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I am testing the quality of AES S-box and using the lookup table I built a function from GF($2^8$) to GF($2^8$) seen as vector spaces. I was wondering if there is a transformation that I can use to find an equivalent permutation of AES S-box that sends $0$ in $0$ without modifying the properties of the S-box such as li... |
What is the historical pattern for key size increases for rsa vs discrete log?
What are the current and future projected sizes for these?
|
I have seen authors taking $G_1=G_2=G_T=G$ to be the same group of prime order $q$.
What I know is that for pairing of type $$e:G_1\times G_2\rightarrow G_T,$$ size of the element in the target group is $kn$ where $n$ is the size of an element in $G_1$ and $k$ is the embedding degree.
Source: A New Family of Pairin... |
Is there an algorithm that lets me sign a value with two keys at the same time, and in turn requires both keys to verify the signature?
For instance, a scheme could work like this:
Sign X with Key1 and Key2 at the same time
Verify X is signed by these two keys
This would be like a joint bank account: to do anything o... |
Let's suppose that Bob has only Alice's IP and no more information about Alice's key, nor the digest of Alice's key.
They exchange keys and need proof that the received keys are the same keys that were sent.
How Bob and Alice can know that the key received is the right key?
Also, I read about Sigma protocol:
The gener... |
Consider an elliptic curve $E$ defined over a finite field $\mathbb{F}_{\!q}$ with a fixed non-zero $\mathbb{F}_{\!q}$-point $P$. For simplicity, let the order of the $\mathbb{F}_{\!q}$-point group $E(\mathbb{F}_{\!q})$ be prime and hence the group is generated by $P$. For the sake of security, in numerous protocols of... |
Consider the Ring-SIS problem for $R_q=\mathbb{Z}_q[x]/(x^n+1)$ when $n$ is power of $2$ and $q=1 \mod 2n$. Does the modulus $q$ need to be prime? if yes, it seems that it is mainly because of the way that we prove the hardness of Ring-SIS by reducing it to a lattice-problem. This means that it might be possible to cho... |
I am going through the Lamport Diffie One-time signature. I am having a hard time understanding
How can long messages (greater than 100 bits) can be mapped into short messages (100 bits) by a one way function and only the short message signed? Can someone explain this with an example?(Refer page no.13 in attached docu... |
What is meant by meta reduction? What does it achieve and how is it different from the normal reduction technique?
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Is using AES GCM with PBKDF2 and 100 000 iterations still considered secure as of 2022?
In our threat model, if we ignore the risks linked to quantum computing, is this secure?
Here is an example working Python implementation:
import Crypto.Random, Crypto.Protocol.KDF, Crypto.Cipher.AES
plaintext = b"hello world hello ... |
Tor vanilla bridges look like this:
Bridge x.x.x.x:1234 9DD03662B50FEDBF6F8D5630CB86D7E8CE4F4432
It's only the IP/Port and a hash of the key.
Can Bob and Alice do an authenticated Diffie–Hellman key exchange if Bob just knows the hashsum of Alice's key?
Thinking by myself is possible, Bob receives Alice's key and ver... |
I read through related questions on this SE, but I still do not understand why we can use the rewinding argument. Specifically, rewinding seems like a really strong superpower to me, and I don't understand why such strong assumption does not undermine the strength of the conclusion. Sure, the adversarial verifier learn... |
My understanding of digital signatures is as follows: Alice hashes a message with a one-way cryptographic hash function, the output of which is called the message digest. She then encrypts the digest with her private key and then sends both the original unhashed/unencrypted message along with the encrypted hashed versi... |
I'm currently trying to get an overview of post-quantum cryptography. Now I'm struggling with correlations and adjustments of the PQ-world and the Modern-world of cryptography.
My Questions:
Can you give me a brief overview of new important assumptions in the PQ-world (e.g. something similar to the factorization or di... |
Are there any methods to prevent version rollback attack while using TLS 1.2 (apart from disabling lower versions)? I've read about how TLS 1.3 provides a downgrade protection mechanism which is embedded in the server’s random nonce. Is there any such mechanism in TLS 1.2?
