instruction stringlengths 15 30k |
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As I understand it elliptic curves are of the form y^2 = x^3 + ax + b
Where a and b are the curve parameters. However not all parameters will give a curve suitable for crypto purposes. Is there any know algorithm that can evaluate a pair of numbers (a,b) and return YES if they are valid ECC parameters. Is this algorit... |
We have a multiplicative cyclic group G which is a subgroup of (Z/nZ)∗. There are two parties, Alice and Bob:
Alice knows: a,b and x such that x^x = b
Bob knows: a,b
What's the easiest non-interactive way Alice can prove to Bob the knowledge of x without leaking x?
|
Is there a simple zero knowledge proof of x for b=x^x (mod p)? |
Is it possible to design a protocol that by itself guarantees that a malicious implementation cannot leak secret data without breaking the protocol?
**Setting:**
* Alice and Bob have a pre-shared secret key K. Using this key, Alice encrypts a bunch of plaintexts and sends them to Bob as a collection of files. The... |
Leak-proof protocol: is such a thing possible? |
Is it possible to design a protocol that by itself guarantees that a malicious implementation cannot leak secret data without breaking the protocol?
**Setting:**
* Alice and Bob have a pre-shared secret key K. Using this key, Alice encrypts a bunch of plaintexts and sends them to Bob as a collection of files. The... |
I'm confused about /Friedman's method 2 (using a table with column of k size of key, and n/k rows, n is the total size for cipher text)
\begin{equation}
m = \Bigl(\varphi(l)-\varphi(o)\Bigr)/\Bigl(\varphi(T)-\varphi(o)\Bigr)
\end{equation}
P.S. <br>
m - stands for how many blocks <br>
$\varphi(l)$ - stands fo... |
I'm confused about /Friedman's method 2 (using a table with column of k size of key, and n/k rows, n is the total size for cipher text)
\begin{equation}
m = \Bigl(\varphi(l)-\varphi(o)\Bigr)/\Bigl(\varphi(T)-\varphi(o)\Bigr)
\end{equation}
P.S. <br>
$\varphi(l)$ - stands for index of coincidence for language <... |
Why does this square root algorithm work? |
I am trying to adapt the following function from SJCL, which does "AES-CCM" style CTR encryption, to do "pure CTR" encryption. I am playing around with SIV and would rather use this well-reviewed implementation rather than build my own CTR cipher from scratch. However, I'm having trouble understanding exactly what the ... |
Why the input cipher for AES encryption, can write in 4x4 matrix with 8 bits entires, and can said is 128bits? if each cell is 8bits in binary, how we said this matrix is represent 128bits? |
How we transfer 128bits cipher to a 4x4 matrix for AES input? |
I have a field F(2^4) and it is represented as a residue ring of the polynomials over F2 modulo the polynomial β4+β3+β2+β+1.
I want to express each element in this field as a power of a primitive element β+1.
My questions are : 1) What are the elements of the fields?
2) How to express them as power of the given... |
How to express each element in a field F as a power of a primitive element? |
I have a field $\mathbb F_{2^4}$, and it is represented as a residue ring of the polynomials over $\mathbb F_2$ modulo the polynomial $\beta^4 + \beta^3 + \beta^2 + \beta + 1$.
I want to express each element in this field as a power of a primitive element $β+1$.
My questions are:
1. What are the elements of ... |
We have a multiplicative cyclic group G which is a subgroup of (Z/nZ)∗. There are two parties, Alice and Bob:
Alice knows: b and x such that x^x = b
Bob knows: b
What's the easiest non-interactive way Alice can prove to Bob the knowledge of x without leaking x?
|
I have a field $\mathbb F_{2^4}$, and it is represented as a residue ring of the
<br>
polynomials over $\mathbb F_2$ modulo the polynomial $\beta^4 + \beta^3 + \beta^2 + \beta + 1$.
I want to express each element in this field as a power of a primitive element $β+1$.
My questions are:
1. What are the eleme... |
How do I express each element in a field F as a power of a primitive element? |
As I understand it elliptic curves are of the form $y^2 = x^3 + ax + b$
Where $a$ and $b$ are the curve parameters. However not all parameters will give a curve suitable for crypto purposes. Is there a known algorithm that can evaluate a pair of numbers $(a,b)$ and return YES if they are valid ECC parameters. Is this ... |
Is there an algorithm to check if an elliptic curve is secure? |
As we know, RSA cryptosystem have both private key(a,p,q) and public key(b,n), by chinese remainder theorem and fermat's little theorem, we know that the importance of keep p and q secret, and from this [Why is it important that phi(n) is kept a secret, in RSA][1] post , we know $\phi$n need kept secret, but my questio... |
How to keep phi(n) secret in RSA? |
> How do we keep $\phi(n)$ secret?
