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I'm preparing myself to exam, but I have a lot of troubles with rigorous proofs.
Let $\Pi=(Gen,Enc,Dec)$ be an efficient secret-key encryption scheme that is not fixed-length. That is, for any $n$ and any $k \leftarrow Gen(1^n)$ the encryption algorithm $Enc_k(\cdot)$ can encrypt arbitrary length messages $m \in \lb... |
I'm preparing myself to exam, but I have a lot of troubles with rigorous proofs.
> Let $\Pi=(Gen,Enc,Dec)$ be an efficient secret-key encryption scheme that is not fixed-length. That is, for any $n$ and any $k \leftarrow Gen(1^n)$ the encryption algorithm $Enc_k(\cdot)$ can encrypt arbitrary length messages $m \in \... |
i'm trying to figure out when an [**Intialization Vector**](http://en.wikipedia.org/wiki/Initialization_vector) (IV) should be used.
There are anecdotal reports that WEP was broken [because of weak IV's](http://en.wikipedia.org/wiki/Wired_Equivalent_Privacy#Flaws). It's also claimed that if two pieces of plaintext ... |
i'm trying to figure out when an [**Intialization Vector**](http://en.wikipedia.org/wiki/Initialization_vector) (IV) should be used.
There are anecdotal reports that WEP was broken [because of weak IV's](http://en.wikipedia.org/wiki/Wired_Equivalent_Privacy#Flaws). It's also claimed that if two pieces of plaintext ... |
If I have a group $\mathcal{G}$ of order $N=npq$ and subgroups $\mathcal{G_n,G_p,G_q}$ of order $n$, $p$, $g$ respectively and if $g$ is a generator of $\mathcal{G}$ why then $g^{nq}$ is a generator of $\mathcal{G_p}$, $g^{np}$ is a generator of $\mathcal{G_q}$ and $g^{pq}$ is a generator of $\mathcal{G_n}$ ? I am tryi... |
Most of the research papers give imaginary applications of multi party computation.
Either they talk about millionare's problem or two or more corporates willing to compute some Intrustion detection stuff collectively on their private data without revealing their network logs or similar
in reality what are the p... |
I have just read about the perfect security of an OTP encryption and what came to my mind was that what if the Pad used for encryption/decryption did not have to be transported separately from the message, but instead together with it? I mean what if it was computed using an algorithm from the message itself (from all ... |
I have just read about the perfect security of an OTP encryption and what came to my mind was that what if the Pad used for encryption/decryption did not have to be transported separately from the message, but instead together with it? And what if it was computed using an algorithm from the message itself (from all the... |
I am using tree hash mode of Skein on a 16 core processor. Will it automatically employ parallelism using more than one cores or do I have to use multi-threading within the tree hash for parallel processing?
Also, the tree hash mode requires three parameters: leaf size encoding, fan-out encoding and tree height. Exc... |
Does chaining random number generators lead to loss of randomness? |
I'm a little bit confused by your notation (what's $1^n$ supposed to mean? based on context, it looks like a key or a passphrase, but I've never seen that notation before), but the exercise itself seems to just amount to proving that an Encrypt-and-MAC scheme, using a deterministic MAC of the plaintext which is sent in... |
I have programmed an implementation of Pollard's Rho factoring algorithm using C++ and the GMP library.
It is reasonably fast with large numbers, however I haven't implemented any form of cycle detection (I just try and avoid the problem, see below), and it struggles with small numbers.
Here is the pseudo code of... |
Given a set of SHA1 hash code, if we know part of the plaintext for each corresponding hash code, and also another part of plaintext is constant value for each hash code. In such cases possible to find out the constant value? |
Given a set of SHA1 hash code, if we knew a portion of the plaintext for each particular hash code, and also the remaining portion of the plaintext is a constant value for each hash code.
Is it possible for us to recover what is the constant value? |
I'm working on a encryption system where each party can store exactly a single ElGamal key-pair in a device. This is a hardware limit. The system must be expanded to support signatures and encryption.
Can each party use the same key-pair for both schemes?