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I'm interested in the Post Quantum Algorithms of the 3rd round of the NIST standardization competition. The algorithms for KEM are Classic McEliece, CRYSTALS-KYBER, NTRU, SABER and their 5 alternatives. The signature algorithms are CRYSTALS-DILITHIUM, FALCON, Rainbow and the 3 alternatives. I was looking for a comparis... |
I need to store sensitive data (like customer photos) in a SQL database in the most secure way in case of security breaches. The data won't be accessed by the clients, only by internal processes that perform some validations.
The customers don't have any input like passwords, they just register with us and we keep trac... |
I'm reading from William Stalling's Cryptography & Network Security - 7th Edition
To me the first line suggests
$$(M^e\bmod n)\times(2^e\bmod n)=((2M)^e\bmod n)$$
which means that if we want to define a message $X$ such that when decrypted it gives $2M$ then we should consider $X=(M^e\bmod n)\times(2^e\bmod n)=C\times... |
The mac1 field in the WireGuard handshake messages is populated as:
msg.mac1 := Mac(Hash(Label-Mac1 || Spub_m'), msgA) // first arg is MAC key
Label-Mac1 is a constant, Spub_m' is the static public key of the peer, and msgA is the bytes of the message before the mac1 field.
I don't understand the purpose of this, g... |
Just a question I thought of while playing an amazing game about time travel (13 sentinals aegis rim). What are the most bullet-proof cryptographic methods for proving you've come from beyond a particular year? (e.g. 2069)
My current idea goes something like this:
A huge trust-worthy company (e.g. Google) creates a su... |
Say $a$ and $b$ are some uniform random $8$ bits so that the entropy of $a$ and $b$ is 8 bits each.
If I show you $(a+b) \bmod{256}$ and $a$ XOR $b$, then what can you tell about $a$ and $b$? Or how much of their entropy is reduced?
|
I'm looking for a quantitative yet simple proof of the EUF-CMA security of a signature scheme obtained by Fiat-Shamir transform.
Recall the Fiat-Shamir transform starts from a 3-pass identification protocol with messages $(I,r,s)$, where $I$ is the prover's commitment, challenge $r$ is chosen uniformly at random in set... |
I wanted to compare the performance of different cryptographic systems. There is a pretty good paper comparing the 3rd round finalists of the NIST competition.
I was wondering if there are good performance comparisons of those PQ-Protocols and modern ECC/RSA protocols (e.g. Curve25519). Sadly I couldn't find a good pap... |
Previously I thought about a pair of 8-bit uniformly distributed random numbers $(a,b) \in \{0,1\}^8$, and $X$ to be bitwise XOR, $Y$ to be 8-bit addition. But it turned out that revealing $a \text{ XOR } b, a+b \bmod{2^8}$ does reveal a lot of information bits about $a,b$.
A smart dude here mentioned "dependence" as ... |
Given a set of plain texts $P \subseteq \{0, 1\}^n$. Assume we know the corresponding set of cipher texts $C \subseteq \{0, 1\}^n$ produced by applying one-time pad with an unknown key $k \in \{0, 1\}^n$.
Question: How to compute $k$, based on $P$ and $C$?
My approach: For every pair $(p, c) \in P \times C$, compute th... |
From what I understand, in BIP 32, the knowledge of the parent public key and the child private key provides the parent private key, in a non-hardened path. Indeed, it's only a matter of substracting the part provides by the current path from the child's key to get back the parent's key.
I have an application in which ... |
May someone please explain how the reduction is done? I am familiar with other algebraic structures but wondering if I am doing reduction correctly for this.
It is understood that a Polynomial Ring of this form, $\mathbb{Z}_{q}[x]/(x^n + 1)$, consists of the set of all polynomials defined by $(x^n + 1)$ with coefficien... |
A bunch of friends are using public-key encryption to send encrypted messages to each other using an open public forum. I.e. each friend has a public key (which you can use to encrypt messages for them) and a private key (which they use to decrypt messages for them).
Bob sends Alice the encrypted message $y$, which, wh... |
In my course about cryptography, we started looking at hash functions. As homework, we had to pick a modern hash function and describe it in class. I chose BLAKE2b, which I can understand well when it is explained in words, but the official implementation raises questions.
static void G(int roundNum, int i, int a, int... |
are there any available tools/libraries that implement the idea of EIGamal-based proxy re-encryption scheme shown below? Preferably in Golang. Thank you!
