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Given a function $F: A \rightarrow B$ and a function $R:B \rightarrow A$, we can create a chain of length $k$ from a starting point $a_0$ to an end point $a_k$ using $a_i = R(F(a_{i-1}))$. A rainbow table for $(F, R, k)$ is a collection of chains with end points $(a_0, a_k)$ organized so that searching for chains ending at $a_k$ is cheap. We use a rainbow ...


3

If the protocol doesn't provide authentication, an attacker can probably mount replay attacks or make deterministic changes to messages. If the nonces in different blocks are not compared in any way, they can just take the ID block of a previous message and use it with a new one, to forge it being from that device. If nonces are required e.g. to be equal in ...


3

One simple approach is to truncate the output to 56 bits. I believe this was considered in Hellman's original paper on time-space tradeoffs. Sometimes people get all excited by rainbow tables (partly because it has a cool name, maybe) but forget about Hellman's original paper on the time-space attack. Hellman's paper is very much worth reading, especially ...


3

It seems to me you can do everything as when calculating a rainbow table for a hash function, except that choosing a good reduction function is very easy. For example, define a chain starting from $k$ as: $$c_k(0) = T(E_k(0))$$ $$c_k(i) = T(E_{c_k(i-1) \oplus i}(0)),$$ where $T$ truncates its input to 56 bits. Now you can create a rainbow table with $n$ ...


2

There are two ways to attack encryption that uses a derived key: You can attack the encryption algorithm. In the case of correctly used* 128-bit AES, that essentially amounts to a brute force attack on the 128-bit keyspace. This would succeed after on average $2^{127}$ tries (if it were practical). If you knew that two files had used the same password ...


2

If your ints are unsigned then the code r = (r * 33) + (int)c and the fact that you're using 32-bit integers yield the equation $\;\;\;\; \text{new_r} \: \equiv \: (\text{old_r} \cdot 33) + \text{(int)}\hspace{.02 in}\text{c} \;\; \pmod{2^{32}} \;\;\;\;$. Since 33 is odd and $2^{32}$ is even, 33 is a unit mod $2^{32}$. $\:$ I used wolframalpha to determine ...


2

On your earlier questions: 1) How secure is this method for generating one-time pads in block- or stream-ciphers? This method in itself is not secure, as the output weakly random entropy source, not a TRNG; there is entropy in the keystrokes, but without any whitening and extraction taking place, the output is - for instance - not well distributed. The ...


2

Am I on the right track with reversing DJB2 (can it be reversed?)? Is there some way of finding the remainder of a large number that has been modded by 232? You were on a right track to explain why it can't be easily inverted. Given an arbitrary $h_i$, every letter of the alphabet will give you another potential $h_{i-1}$ that the value was before that ...


2

Your idea for constructing a distinguisher from a predictor is fine, assuming you know that the predictor predicts the last bit. The more general statement is: if you can predict any bit of the output, say the $i$th bit, given the first $i-1$ bits, then you can also build a distinguisher. A similar idea to what you showed also works to prove this ...


2

Dinh, Moore, Russell have shown that the quantum algorithm (Quantum Fourier sampling) used to attack RSA and ElGamal does not work on McEliece-like crypto systems. (I think) this means, that there are no known algorithms on quantum computers that decrease the complexity of attacks on McEliece, and thus McEliece is just as safe post-quantum computers as it is ...


1

How to prove the security of the PRNG? My best advice would be to start with a statistical test suite like the one NIST describes in "A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications" (PDF). It’s a battery of statistical tests to detect non-randomness in binary sequences constructed using random ...


1

Yes, according to NIST SP 800-56A revision 2, a KDF based on HMAC-SHA-256 is a suitable option. The basic idea behind using a Key Based Key Derivation Function KBKDF is that the output of the the primitive within the key agreement protocol (DH, ECDH) returns enough entropy for a key to be created. However that entropy may still be distinguishable from ...


1

Lets assume an adversary knows one LD signature for message $M$ as well as public key $pk$ and can generate a forgery for an arbitrary different message $M'$. Clearly, there exists at least one bit position where the messages differ, i.e. $M_i \neq M'_i$, as $M \neq M'$. So, for simplicity assume there is only one bit difference. Then the adversary can take ...



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