I know that encryption/signature key lifetimes and securit... |
Can an ElGamal encryption and ElGamal signatures be used together sharing the same key-pairs? |
Can ElGamal encryption and ElGamal signatures be used together sharing the same key-pairs? |
I'm working on a encryption system where each party can store exactly a single ElGamal private key in a device. This is a hardware limit. The system must be expanded to support signatures and encryption.
Can each party use the same key-pair for both schemes?
I know that encryption/signature key lifetimes and secu... |
I have just read about the perfect security of an OTP encryption and what came to my mind was that what if the Pad used for encryption/decryption did not have to be transported separately from the message, but instead together with it?
And what if it was computed using an algorithm from the message itself (from all ... |
Alice is going to use some existing RSA infrastructure, which she can't change, or influence beyond her choice of key. All public modulus $n$ must be exactly $b$ bits with $b$ even (e.g. $b=4096$). Any odd public exponent $e$ with $3\le e<e_\mathtt{lim}$ is allowed, for some $e_\mathtt{lim}$ at least $n$ (this is commo... |
Is an RSA variant with public exponent $e=f+(p-1)\cdot(q-1)$ safe? |
Alice is going to use some existing RSA infrastructure, which she can't change, or influence beyond her choice of key. All public modulus $n$ must be exactly $b$ bits with $b$ even (e.g. $b=4096$). Any odd public exponent $e$ with $3\le e<e_\mathtt{lim}$ is allowed, for some $e_\mathtt{lim}$ at least $n$ (this is commo... |
Alice is going to use some existing RSA infrastructure, which she can't change, or influence beyond her choice of key. All public modulus $n$ must be exactly $b$ bits with $b$ even (e.g. $b=4096$). Any odd public exponent $e$ with $3\le e<e_\mathtt{lim}$ is allowed, for some $e_\mathtt{lim}$ at least $n$ (this is commo... |
Alice is going to use some existing RSA infrastructure, which she can't change, or influence beyond her choice of key. All public modulus $n$ must be exactly $b$ bits with $b$ even (e.g. $b=4096$). Any odd public exponent $e$ with $3\le e<e_\mathtt{lim}$ is allowed, for some $e_\mathtt{lim}$ at least $n$ (this is commo... |
Alice is going to use some existing RSA infrastructure, which she can't change, or influence beyond her choice of key. All public modulus $n$ must be exactly $b$ bits with $b$ even (e.g. $b=4096$). Any odd public exponent $e$ with $3\le e<e_\mathtt{lim}$ is allowed, for some $e_\mathtt{lim}$ at least $n$ (this is commo... |
Alice is going to use some existing RSA infrastructure, which she can't change, or influence beyond her choice of key. All public modulus $n$ must be exactly $b$ bits with $b$ even (e.g. $b=4096$). Any odd public exponent $e$ with $3\le e<e_\mathtt{lim}$ is allowed, for some $e_\mathtt{lim}$ at least $n$ (this is commo... |
Yes, it's safe (for some definition of *safe*), but it will be very slow. The reason we typically use other ones is for speed. The usual exponents of 3, 5, 17, and 65537 all have the characteristic that they are primes with two one bits and other bits being zero. This means that the exponentiation will be reasonably fa... |
In a special ElGamal encryption scheme, every user has an ElGamal encryption key-pair using the same cyclic group G and generator g.
The system has a special function :
ShuffleEncrypt(k1, k2, h1, h2 ) = RandomPermutationOf ( ElGamalEnc( h1, k1) , ElGamalEnc( h2, k2) ) = ( a, b)
k1 are k2 plaintexts.
So gi... |
How can I proof in zero knowldege that an ElGamal shuffle is correct for a special setting? |
In a special ElGamal encryption scheme, every user has an ElGamal encryption key-pair using the same cyclic group G and generator g.
The system has a special function :
ShuffleEncrypt(m1, m2, h1, h2 ) = RandomPermutationOf ( ElGamalEnc( h1,m1) , ElGamalEnc( h2, m2) ) = ( a, b)
m1 are m2 plaintexts.
So giv... |
In a special ElGamal encryption scheme, every user has an ElGamal encryption key-pair using the same cyclic group $G$ and generator $g$.