Source of this picture: https://www.cs.jhu.edu/~susan/600.641/scribes/lecture17.pdf
|
Let $E$ be an elliptic curve over a binary extension field $GF(2^m)$, with constructing polynomial $f(z)$ be an irreducible, primitive polynomial over $GF(2)$, and let $G(x_g,y_g)$ be a generator point on the curve.
Is there any possibility that two (or more) different $f(z)$ can produce exactly the same GAL group for ... |
In our Python codebase, some random bytes were generated that we wanted to be cryptographically secure. Previously, the code was:
capability = "".join(secrets.choice(string.digits) for i in range(33))
I've changed it to:
capability = secrets.token_bytes(16)
By my estimation, the first version chose 33 times between 1... |
Suppose for $sk = x$, $pk = g^x$ we encrypt message $m$ with ElGamal encryption as $(g^r,m\cdot pk^r)$. My goal is to prove that I performed the encryption correctly, i.e. that the same $r$ is used across $g^r$ and $m\cdot pk^r$.
I thought of a simple $\Sigma$-protocol to show this as follows:
Prover samples $q_1,q_2$... |
I'm having difficulty understanding this.
Consider two messages are encrypted using the same cyclic group order $q$, generator $g$, private key $x$, and random parameter $y$.
The attacker knows a plaintext $m_1$ and its corresponding ciphertext $c_1=\left(r_1,s_1\right)$.
I was told that, under these circumstances, if ... |
For example, Alice and Bob have two numbers $a$ and $b$, respectively. They want to calculate the multiplication $a\cdot b$ without Alice knowing $b$ or Bob knowing $a$ and send this multiplication $a\cdot b$ to Carol. Carol will use this $a\cdot b$ to do further application. Carol will not collude with Alice or Bob. A... |
The private (secret) key in DL (discrete logarithm) based algorithms is uniformly selected from the group Zq*. This private key is then used to compute the public key. Could the opposite be done, for instance, select the public key uniformly from Zq* and then compute the private key?
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We are manufacturing a sensor which transmits in 8 byte packets. This sensor will be used by several different receivers, some of which have very little spare RAM available (< 3 kb). On some of the receivers we will provide the software, in other cases, we will be providing the code to the manufacturer under NDA.
It is... |
Is there a way to modify the RSA so that it's homomorphically additive?
I did some research and came across a paper which describes MREA (Modified RSA Encryption Algorithm), an RSA modification that, supposedly, is homomorphically additive.
The authors define the encryption algorithm as follows:
$$ E(message) = g^{mess... |
I'm having difficulty understanding this.
Consider two messages are encrypted using the same cyclic group of order $q$, generator $g$, private key $x$, and random parameter $y$.
The attacker knows a plaintext $m_1$ and its corresponding ciphertext $c_1=(r_1,s_1)$.
I was told that, under these circumstances, if an attac... |
I have to solve the following problem:
What I have:
$n$, a 2048 bit number
What I need to find:
$p$ and $q$ such that $n = p\cdot q$.
What I know:
With $p_1$ the first half of $p$ and $p_2$ the second half, the same with $q_1$ and $q_2$:
$$p_1 = q_2\ \text{ and }\ p_2 = q_1$$
Therefore finding $p$ you could also ... |
Assume that block cipher scheme $(KeyGen, Enc, Dec)$ is CPA-secure. Show that $CTR_{Enc_k(0^n)}$ is a good PRNG.
Counter mode works as follows:
$Y_i = Enc_k(IV + f(i))$
$C_i = Y_i \bigoplus P_i = Y_i \bigoplus \{0^k\}= Y_i$
So the output here is simply $Enc_k(IV + f(i))$. Now, as good PRNG I understand that it needs to... |
There is a Feistel block cipher based on Blowfish called Kaweichel. In one of its papers, there is this affirmation:
For the construction of the round function one choses usually parallel
substitutions (s-boxes). The output bits of these s-boxes are permuted
in order to achieve diffusion. For the derivation of the ro... |
Hi I am quite new to NIZK. I know a trusted party (Generator) generates proving key and verifying key and then distributes them to Prover and Verifier. Apparently, the verifying key can be seen as public for anyone in the system, but what about the proving key? If the proving key is known to a different party other tha... |
I am familiar with Fourier Transform and computing the DFT and FFT matrix for fast multiplication of integers. However, this is the first time I work with NTT applied to polynomial rings of the form $\mathbb{Z}_q[x]/x^{n} + 1$.
