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Jul
1
comment Exactly two of the four roots must be greater than N/2
It is correct for all primes greater than 2. There are (at least) 4 square roots if $\phi(N)$ is a multiple of 4. And for every uneven $p,q$, that's the case.
Jun
30
comment How to prove NIZK proof of knowledge?
The problem is, there is no $s$. Of course you can base $st_i$ on some value $s$ and reuse this. But you can not prove that to anyone. The protocol would have the very same statistical distribution as if you chose $st_i$ at random in every round. Assume e.g. the cyclic group $\mathbb{Z}_3^*=\{1,2\}$. Assume $s$ is from that group, too, but fixed, and $s'$ the other element (also fixed). Now it doesn't matter if I give you $t_i$, $s\cdot t_i$ or (s' \cdot t_i). In either case, if $t_i$ is chosen uniform, those 3 choices are uniform, too. But you can not prove that you used a fixed $s$ either.
Jun
30
comment Functions that are only second-preimage resistant?
I don't think that there is such a function. Noncryptographic hash functions are neither designed for nor examined w.r.t. preimage resistance. Either you care for cryptographic aspects and then you need to do it properly, or you don't. I don't think there is a middle ground.
Jun
26
comment RSA example-calculation: Public Key = Private Key (e = d)
Have a look here, that's the same problem with different numbers ($e=d=5, N=15,\phi(N)=12$)
Jun
24
revised Choose a random number that is different from a bunch of other secret numbers
revised my statement
Jun
24
comment Choose a random number that is different from a bunch of other secret numbers
Hm, you're right about that, there is a ZK proof. But even thinking about it makes my head hurt... I'll change my answer accordingly, and add how to go about it.
Jun
23
comment What algorithm would give the shortest ciphertext for very short plaintexts?
Ah, you're right about counter mode offering no integrity any more. But it does avoid the weakness of ECB that the same plaintext is always transformed into the same ciphertext. But I guess, counter mode is after all a bad idea.
Jun
23
comment What algorithm would give the shortest ciphertext for very short plaintexts?
Alternatively, AES in counter mode also hides the ECB weakness. If you have some part of the message as verification means (something like 3 bytes zero at the end), it doesn't even matter if packages arrive slightly out of order, because multiple counter increments can be tested.
Jun
23
comment What algorithm would give the shortest ciphertext for very short plaintexts?
Do not do this. Especially if you have a very small plaintext space, ECB performs poorly. Imagine using AES in ECB mode on messages with length 1 bit. Every message would be an encryption of $0$ or $1$. Finding out what is $E(0)$ and $E(1)$ is not that much guesswork any more. Especially with short messages, it is very important to have some form of randomization to hide the fact that the same message has been encrypted.
Jun
23
answered Choose a random number that is different from a bunch of other secret numbers
Jun
23
comment Functions that are only second-preimage resistant?
The definition of collision resistance means "find two values, which result in the same hash". If such a value is already baked in the definition of the function, collision resistance is broken. Additionally, the (small) difference between first and second preimage resistance becomes clear when you look for the $a\neq b$ statement, although in real functions are considered pretty much the same. But for example the identity function is collision resistant and second preimage resistant but not first preimage resistant.
Jun
23
comment Functions that are only second-preimage resistant?
Dingo, you might want to state what your actual goal is. Avoiding to use a "normal" cryptographic hash function? Or do you actually want to have something that is not collision resistant? As practical example of such a function, you can use MD5, which is broken for collision resistance but preimage resistance is still considered okay-ish.
Jun
23
comment In public key cryptography, how many keys are required for secure communication between n parties?
You're welcome. But tbh, most of this discussion still should be deleted. This isn't a discussion forum. Next time you have a question try asking the real question instead of providing the answer and asking "Am I right?". If you focus on what is actually unclear to you, you will get more helpful answers. And I suggest keeping an open mind instead of insisting on your own thought process.
Jun
23
comment In public key cryptography, how many keys are required for secure communication between n parties?
I'm voting for closing this thread now, because it started to become a discussion. Besides being pretty much "below homework level", this question isn't beneficial for anyone else, because the basic understanding of the question is just wrong.
Jun
23
comment In public key cryptography, how many keys are required for secure communication between n parties?
I have absolutely no clue what that diagram shows, but your thought process is totally wrong, yes. The assumption in your question is "there are public keys". and that means "they are secure". Questioning the assumption of the question is plain wrong.
Jun
23
revised In public key cryptography, how many keys are required for secure communication between n parties?
removed "cryptanalysis" tag
Jun
23
comment In public key cryptography, how many keys are required for secure communication between n parties?
As mikeazo said, the answer is $2n$: each user has one private key and one public key. That's it. But because public keys are public, everyone has all $n$ public keys (including his own). Since people don't need their own public key, it's enough to know the own private key and all $n-1$ public keys of the other users.
Jun
23
comment Is email an example of public-key cryptography?
The lockbox analogy is usually used for symmetric encryption or commitments, and it is a little off for public key encryption (everynoe can create the lock, but only the owner has the key to unlock it). However, I think email is an even worse example, since it provides a false sense of confidentiality or is based on wrong assumptions about email. There is no confidentiality for transmission of emails. There is no proof that an email actually came from a certain email address or that the email wasn't tempered with. Email doesn't fulfill any security definition on its own.
Jun
23
reviewed Reviewed In public key cryptography, how many keys are required for secure communication between n parties?
Jun
23
comment In public key cryptography, how many keys are required for secure communication between n parties?
Why would every party have one public key and $n$ private keys? That would mean there are $n$ public keys and $n^2-n$ private keys in the total system. Usually there is one public key for every private key, so the answer you proposed in the question is wrong. It is correct, that each user will have a total of $n$ keys, but the distribution of public and private keys will be different, and there are duplicates over all users (the questions states how many keys are required, not how many keys are in the system).