The system has a special function :
$$ \mathrm{ShuffleEncrypt}(m_1, m_2, h_1, h_2 ) = \text{RandomPermutationOf} ( \operatorname{Enc}( h_1,m_1) , \operatorname{Enc}( h_2, m_2) )... |
Since i cannot comment on questions, I give my own:
If a secret key encrypt algorithm can encrypt messages of arbitrary length and the encrypt algorithm is probabilistic then: suppose the adversary selects two messages of different length, $||m_0||=n$, $||m_1||=l$ and $n<l$. She gets back a ciphertext $c$. How can s... |
Alice is going to use some existing RSA scheme (employing industry-standard signature or/and encryption with proper padding), which she can't change, or influence beyond her choice of key. In this scheme, all public modulus $n$ are exactly $b$ bits with $b$ even (e.g. $b=4096$); and any odd public exponent $e$ with $3\... |
Alice is going to use some existing RSA scheme (employing industry-standard signature or/and encryption with proper padding), which she can't change, or influence beyond her choice of key. In this scheme, all public modulus $n$ are exactly $b$ bits with $b$ even (e.g. $b=4096$); and any odd public exponent $e$ with $3\... |
How can I prove in zero knowldege that an ElGamal shuffle is correct for a special setting? |
This seems a strange question to ask. Is it for an assignment or are you trying to select the best mode for a particular application? Regardless:
1. **ECB** does not use an IV.
1. **CTR** has a nonce value, which could be considered an IV. A bit error there will produce an entirely different key stream for every ... |
When a bit error happens in an IV, what would the result of decrypting a cipher-text be in the different encryption modes like ECB, CBC, CFB, OFB, and CTR? |
The encryption scheme in the experiment you describe does not have to be fixed-length. We simply require that the two messages the adversary sends to its oracle have the same length. The restriction is on the adversary, not on the encryption algorithm.
So why do we put this requirement on the adversary? The reason i... |
Alice is going to use some existing RSA scheme (employing industry-standard signature or/and encryption with proper padding), which she can't change, or influence beyond her choice of key. In this scheme, all public modulus $n$ are exactly $b$ bits with $b$ even (e.g. $b=4096$); and any odd public exponent $e$ with $3\... |
Is an RSA variant with public exponent $e=f+(p-1)\cdot(q-1)$ safe (for $f$ random in some small interval)? |
I don't understand the question (what is public? what is secret? what is the definition of all variables and functions?), but I can give you a pointer to literature that I strongly expect is highly relevant:
Take a look at mixnets. There's an enormous amount of research literature on the subject. It solves the fol... |
This is already explained well, at a conceptual level, at a different question: [Why is a non fixed-length encryption scheme worse than a fixed-length one?](http://crypto.stackexchange.com/q/5146/351)
To turn it into a formal proof, write down an adversary $A$ that breaks the security of $\Pi$. You may want to firs... |
I build the [computer appliance][1] system that consist of software server and multiple controllers. The system I want to build must be pluggable in the sense that when I connect a controller **C** to the network, the server **S** will immediately finds it after initial message exchange(*Step 1*). After an initiation p... |
In a cyclic group G with generators g and h.
Alice knows: g, h, x1, x2 and (a,b,c)
Bob knows: g, h and (a,b,c)
Can Alice prove to Bob in zero knowledge that he knows x1 and x2 such that
(a,b,c) = (g^x1 , x2*(h^x1), h^x2) ?
This proof must me practical and non-interactive.
|
Is there a practical zero-knowledge proof for this special discrete log equation? |
In a cyclic group $G$ with generators $g$ and $h$,
* Alice knows: $g$, $h$, $x_1$, $x_2$ and $(a,b,c)$,
* Bob knows: $g$, $h$ and $(a,b,c)$.
Can Alice prove to Bob in zero knowledge that she knows $x_1$ and $x_2$ such that $(a,b,c) = (g^{x_1} , x_2·(h^{x_1}), h^{x_2})$?
This proof must me practical and non-i... |
In a cyclic group $G$ with generators $g$ and $h$,
* Alice knows: $g$, $h$, $x_1$, $x_2$ and $(a,b,c)$,
* Bob knows: $g$, $h$ and $(a,b,c)$.
Can Alice prove to Bob in zero knowledge that she knows $x_1$ and $x_2$ such that $(a,b,c) = (g^{x_1} , x_2·(h^{x_1}), h^{x_2})$?