We don't tell people what it is. The problem of finding $\phi(n)$ given $n$ is a hard problem (if $n$ is hard to factor). So, if we give people a number that they can't factor, and we don't give them $\phi(n)$, they can't determine it on their own. |
How a cryptographic hash function can be implemented using the block cipher? I was wondering can we use AES in cipher block chaining mode to implement it.
|
How can a cryptographic hash function be implemented using the block cipher?
<br>
I was wondering if we can use AES in cipher block chaining mode to implement it.
|
Can a protocol proved secure in the standard model be considered secure in the random oracle model ? |
security in the standard model -> random oracle model? |
Yes, we can build a hash function from a block cipher, and that's common (although with block ciphers designed for that purpose); but CBC does not seem appropriate. What would the key be? Notice there is no secret in a hash function!
One standard construction of hash function from a block cipher is the one used in t... |
How can a cryptographic hash function be implemented/created using the block cipher?
I was wondering if we can use AES in cipher block chaining mode to implement it.
|
Can a protocol proved secure in the standard model be considered secure in the random oracle model? |
security in the standard model → random oracle model? |
We have a multiplicative cyclic group $G$ which is a subgroup of $(\mathbb{Z}/n\mathbb{Z})∗$. There are two parties, Alice and Bob:
If:
1. Alice knows: $b$ and $x$ such that $x^x = b$;
2. Bob knows: $b$.
Then what's the easiest non-interactive way Alice can prove to Bob the knowledge of $x$ without leaking ... |
This question is a variant on http://crypto.stackexchange.com/questions/8902/given-a-message-and-signature-find-a-public-key-that-makes-the-signature-valid, which discusses the analogous question for RSA. It was suggested to me by [this post](http://bitcoin.stackexchange.com/questions/24280/can-you-always-derive-a-pub... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One standard constru... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One standard constru... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One standard constru... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One standard constru... |
Is there a simple zero knowledge proof of $x$ for $b=x^x\pmod p$? |
You have just to look at the signing/verification relation.
Just write it as $$m\cdot s \equiv r\cdot \alpha + k \bmod (p-1)$$
And the verification relation should be $$g^{s\cdot m}\stackrel{?}{\equiv} y^r\cdot r \bmod p$$
where $y=g^\alpha$ is the public key and you eavesdrop a signature $(r,s)$ for $m$.
O... |
I'm reading Ferguson, Schneier, and Kouno's *Cryptography Engineering*, and it has a section on MACs. It discusses different types of MACs, but it seems to claim that to acheive 128-bit level security, you need a 256-bit MAC due to the birthday attack.
Why is this the case? Why are collision attacks a concern in MAC... |
Why are collision attacks important when talking about MAC schemes? |
This question is a variant on http://crypto.stackexchange.com/questions/8902/given-a-message-and-signature-find-a-public-key-that-makes-the-signature-valid, which discusses the analogous question for RSA. It was suggested to me by [this post](http://bitcoin.stackexchange.com/questions/24280/can-you-always-derive-a-pub... |
In the case of emails your solution is not really practical. The problem is that the sender of an email uses the public key whereas the receiver should have the secret key. This means that whenever somebody wants to send you an email (and therefore generate a new key) you have to be online or you have to provide a set ... |
Let's suppose that you work in field $\mathbb{F}_p$ for a prime $p$; i.e. the $x$, $y$, $a$ and $b$ values are integers modulo $p$. The **curve order** $n$ is the number of points on the curve. By [Hasse's theorem][1] we know that $n$ is relatively close to $p$; namely, the theorem states that:
$$|n-(p+1)| \leq 2\sqrt... |
One-way accumulators are built upon a (quasi)-commutative one-way function. With quasi-commutativity, I refer to the following property:
For $f : X \times Y \to X$, it is true that $f(f(x, y_1), y_2) = f(f(x, y_2), y_1)$.
Although accumulators seem like a very useful cryptographic building block, I don't see them... |
Disadvantages of one-way accumulators? |
An advantage of a cryptographic accumulator is that due to the quasi commutativity you can compute witnesses for
membership of values in the accumulator where the accumulator and the witnesses are of constant size.
Say you
have a set $Y=\{y_1,y_2,y_3\}$ and compute the accumulator as $acc=f(f(f(x,y_1),y_2),y_3)... |
An advantage of a cryptographic accumulator and actually the reason to use them is that due to the quasi commutativity you can compute witnesses for
membership of values in the accumulator where the accumulator and the witnesses are of constant size.
