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Oct
20
comment Security proof of FO(Fujisaki-Okamoto) hybrid encryption
ECIES. RSA-KEM.
Sep
11
comment Proof for composed signatures
If $\epsilon_3$ is smaller than all three of $\epsilon$, $\epsilon'$ and $\epsilon''$, it will be smaller than the minimum, not the maximum...
Sep
4
comment Proof for composed signatures
You have $\epsilon_3 \leq \epsilon$, $\epsilon_3 \leq \epsilon'$ and $\epsilon_3 \leq \epsilon''$. Can you find a smaller bound?
Aug
30
comment Proof for composed signatures
Recall that a scheme is $\epsilon$-secure if any adversary has advantage at most $\epsilon$. For any $\epsilon_3$-forger (adversary with advantage $\epsilon_3$) against the composed system, we get an $\epsilon_3$-forger against any of the three systems. Now we apply the definition of secure.
Jul
31
comment Rainbow table for DES with all-zero plaintext?
No, $L$ chains of length $k$; checking if we are in a chain requires computing $k$ sequences of average length $k/2$.
Jul
22
comment RSA with modulus n=p²q
The Okamoto–Uchiyama cryptosystem uses a modulus $p^2 q$ to good effect. It is a precursor to Paillier's cryptosystem, which has proven fantastically useful.
Jul
15
comment Does CCA security imply authenticated encryption?
Ah, I see. Malleable was indeed the wrong word. Sorry.
Jul
15
comment Does CCA security imply authenticated encryption?
Please note that AE is not the same as NM-CCA (which is equivalent to IND-CCA). AE usually requires some form of integrity, ie. it should be hard for an adversary to come up with a ciphertext that decrypts correctly.
Jul
14
comment Does CCA security imply authenticated encryption?
CCA is an attack model. AE is usually a security. So the two aren't immediately comparable. Probably, you should be asking if IND-CCA implies AE, which isn't the case. (Start with an IND-CCA scheme, make it malleable by returning pseudo-random decryptions for malformed ciphertexts, observe that the resulting scheme remains IND-CCA, but is not AE.)
Jun
5
comment Modulo properties of two prime numbers
Recall the definition for when two numbers are congruent modulo some number. Then prove for yourself that if two numbers are congruent modulo some product, they are also congruent modulo the factors of the product. Then prove for yourself that if two numbers are congruent modulo two different moduli, then they are congruent modulo the least common multiple of the moduli. Then apply these results, and you are done.
May
30
comment What's the advantage of using OFB/CFB/CTR modes over a stream cipher
If you use $IV=1$ for the first encryption and $IV=2$ for the second encryption, you will probably evaluate the block cipher twice at the value $2$. That would be bad. So you have to be careful not only to have unique IVs, but also make sure there won't be any overlap in the evaluation. It is usually easy to ensure this, but it may require some thinking.
May
29
comment What's the advantage of using OFB/CFB/CTR modes over a stream cipher
Side Note #3: CTR mode is extremely sensitive to how you choose the IV.
Apr
24
comment Generalize the Merkle-Damgard construction for any compression function
Let $m = m_1 m_2 \dots m_n$. Suppose $y_0$ is fixed and let $y_i = f(y_{i-1}, m_i)$, $h(m) = y_n$. This is the basic Merkle-Damgård construction, but some extra tricks are needed. You first need to understand why these tricks are needed. Study how you recover a collision for $f(\cdot)$ from a collision in $h(\cdot)$. Then come up with a suitable trick. Hint: expansion.
Apr
20
comment Diffusion in Shamir's secret sharing scheme
Based on your description, it serves no purpose.
Apr
11
comment Is there a simple zero knowledge proof of $x$ for $b=x^x\pmod p$?
If you allow $x>p-1$ it is easy. Can you do it with $0 < x < p-1$?
Mar
27
comment Security proof of FO(Fujisaki-Okamoto) hybrid encryption
Note that this only works because the decryption algorithm recreates $C_1$ after recovering $\sigma$. Modern schemes do without recreating $C_1$.
Mar
19
comment How do the following new (2013) ECC curves compare in security or efficiency?
arxiv.org/abs/quant-ph/0301141
Mar
19
comment How do the following new (2013) ECC curves compare in security or efficiency?
Quantum computers can compute d.logs. on all of these curves. "Post-quantum" they have no security.
Mar
19
comment Subexponential algorithms for DLP in $\mathbb{Z}_s \times \mathbb{Z}_t$
This is reasonably correct. One quibble: Can $h_1g_1^{-1}$ and $h_2 g_2^{-1}$ be different?
Mar
18
comment How do the following new (2013) ECC curves compare in security or efficiency?
"post-quantum"?