This proof must be practical and non-i... |
The example for IND-CPA secure schemes given is generally:
for a random r, $Enc_k(m) =(r|| E_k(r) XOR m)$ where $E$ is a $PRF$
But does the role of r and k really matter--i.e. isn't this equally secure? $Enc_k(m) =(r|| E_r(k) XOR m)$ ? |
Suppose I want to prove that a given symmetric encryption scheme is not IND-CPA secure. The first thing I do is to define a specific adversary that attacks the scheme. How can I proof neatly, (using the game where A chooses two messages and is given a ciphertext $c$) that the adversary indeed almost always can determin... |
The example for IND-CPA secure schemes given is generally:
for a random r,
$Enc_k(m) =(r|| E_k(r)$ $XOR$ $m)$ where $E$ is a $PRF$
But does the role of r and k really matter--i.e. isn't this equally secure?
$Enc_k(m) =(r|| E_r(k)$ $XOR$ $m)$ ?
|
Suppose I want to prove that a given symmetric encryption scheme is not IND-CPA secure. The first thing I do is to define a specific adversary that attacks the scheme. How can I proof neatly, (using the game where A chooses two messages and is given a ciphertext $c$) that the adversary indeed almost always can determin... |
No, it is not equally secure. Consider an instantiation where $E$ is instantiated with AES, and where the message is always 128 bits long. Can you find an attack on this particular version of the scheme?
This smells like homework (I'm guessing?), so to avoid ruining the problem and give you a chance to learn from ... |
No, it is not equally secure. Consider an instantiation where $E$ is instantiated with AES, and where the message is always 128 bits long. Can you find an attack on this particular version of the scheme?
This smells like homework (I'm guessing?), so to avoid ruining the problem and give you a chance to learn from ... |
I build the [computer appliance][1] system that consist of software server and multiple controllers. The system I want to build must be pluggable in the sense that when I connect a controller **C** to the network, the server **S** will immediately finds it after initial message exchange(*Step 1*). After an initiation p... |
Apologies if this is a stupid question, but I'd be grateful if someone could provide an answer. I'm assuming that you need to use different keys to provide these functions, is that correct? |
Can you use the same key to provide a signature and a MAC? |
If I encrypt a file with gpg -c file.zip, and change the file name Is there any way I can restore the file name as I used as a password. or the name encrypted to? |
Is gpg stmmetrec encrypt file name? |
If I encrypt a file with `gpg -c file.zip`, and change the file name. Is there any way I can restore the file name as I used as a password. or the name encrypted to? |
Is gpg symmetric encrypt file name? |
If I encrypt a file with `gpg -c file.zip`, and change the filename. Is there any way I can restore the filename as I used as a password. or the name encrypted to? |
Does gpg encrypt the filename symmetrically? |
Does gpg's symmetric encryption keep information about the filename? |
The usual meaning of **signature** (in cryptography) is this:
* Bob has a pair of keys, a public and a private one. The public one is known to Alice, too. (And to any possible attackers, too.)
* Bob wants to send a message to Alice.
* Bob does some operation with the message and his private key (*he signs the mess... |
In the [HOTP][1] protocol after calculating a 20 byte hash it is truncated to 4 bytes.
For this first an offset is calculated (low-order 4 bits of the last byte) which determines the four bytes to be selected.
Why is this more 'secure' than simply always taking the first four bytes of the hash?
[1]: http:... |
The example for IND-CPA secure schemes given is generally:
for a random r,
>Enc_k(m) =(r|| E_k(r) XOR m) where E is a PRF
But does the role of r and k really matter--i.e. isn't this equally secure?
> Enc_k(m) =(r|| E_r(k) XOR m) ? |
> **Possible Duplicate:**
> [CPA Secure Chosen plaintext scheme](http://crypto.stackexchange.com/questions/5250/cpa-secure-chosen-plaintext-scheme)
<!-- End of automatically inserted text -->
The example for IND-CPA secure schemes given is generally:
for a random r,
$Enc_k(m) =(r|| E_k(r)$ $XOR$ $m)$ where... |
I have an exercice to do regarding Vegenere encryption.
