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Jan
22
comment Is it an example of bilinear pairing?
To be useful in crypto, the bilinear function has to be nondegrading, and the dlog problem has to be hard in all three groups (well, if it is hard in the target group, the other two follow).
Jan
21
comment RSA Key generation: How is multiplicative inverse computed?
@Henno Brandsma From $n,e,d$ it is even deterministic in polynomial time to factor $n$, see Computing the RSA Secret Key Is Deterministic Polynomial Time Equivalent to Factoring (May 2004) or Deterministic Polynomial-Time Equivalence of Computing the RSA Secret Key and Factoring (Coron and May,2007) - they are quite similar.
Jan
21
comment Find private exponent in RSA
@Mac What you missed is "use the extended euclidean algorithm to calculate the inverse". Check out wikipedia for this.
Jan
19
comment What kind of attack does the current brokenness of SHA-1 allow?
That is only true for brute forcing an algorithm, and there you can argue about the size of the keyspace. But any advantage beyond that comes from unique weaknesses in specific algorithms - regardless if this is some correlation of values (linear and differential cryptanalysis) or in the underlying mathematical problem (factoring for RSA). Even arguing about common standards like SHA and MD5, they are both considered broken. but the attacks differ quite a lot. There is a reason, why every new hash function or symmetric cipher has to withstand a lot of cryptanalysis before being used.
Jan
16
comment RSA public key exponent generation confusion
"When e=3 for exemple the public modulus and the Euler totient $\phi(n)$ share approximatly half of the most significant bits." The fact is correct, the reasoning is wrong. The choice of $e$ has no influence on $\phi(n)=(p-1)(q-1)$. But the fact is also meaningless: If we assume two random numbers of equal length (that's the case for $\phi(n)$ in general), then they share the same bit in half of all positions.
Jan
16
comment What kind of attack does the current brokenness of SHA-1 allow?
The correlation between bit length and "costs" as some security measure is nothing that could be generalized in a meaningful way. At worst, thought processes like that can be dangerous pitfalls. The statement with factor $2^{16}$ ist valid for brute force attacks only. It has absolutely no meaning for sophisticated attacks, which target a specific algorithm.
Jan
16
comment Hash which can be used to verify one of multiple inputs?
This should not end up in a discussion of sorts, but using correct terms is quite important. If an accumulator fits your idea, then that's fine.
Jan
16
comment Unbreakable code and mathematical impossibility
codes are no security measure.
Jan
16
comment Hash which can be used to verify one of multiple inputs?
That has nothing to do with the term hash function, even without the property cryptographically secure. Because what you need to achieve something like that is a trapdoor one-way function.
Jan
15
comment Hash which can be used to verify one of multiple inputs?
If you want to keep your assumption, that $H_1$ and $H_2$ are hash functions, then this is very unlikely to exist. Because in this case, $H_2$ could somehow identify partial-preimages of $Z$... Then either $H_1$ is not a cryptographically secure hash function or $H_2$ is not computationally feasible.
Jan
15
revised Comparison among algorithm based on key length
added 135 characters in body
Jan
15
comment Comparison among algorithm based on key length
Ah, you're right... I'll correct that.
Jan
13
comment Can you help me with this Random Number Generator function?
In that case, yes. But in the question is an example of how he wants the output... and that is the full list of elements.
Jan
13
comment Can you help me with this Random Number Generator function?
The required memory of the algorithm is the same as the data of the output. If you can't handle that in memory, how can you handle it in the output... this just doesn't make any sense.
Jan
13
comment Difference between Hash function and Random Oracle
This answer misses the connection to the referenced paper: In that paper, they do not use random oracles to show anything. They use the collision resistance property of a hash function. The Proof of security is not in the random oracle model, if you don't use random oracles in the security proof. And they don't.
Jan
13
comment Can one deduce the symmetric key size used to encrypt a given a piece of ciphertext?
In that link there is plenty of information to answer your question, just read it again carefully. Anyway, usually the key size is fixed in symmetric encryption algorithms, and therefore we give that information to the attacker anyway. If you assume that this isn't the case, your attacker model is weaker than "ciphertext only"... which is already considered too weak for today's standards.
Jan
13
comment What is the importance of adding round key in AES
It is not about "complicated enough". If you are given a (fixed) single bit and then combine it with some other bit with XOR, you get a bijection: input equals output or input is unequal to the output. OR does not have this property, if one of its inputs is True. In general, XOR has much nicer properties than logical AND and OR.
Jan
13
answered Comparison among algorithm based on key length
Jan
12
comment Is it possible to use structures other than finite fields?
It is the other way around: In continous structures, there are no "hard to inverse" problems, as far as I know. In the mathematical sense, there "is no inverse" if either it does not exist or the inverse is not unique. But this is something else than "you cant compute the inverse". And then there is the fact, that we usually deal with discrete elements e.g. 0 and 1.
Jan
12
comment P = NP and current cryptographic systems
General statements about complexity classes should not be mixed with actual numbers. Even if breaking RSA was possible in $P$ and expressed in some polynomial in $O$ notion, this does not mean you can derive 1024 is unsafe and 3072 bit is safe. First, P contains any power over $n$. Second: This still does not put a relation to computation power, time required and bitsize. There are constants (or better: coefficients) to required, to get the actual relations.