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Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
Also, testing if $x|0$ is just a matter of testing if $GCD(x,n) = 0$.
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
The value of $n - \varphi(n)$ is highest for $n$ that consist of a product of the smallest primes, each with exponent $1$. For $n = 2\times3\times5\times7\times11\times13\times17\times19\times23$ it is approximately $5/6$.
Feb
24
revised $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
If $x|0$ then $f(x) = 1$.
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
If it does invalidate the 'invertible' term, then, by the pigeon hole principle, there are no functions that satisfy the criterion in the question.
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
I think this depends on the definition of $\mathbb Z_n^\times$. If we exclude not only 0 but also all divisors of 0, and $n$ is composite, then there are more bad points, yes. In such case a trivial example is the identity function except $f(x) = 1$ if $x|0$.
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
Of course there are. A trivial example is the identity function except $f(0) = 1$.
Feb
24
comment Get permutations from password
@fgrieu: I am afraid using a slow PBKDF will not matter much unless a salt is used as well. If no salt is used, slowing the PBKDF down will just slow down the precomputations (generation of permutations corresponding to common passwords).
Feb
24
revised Get permutations from password
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Feb
24
comment Get permutations from password
@fgrieu: Yes, that would be a more efficient algorithm. It requires a deeper understanding of permutation composition for the reader to deduce surjectivity, though, but it should be added to my answer.
Feb
23
revised Get permutations from password
added 2 characters in body
Feb
23
answered Get permutations from password
Feb
21
comment Why do we use XTS over CTR for disk encryption?
Nice answer, but newer content replaced with older content will be a concern even if you use authenticated encryption. Prevention of replay attacks requires more than just authenticated encryption.
Feb
21
comment Is script execution time a decent source of pseudorandom number generation?
There might be a certain amount of unpredictability in this (presuming the adversary doesn't have full access to the parent system and you don't do this in the context of responding to the request), but you need a high resolution timer (not just microtime) and more than a single timing.
Feb
20
comment What informal indicators exist for estimating the computational infeasibility of cryptographic problems?
Also, it would be possible to formulate a valid hypothesis based on anecdotal experience, either if it demonstrates that no such study could ever eliminate a significant amount of inherently unknown hidden statistics, or, conversely, if it indicates exactly what kind of evidence should be collected to reach a reliable answer.
Feb
20
comment What informal indicators exist for estimating the computational infeasibility of cryptographic problems?
These kinds of things are very similar to what is studied in social sciences and economics. In principle, we don't have to guess. However, if no such research has been done, either due to lack of interest or lack of opportunity to collect the necessary data, that would also be an interesting answer.
Feb
20
revised What informal indicators exist for estimating the computational infeasibility of cryptographic problems?
edited body
Feb
20
revised What informal indicators exist for estimating the computational infeasibility of cryptographic problems?
added 309 characters in body
Feb
20
asked What informal indicators exist for estimating the computational infeasibility of cryptographic problems?
Feb
16
comment My SSH server public key is 2048 bits, but my account's private key is 4096. What is my effective security?
@Gilles: Right, the question makes more sense if the second key is a public key server side, and is used for client auth.
Feb
14
comment Why is a 2048-bit public RSA key represented by 540 hexadecimal characters in X.509 Certificates?
Minor nit: X.509 objects are always DER encoded and not just BER encoded. DER is a subset of BER, so you might decode any DER encoding with a BER decoder, but the converse is not (necessarily) true, because DER encoding is unequivocal, while BER encoding is not.