M2$, => $C1 \oplus C2$ = $K\oplus M1 \oplus K\oplus M2$ = $M1 \oplus M2$ If you have the same ciphertext, that means that the same message was encrypted. E.g. messages 4,6,7,11 have the same first 6 symbols.


For the one time pad, your key must be The same length as the message. Whatever your unit of measurement (bits, bytes, etc), they must be the same length. The key must be perfectly random. The key is only ever used once.


No, you can reuse a message as often as you want with the OTP. (But never reuse the key!) What happens if you reuse a key? The attacker can xor the two encrypted messages (ciphertexts) and gets the xor of the two plaintexts. The xor of two messages is highly insecure and can be easily turned into two plaintexts with some know patterns. What happens if you ...


No. As the key should be fully random - a premise that invalidates the use of an OTP in practice - that should not matter at all.


It depends on what you think of as an alternative. If you think of the scheme where you do not use M as a modulus, but the keys a picked as: $$ k \leftarrow \{1, \ldots, M-1\} $$ Encryption: $$ C = d + k $$ Decryption: $$ d = C - k $$ Then the scheme is insecure. One way to see this is to note that we have C >= d. So the ciphertext communicates the ...

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