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Results tagged with perfect-secrecy
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user 12016
Confidentiality in a very strong sense. Ciphers reaching perfect-secrecy can't be broken to disclose informations over the plaintext from the ciphertext, even with unlimited computing power. The most known example cipher reaching perfect screcy is the one-time-pad.
1
vote
Accepted
Understanding how to proof an encryption scheme is perfectly secret
Where is the problem? Your reasoning seems correct, but you obviously are uncomfortable with probability (at least).
You used the definition of the encryption scheme in (1) and then the standard expr …
- 23.7k
1
vote
Why is perfect secrecy defined under a ciphertext-only threat model?
Perfect secrecy is about confidentiality (secret = confidential), and the weakest setting where it makes sense is in a ciphertext only attack. The other attacks are stronger, namely chosen ciphertext …
- 23.7k
5
votes
Is the one-time pad still perfectly secret if all-zero keys are excluded?
Yes your solution is correct; the flawed OTP scheme is no longer perfectly secret if there are fewer keys than messages.
Once you remove the all zero key the property
$$
\mathbb{P}[M=m|C=c]=\mathbb{P …
- 23.7k
3
votes
Accepted
What does the probability subscript mean in Shannon's secrecy definition?
This is standard notation in information theory but it is redundant as given here, usually it is used as below.
For example
$P_M(m)$ would be used instead of $P_M(M=m)$ both of which refer to the ra …
- 23.7k
0
votes
Proving security of (2,2)-Blakley's Secret Sharing scheme
Edit: The randomness in this setup comes from the uniform choice
of $a_i,b_i,y_0,$ there are $p^3$ possible values equally likely and each of the values for $S$ occurs $p$ times. So the probability of …
- 23.7k
2
votes
Secret sharing is based in random variables that are uniformly distributed?
Yes because
Uniform distribution has the highest entropy.
Even if you have a good mixing function $f$ that is part of a secret sharing scheme, it is very difficult to have $f(X,X’)$ uniform if at lea …
- 23.7k
25
votes
Are one-time pads crackable in theory?
To begin with, your definition of perfect secrecy is non-standard. The standard definition is given in an excellent answer to the question how is the OTP perfectly secure?.
Essentially, perfect secr …
- 23.7k
1
vote
Shannon theorem of perfect secrecy
The statement "But, for this we need a different key per message m" implies a different key for each fixed message, that's what "per message" is intended to mean. So the number of keys must be at leas …
- 23.7k
2
votes
Accepted
Does an information-theoretically secure hash function exist?
The Gilbert-MacWilliams-Sloane MAC referred to by @SqueamishOssifrage in the comments is information theoretically secure "for single use", at the cost of having hashes that have length $2\ell$ for fi …
- 23.7k
-1
votes
Defining the random variables $K,M,C$ and Perfect Secrecy
I don't really understand the significance of a more formal definition of random variables in this context. What would they bring to the table? What is there that we can't do under the current formali …
- 23.7k
8
votes
why XOR is recommended/Used in every paper I read for encryption and decryption stream cipher?
Edit: For any additive group operation, including addition modulo $k$ if the added keystream symbols $z_t$ are uniformly distributed, which means
$$
Pr(z_t=a)=1/k, \quad \forall a \in
\{0,\ldots, k-1 …
- 23.7k