Say you
have a set $Y=\{y_1,y_2,y_3\}$ and compute the accumu... |
As everybody knows in order to calculate HMAC we have to concatenate padding to the message.<br>
I just curious why the padding need to be fixed-length one.<br>
I mean why we need blocksize parameter here?<br>
<br>
Why not use arbitrary length key with arbitrary length 0x5c5c5c…5c, 0x363636…36?<br>
Why we need to ... |
Why HMAC need a fixed length padding? |
As everybody knows in order to calculate HMAC we have to concatenate padding to the message.<br>
I am just curious why the padding needs to be fixed-length.<br>
Why do we need the blocksize parameter here?<br>
<br>
Why not use an arbitrary length key with arbitrary length 0x5c5c5c…5c, 0x363636…36?<br>
Why do we ne... |
Why does HMAC need a fixed length padding? |
Consider the El Gamal encryption scheme, a symmetric encryption scheme (KG,E,D), and the following hybrid encryption scheme having an encryption algorithm that, on input a public key (G,q,g,h), where h=g^x, returns (c1,c2). For which of the following c1,c2 values (and assuming a suitable definition of the key generatio... |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
How low can the public exponent be in RSAP? |
As everybody knows in order to calculate HMAC we have to concatenate padding to the message. I am just curious why the padding needs to be fixed-length. Why do we need the blocksize parameter here?
Why not use an arbitrary length key with arbitrary length `0x5c5c5c…5c, 0x363636…36`?
Why do we need to truncate the... |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
ECB and CBC use encryption function and decryption function while CFB, OFB and CTR use encryption function for decryption as well. What is the logic behind it ?
"Is it why because ECB and CBC generates output of Block Cipher type and CFB, OFB and CTR generates output of Stream Cipher type"
Question is originally... |
Why do some block cipher modes of operation only use encryption while others use both encryption and decryption? |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
RSAP is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE: A Single-Party Public-Key Auth... |
Unbalanced RSA (also known as RSAP) is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE:... |
How low can the public exponent be in unbalanced RSA? |
Unbalanced RSA (also known as RSAP) is a variant of RSA proposed in 1995 by Adi Shamir's [_RSA for Paranoids_][1] as a mean to increase the RSA public modulus size while keeping computation cost moderate. It is getting renewed interest, as part of a lightweight authentication and key agreement protocol born as [_SPAKE:... |
For example, I have 3 plaintext $a$,$b$,$c$, and 4 keys $k1$,$k2$,$k3$,$k4$, making a table map to the cipher text, key as row and plaintext as column
![enter image description here][1]
This is not a perfect secrecy system, because if we know cipher text not $B$, then plaintext confirm not $b$. to avoid this, we ... |
How we can said a crypto system have perfect secrecy? |
Chapter 6, Question 6.8 of William Stallings book “Cryptography and Network Security Principles and Practices” asks:
> Why do some block cipher modes of operation only use encryption while others use both encryption and decryption?
ECB and CBC use encryption function and decryption function while CFB, OFB and CTR... |
In Chapter 6, Question 6.8, of his book [“Cryptography and Network Security Principles and Practices”](http://books.google.de/books/about/Cryptography_and_Network_Security.html?id=kOxLPgAACAAJ&redir_esc=y), William Stalling asks:
> Why do some block cipher modes of operation only use encryption while others use both... |
For example: I have 3 plaintexts ($a$, $b$, $c$) and 4 keys ($K_1$, $K_2$, $K_3$, $K_4$), making a table map to the cipher text, key as row and plaintext as column
$\begin{matrix}
\ \ \ \ \ \ \ \ \ \ \ \ a\ \ \ \ b\ \ \ \ c\\
\\
K_1\ \ \ \ \ \ \ A\ \ \ C\ \ \ B\\
K_2\ \ \ \ \ \ \ B\ \ \ A\ \ \ C\\
K_3\ \ \ \ \ ... |
Yes. We can easily generate the malicious public key as in DSS case.
The following attack was proposed in Section 4.5 of [Blake-Wilson and Menezes: Unknown Key-Share Attacks on the Station-to-Station (STS) Protocol (PKC 1999)](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.1051).
Let $(G,q,n,P)$ be the ... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One classic method t... |
I read that TLS does PFS using Diffie Helman. However, DH can be used even without certificates - so how is DHE-RSA better than plain DHE?
Is DHE a insecure algorithm, that DHE-RSA is needed? |
I read that TLS does PFS using Diffie Hellman. However, DH can be used even without certificates - so how is DHE-RSA better than plain DHE?
Is DHE a insecure algorithm, that DHE-RSA is needed? |
I'd be a noob in cryptography but reading up a little on RSA, I do get some understanding and I want to specifically resolve this issue.
**UPDATED**
Lets say we have the following values in place:
KEYSIZE = 512
HASHSIZE = sha.digestsize*8
digest = some SHA 512 function
We calculate the pub... |
I recently read questions about "MAC then Encrypt/Encrypt then MAC" which made me curious about how they actually use the algorithm.