I've got the cipher text : WNZTNVIEEGTJYKRRWYUELWNZTNV
and a partial plain text : S''''R''R''''R''''PASS'''''
The key length is unknown.
The question is : is it possible to find the key and the plain text?
Regarding what I've seen in class, I don't think ... |
In a multiplicative cyclic group $G$ with generators $g$ and $h$, as in ElGamal,
* Alice knows: $g$, $h$, $x_1$, $x_2$ and $(a,b,c)$,
* Bob knows: $g$, $h$ and $(a,b,c)$.
Can Alice prove to Bob in zero knowledge that she knows $x_1$ and $x_2$ such that $(a,b,c) = (g^{x_1} , x_2·(h^{x_1}), h^{x_2})$?
This pro... |
I'm extremely new to crypto, and very much inexperienced. Lately I've been reading about the Diffie-Hellman key-exchange methods, and specifically about the computational diffie-hellman assumption vs. decision diffie-hellman assumption. Specifically I'm referencing Dan Boneh's paper on DDH problem. However, I'm having ... |
We have a multiplicative cyclic group $G$ with generators $g$ and $h$, as in El Gamal. Assume $G$ is a subgroup of $(\mathbb{Z}/n\mathbb{Z})^*$. There are two parties, Alice and Bob:
* Alice knows: $g$, $h$, $x_1$, $x_2$ and $(a,b,c)$,
* Bob knows: $g$, $h$ and $(a,b,c)$.
Can Alice prove to Bob in zero knowle... |
I have an exercise to do regarding Vigenère encryption.
I've got the cipher text: `WNZTNVIEEGTJYKRRWYUELWNZTNV`
and a partial plain text: `S''''R''R''''R''''PASS'''''`
The key length is unknown.
The question is: is it possible to find the key and the plain text?
Regarding what I've seen in class, I don't t... |
In the [HOTP][1] protocol after calculating a 20 byte hash it is truncated to 4 bytes.
For this first an offset is calculated (low-order 4 bits of the last byte) which determines the four bytes to be selected:
> DT(String) // String = String[0]...String[19]
> Let OffsetBits be the low-order 4 bits of St... |
Why does HOTP use such a complex truncate function? |
What you're proposing is an algorithm, which is very much *not* a one-time pad. This is frequently a source of confusion. People have even sold commercial "one-time-pad encryption" software based on this flawed idea.
In cryptography, a one-time pad has a very specific meaning. Each byte/character/whatever of plai... |
It is known that the two prime factors $p$ and $q$ of an RSA modulus $n$ should not be too close to each other. In other words, $\Delta = \left| p - q \right|$ should not be too small.
Given a modulus of $k$ bits, how large should $\Delta$ be?
The [DSS](http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.... |
It is known that the two prime factors $p$ and $q$ of an RSA modulus $n$ should not be too close to each other. In other words, $\Delta = \left| p - q \right|$ should not be too small.
Given a modulus of $k$ bits, how large should $\Delta$ be?
Section B.3 of the [Digital Signature Standard](http://csrc.nist.gov/p... |
This recommendation is here specifically to prevent [Fermat's Factorization Method][1] from yielding a factorization. This method can yield factor a number if its two factors are sufficiently close; this recommendation would prevent that from being a possibility.
Now, you ask 'is such a recommendation reliable'? W... |
This is not how you should choose a RSA modulus. It sounds like you are operating under the premise that you would choose a $\Delta$ and then choose $p,q$ based upon this $\Delta$. That's not a good way to choose a RSA modulus.
Instead, you should choose $p$ and $q$ independently at random. If you want a 2048-bit... |
This is not how you should choose a RSA modulus. It sounds like you are operating under the premise that you would choose a $\Delta$ and then choose $p,q$ based upon this $\Delta$. That's not a good way to choose a RSA modulus.
Instead, you should choose $p$ and $q$ independently at random. If you want a 2048-bit... |
I have the following requirement for hashing using **MD5**.
H(A,B,C,X);
Where values A,B & C are given. However X is not given.
