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Mar
17
comment Hash Based Encryption (fast & simple), how well would this compare to AES?
Why did you mark the first entry as a duplicate?
Mar
17
comment Hash Based Encryption (fast & simple), how well would this compare to AES?
@fgrieu: You are right, related key attacks against SHACAL-2 is an independent topic, and it has been studied.
Mar
17
revised Hash Based Encryption (fast & simple), how well would this compare to AES?
deleted 14 characters in body
Mar
17
answered Hash Based Encryption (fast & simple), how well would this compare to AES?
Mar
3
answered How does TLS generate the shared secret?
Mar
1
comment Need Help Reversing my Encryption Algorithm
This is off topic, because any answer would be of little or no use to anyone else. If you want to read up on one common way of making encryption algorithms invertible, you could e.g. check out en.wikipedia.org/wiki/Feistel_cipher
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
Perfectly correct, thanks.
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
$n$ that is a product of the smallest primes is a 'worse' case than powers of $2$.
Feb
24
comment $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$?
If $GCD(x-1,n) \neq 0$, then $f^{-1}(x) = x$. Otherwise, if $GCD(x-2,n) \neq 0$, then $f^{-1}(x) = \{x-1,x\}$ etc. I think this recursion has an estimate worst case running time of $ln(n)$.
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
added 1128 characters in body
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