MAC only calculated once either case (according to what I read).<br>
However, in my experience surfing website via HTTPS, I think we should check the authenticity in every chunk of da... |
How do they implement MAC in TLS? |
For my cryptography class project in university I have selected `Paillier Cryptosystem` as a course project http://en.wikipedia.org/wiki/Paillier_cryptosystem#Key_generation
In key generation it says
>Choose two large prime numbers $p$ and $q$
I have selected $p$ = 11 and $q$ = 17, it also satisfies the condi... |
For my cryptography class project in university I have selected `Paillier Cryptosystem` as a course project http://en.wikipedia.org/wiki/Paillier_cryptosystem#Key_generation
In key generation it says
>Choose two large prime numbers $p$ and $q$
I have selected $p$ = 11 and $q$ = 17, it also satisfies the condi... |
*Perfect Secrecy* (or *information-theoretic secure*) means that the ciphertext conveys no information about the content of the plaintext. In effect this means that, no matter how much ciphertext you have, it does not convey anything about what the plaintext and key were. It can be proved that any such scheme must use ... |
I recently read questions about "MAC then Encrypt/Encrypt then MAC" which made me curious about how they actually use the algorithm.
MAC only calculated once either case (according to what I read). However, in my experience surfing website via HTTPS, I think we should check the authenticity in every chunk of data re... |
> Do you want DDH/RSA-based PRFs? If so, we have them and I will answer. – xagawa
>
> @xagawa Yes, I want that :-) – Dingo13
I list the PRFs based on the number-theoretical assumptions.
They are ``arithmetic or mathematical function.''
You can use the Feistel network to obtain (S)PRPs from PRFs in theory.
... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One classic method t... |
**Yes, we can build a hash function from a block cipher**, and that's common (although with block ciphers designed for that purpose, when in the following I focus on AES). CBC is not directly appropriate: what would the key common to all the encryptions be? There is no secret in a hash function!
One classic method t... |
Assume it is made a hash based on AES-256 encryption (perhaps because this is hardware-accelerated, but no hash is), using the [Merkle–Damgård][1] structure with padding into $n$ message blocks $M_i$ (appending to the message a 1, a minimal number of 0, and the 64-bit message length in bits), and a compression function... |
Are AES-256 related-key weaknesses exploitable if it is used to build a hash? |
Assume it is made a hash based on AES-256 encryption (perhaps because this is hardware-accelerated, but no standard hash is); and it is used the [Merkle–Damgård][1] structure, that is padding of the message into $n$ padded message blocks $M_i$ (appending to the message a 1, a minimal number of 0, and the 64-bit message... |
Are AES-256's related-key weaknesses exploitable if it is used to build a hash? |
Assume it is made a hash based on AES-256 encryption (perhaps because this is hardware-accelerated, but no standard hash is); and it is used the [Merkle–Damgård][1] structure, that is padding of the message into $n$ padded message blocks $M_i$ (appending to the message a 1, a minimal number of 0, and the 64-bit message... |
I am implementing a key distribution protocol described by Torben Pedersen in *A Threshold Cryptosystem without a Trusted Party* (EUROCRYPT'91). In the protocol, the $n$ parties distribute a public key for the ElGamal cryptosystem, where each party ends up with "part of" the private key and can work together to decrypt... |
In Pedersen Key Distribution, can the public key be persistent? |
The definition of DH key exchange was given as the method let two authenticate each other & exchange the crypto key over an insecure channel.
DH-key-exchange was innovated to defence man-in-the-middle attack, because hackers can not pretend the one you want to communicate without correct share key? or hacker don't k... |
I believe that you misunderstand what DH is doing.
> DH-key-exchange was innovated to defence man-in-the-middle attack, because hackers can not pretend the one you want to communicate without correct share key? or hacker don't know the key generator that Alice and Bob pre-agreed?
Well, no, defending against activ... |
When I use the same 128-bit key for AES-128 and AES-256 with a known/public padding for the latter, is there some weakness in AES-256 that is not present in AES-128 with essentially the same key?
This might be the case when I'm receiving the key from an algorithm which just doesn't produce enough bits (128 or less).... |
Has AES-128 the same strength as AES-256 with a padded key? |
I found myself wondering today, how much security is lost if you take a plaintext - assume that its content, including any metadata is unknown to an attacker, for example it may be random data - and encrypt it with multiple keys (not chained) and give all resulting cyphertexts to an attacker, how much higher is the pro... |
# The LWE assumption
I think we should start from the LWE assumption.
Let $n$ and $q$ be integers and let $\chi$ be a distribution over $\mathbb{Z}_q$. We often take $\chi$ as a Gaussian with small variance. (We take an error $e$ from this distribution $\chi$ and assume that $|e| \ll q$.)
The LWE assumption stat... |
I found myself wondering today, how much security is lost if you take a plaintext - assume that its content, including any metadata is unknown to an attacker, for example it may be random data - and encrypt it with multiple keys (not chained) and give all resulting ciphertexts to an attacker, how much higher is the pro... |
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