I would like to find out what value of X would give a hash beginning with 32 1's bits
meaning H(A,B,C,X) = Begin with 32 '1' bits
I can brute force by testing all kinds of chara... |
It is known that the two prime factors $p$ and $q$ of an RSA modulus $n$ should not be too close to each other, otherwise an attacker may factor the modulus. In other words, $\Delta = \left| p - q \right|$ should not be too small.
However, "*too small*" is a somewhat subjective measure. "*Too small*" with respect to... |
This question is only relevant if you choose $p,q$ in a non-standard way. The standard way to choose $p,q$ is to choose them as two independent random $k/2$-bit numbers. If you do it the standard way, the question is not relevant (the probability that $|p-q|$ is too small is negligible -- and is dominated by the chan... |
This question is only relevant if you choose $p,q$ in a non-standard way. The standard way to choose $p,q$ is to choose them as two independent random $k/2$-bit numbers. If you do it the standard way, the question is not relevant (the probability that $|p-q|$ is too small is negligible -- and is dominated by the chan... |
This question is only relevant if you choose $p,q$ in a non-standard way. The standard way to choose $p,q$ is to choose them as two independent random $k/2$-bit numbers. If you do it the standard way, the question is not relevant (the probability that $|p-q|$ is too small is negligible -- and is dominated by the chan... |
This question is only relevant if you choose $p,q$ in a non-standard way. The standard way to choose $p,q$ is to choose them as two independent random $k/2$-bit numbers. If you do it the standard way, the question is not relevant (the probability that $|p-q|$ is too small is negligible -- and is dominated by the chan... |
This question is only relevant if you choose $p,q$ in a non-standard way. The standard way to choose $p,q$ is to choose them as two independent random $k/2$-bit numbers. If you do it the standard way, the question is not relevant (the probability that $|p-q|$ is too small is negligible -- and is dominated by the chan... |
This question is only relevant if you choose $p,q$ in a non-standard way. The standard way to choose $p,q$ is to choose them as two independent random $k/2$-bit numbers. If you do it the standard way, the question is not relevant (the probability that $|p-q|$ is too small is negligible -- and is dominated by the chan... |
I've been reading a bit about block cipher modes and I have a relatively straightforward question regarding CTR. In essence, I was hoping you guys would be kind enough to validate my understanding of things.
As I understand it, CTR does the following:
1. Take the first output of the nonce (let us assume an incre... |
Why doesn't CTR mode require blocking? |
Might it be possible that reversible combinatorial circuits (or some emulating software) are going to be used to get the input of the white box?
I mean if I have constructed a proper reversible circuit then (in theory) I can obtain the input of whatever output I get. Am I missing the point?
Here is the relevant W... |
Crack cryptographic hash functions using Toffoli gates? |
Its interesting to see critical thinking being applied to cryptDB in contrast to all the hoopla around it [here][1] . cryptDB is not a major theoretical breakthrough but potpourri of technologies to make it work. But then am curious if there is a formal security analysis done by anybody on cryptDB. all over the web its... |
Is there a security analysis of CryptDB? |
Unsure whether this is the right forum for this question, worth a try.
The task im faced with is to implement a poly-time algorithm that finds a nontrivial factor of a carmichael number. Many resources on the web states that this is easy, however, without further explanation why that is?
Furthermore, since miller... |
Unsure whether this is the right forum for this question, worth a try.
The task im faced with is to implement a poly-time algorithm that finds a nontrivial factor of a carmichael number. Many resources on the web states that this is easy, however, without further explanation why that is?
Furthermore, since miller... |
<br>
i want to know what is the best pseudo-random number generation algorithm for passwords? for example my scenario is I have to generate 5K pseudo-random bits from a user-supplied password(6 character).what are possible options and which one do you recommend? |
I usually choose bcrypt when hashing as I can set the work factor to slow down the calculations of the hash. However, I have to keep a copy of the hash in order to verify it (since it includes the salt) when the same input comes around again.
Are their any A) common and B) slow hashing algorithms that do not require... |
Slow hash algorithm that does not require salt? |
The way I understand it, an algorithm is said to be randomized if it uses randomness as part of its logic (quoting [Wikipedia](https://en.wikipedia.org/wiki/Randomized_algorithm)). Now, in the case of encryption algorithms, I assume this means that for the same input, different outputs (i.e. ciphertexts) will be produc... |
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