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Nov
30
comment Is this problem based on a known hard problem?
Well for starters the set of $a_i$ can't be linearly independent otherwise this amounts to solving an $i \times n$ system $Ab = c$ for $b$ with $A$ invertible. It can be solved in the rationals and then scaled to get an integer solution. And for linearly dependent $a_i$, I would imagine some partial solution could be obtained as well (if one exists) using the same techniques. Unless I am misreading the problem...
Nov
29
comment Does SHA-1 hash have quasi commutative property?
Are you going to ask the same question for SHA-2 and SHA-3 as well? crypto.stackexchange.com/questions/20497/…
Nov
28
comment Issue about randomness : what if random looks “human” ?
The very first thing to realize is that randomness is not a property of any particular output sequence. The sequence "1234" is neither random nor predictable, it's meaningless to refer to it as random. Rather, randomness is a property of the process used to generate them. Once you understand that, things begin to seem less paradoxal.
Nov
22
comment Addition / Multiplication modulo 13
I'm not sure what you're asking. Are you wondering why $g = 2$, a generator of $Z_{13}^*$, is also a generator of $Z_{13}^+$ (it is)? If so, have you considered finding all the generators of $Z_{13}^*$, and all the generators of $Z_{13}^+$?
Nov
21
comment java.util.Random and Dice Rolls
@GuutBoy He wants to recover the state of an instance of the Java Random class given its outputs (as dice rolls) efficiently.
Nov
18
comment special public keys and modulo n
Are you talking about textbook RSA (no padding, just interpret the message as a number and raise it to an exponent) or real world RSA (with padding)?
Nov
4
revised Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
typo
Nov
3
comment Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
@fgrieu No, because we have a multiple of $p$: the modulus $n$ itself. So we get that particular prime factor "for free" by adding $n$ to the product of prime powers.
Nov
2
comment Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
@fgrieu As I suspected (it was fairly obvious in retrospect) we also need $k$ to be non-smooth: the trick is that $n$ automatically gives us the factor of $p$, which gets us most of the way to $q - 1$ in the context of the Pollard $p - 1$ algorithm. This doesn't really change much, though, it just means that the key generation procedure needs to be adjusted to avoid $k$ being smooth, it is still open whether we can exploit the length difference between $p$ and $q$.
Nov
2
revised Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
better attack, supersedes old one completely
Nov
1
reviewed Approve Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
Nov
1
comment Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
@fgrieu Thanks! Hopefully there is a way to improve on the number theory to provide a faster algorithm to find $k$ than brute force.
Nov
1
comment Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
@fgrieu Hmm, the square root approach seems more direct, looks like I missed the obvious! But in any case, yes, it means that subject to the restrictions the modulus has to be pretty unbalanced to offer any security, but I don't have anything better than that so far :/
Nov
1
revised Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
added 294 characters in body
Nov
1
answered Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$
Oct
30
comment Password generation/storage scheme
Related: crypto.stackexchange.com/questions/9035/… ... and I guess basically every question containing the words "password generation", as this is hardly a novel concept
Oct
29
comment Encryption algorithm designed to be easy to decrypt by machine but impractical to decrypt by hand
@owlstead Yes, as long as you add any kind of nondeterminism in the scheme, that will be enough to defeat precomputation and lookup for a human without access to a computer! (admittedly the question didn't specify the exact threat model, so this may be overkill, but since we're talking about giving the computer an advantage we can be as overkill as we want :))
Oct
29
comment Encryption algorithm designed to be easy to decrypt by machine but impractical to decrypt by hand
Looks like you're referring to a generic feedback scheme. CBC and CFB mode are two such schemes for block ciphers (en.wikipedia.org/wiki/Block_cipher_mode_of_operation)
Oct
29
comment Encryption algorithm designed to be easy to decrypt by machine but impractical to decrypt by hand
Yes, until someone precomputes the value of every letter when encrypted with that exponent and modulus, then it suffices to look up the ciphertext in a small table. To counter this, you could pack multiple letters in a single plaintext, or simply change exponents and modulus often.
Oct
27
revised RSA prove $a^{\varphi(n)/g} \equiv 1 \pmod{n}$
LaTeXified + fixed a few typos + edited tags