2 ms·

I'm not sure I agree. In the case of new source D, C is being used as the key, not the encoded data. > B^C gives you back A If both B and C are pure noise, wh

I'm not sure I agree. In the case of new source D, C is being used as the key, not the encoded data. > B^C gives you back A If both B and C are pure noise, where did the information for A come from?

account42 1y ago
XOR is commutative so for a one-time pad key and ciphertext can be swapped. In this example given ciphertext C = A ^ B you can decrypt plaintext A using key B or you can decrypt plaintext D using key E = C ^ D: ( A ^ B ) ^ B = A ( A ^ B ) ^ ( C ^ D ) = ( A ^ B ) ^ ( A ^ B ) ^ D = D B and C are pure noise individually but they are not uncorrelated just like E and C are not uncorrellated.
- lioeters 1y ago
  Thanks for engaging in this discussion and explaining your thoughts. I'm still trying to understand. > given ciphertext C = A ^ B you can decrypt plaintext A using key B Right, C ^ B = A, to get back the original. Already here, it seems to me that C is not pure random noise if A can be recovered from it. C contains the encoded information of A, so it's not random. Is that wrong? --- > or you can decrypt plaintext D using key E = C ^ D In this example, isn't E the cyphertext and C is the key? E (cyphertext) = D (original) ^ C (key). Then E ^ C = D, to get back the original. Here, it seems to me that E contains the encoded information of D, so it's not random. And C plays the role of a key similar to B, so it's not being decoded as a ciphertext in this case, and nothing is implied whether it's random or not. > XOR is commutative so for a one-time pad key and ciphertext can be swapped. Maybe this is what I'm missing. In the second example, I'll swap the ciphertext and key: C ^ E = D Hmm, so both C and E are required to recover D the original information. Does that mean that the information was somehow distributed into C and E, so that they are both meaningful data, not random? --- But what about B in the first example, a key that was supposed to be pure random? If I swap the ciphertext and key: B ^ C = A The information in A is recovered from the interaction of both B and C. So the entirety of the information is not in C, the ciphertext (or key in this case). Does that mean, B is no longer pure noise? When it was used as a key, it became meaningful in relation to A. That's information, isn't it?

I'm not sure I agree. In the case of new source D, C is being used as the key, not the encoded data. > B^C gives you back A If both B and C are pure noise, where did the information for A come from?

account42 1y ago

XOR is commutative so for a one-time pad key and ciphertext can be swapped. In this example given ciphertext C = A ^ B you can decrypt plaintext A using key B or you can decrypt plaintext D using key E = C ^ D: ( A ^ B ) ^ B = A ( A ^ B ) ^ ( C ^ D ) = ( A ^ B ) ^ ( A ^ B ) ^ D = D B and C are pure noise individually but they are not uncorrelated just like E and C are not uncorrellated.

lioeters 1y ago
Thanks for engaging in this discussion and explaining your thoughts. I'm still trying to understand. > given ciphertext C = A ^ B you can decrypt plaintext A using key B Right, C ^ B = A, to get back the original. Already here, it seems to me that C is not pure random noise if A can be recovered from it. C contains the encoded information of A, so it's not random. Is that wrong? --- > or you can decrypt plaintext D using key E = C ^ D In this example, isn't E the cyphertext and C is the key? E (cyphertext) = D (original) ^ C (key). Then E ^ C = D, to get back the original. Here, it seems to me that E contains the encoded information of D, so it's not random. And C plays the role of a key similar to B, so it's not being decoded as a ciphertext in this case, and nothing is implied whether it's random or not. > XOR is commutative so for a one-time pad key and ciphertext can be swapped. Maybe this is what I'm missing. In the second example, I'll swap the ciphertext and key: C ^ E = D Hmm, so both C and E are required to recover D the original information. Does that mean that the information was somehow distributed into C and E, so that they are both meaningful data, not random? --- But what about B in the first example, a key that was supposed to be pure random? If I swap the ciphertext and key: B ^ C = A The information in A is recovered from the interaction of both B and C. So the entirety of the information is not in C, the ciphertext (or key in this case). Does that mean, B is no longer pure noise? When it was used as a key, it became meaningful in relation to A. That's information, isn't it?