Say for small q=5 and $n$=2. My elements consists of all polynomials of degree at most $n-1$... |
I want to implement LWE-based encryption scheme, the modulo $q$ could be decomposed as $q = q_0\cdot q_1\cdots q_k$ according to CRT. I guess the modular arithmetic by $q_i$ is key operation, so I try to choose the Mersenne prime. However, there are only two primes satisfied: $2^{31}-1$ and $2^{61}-1$.
Are there any o... |
Say a server plays a game of blackjack with a client, and the cards are shuffled and dealt by the server. The shuffle itself may or may not be fair, but what needs to be shown is that the cards dealt weren't altered during the course of gameplay, ie: after the start of the hand, the cards in the deck do not secretly ha... |
While coding for Edwards curve, I noticed that, the addition formula and the doubling formula return what seems to be different result.
I took the adding and doubling formula from both RFC-8032 and https://eprint.iacr.org/2008/522 and confirmed this difference.
Why is that? How does it, if it does effect computations w... |
What does it mean to solve $\mathsf{SVP}_{\gamma}$ in worst-case?
Does it mean that the problem is solvable for any lattice we choose?
|
Would secrets.choice be random enough to pick winners in a raffle?
|
I admit I don't know a lot about the math behind Curve25519 and the DH exchange based on it.
I'm asking if after publishing the result of this operation:
ephemeral_share = X25519(ephemeral_secret, BASEPOINT)
Can ephemeral_secret be found by whomever obtains ephemeral_share, given that they know the used curve (and the... |
This was a practice problem for a class. The class is over now and I never solved it, so I thought I'd ask here.
Let's ignored the fact that adding extra security to single textbook RSA is unnecessary. As hilariously stated here:
Think about it this way, if it is estimated to take 500 years for a prisoner to chew thro... |
Given the following definitions for $\mathbb{Z}[x] /\left(x^{n}-1\right)$:
$$
a \cdot b \equiv \sum_{i=0}^{n-1} \sum_{j=i+1}^{n-1} a_{i} \cdot b_{j} \cdot x^{i+j}+\sum_{j=1}^{n-1} \sum_{i=n-j}^{n-1} a_{i} \cdot b_{j} \cdot x^{i+j-n}\left(\bmod x^{n}-1\right)
$$
Similarly, for $\mathbb{Z}[x] /\left(x^{n}+1\right)$ the m... |
Why do we take Gaussian-like errors in $\mathsf{LWE}$?
Why for example we don't take uniform errors?
|
While implementing SM2 DSS and reading RFC-8032 for EdDSA, I noticed that, both families of schemes provide provisions for including a "context" (in EdDSA) or "signer info" (in SM2 digital signature) in the signature.
Q1: What non-trivial benefit does it provide? Does it help prevent duplicate key attack?
Q2: Are there... |
In secret sharing schemes, we usually give rational fractional parts of a secret out. E.g. Alice gets 4/10ths of the secret, Bob gets 7/10ths, Charlie gets 5/10ths, David gets 1/10th, etc., and you need 10/10ths total to unlock the secret.
My question is: is there a scheme that allows for an irrational fraction of sha... |
Suppose $f_k$ is an arbitrary block cipher. Can OFB via $f_k$ be used to make a MAC. I argue that you can't even with fixed l, $m = l \times k$ because in OFB, $\mu = f_k(f_k(...((IV))) \oplus m$, and with an oracle, you would be able to get $\mu$ for a given message and find $f_k(f_k(...(IV)))$ and so can find $\mu$ f... |
hello guys hope you are doing well :),
i am trying to simulate the Schnorr Signature, but i have encountered some difficulties finding the generator,
i have chosen a prime P of 1024bit and took a factor of 160bit as Q but for the generator i'm trying to produce,
i'm using the equation => g^Q = 1 mod P
how can i impleme... |
In RSA-FDH to sign a message $m$, we apply a hash function $H$ and then "decrypt" it using the private key $d$, so $Sign(m) = H(m)^d \mod N =: \sigma$ and then to verify, we use the public key, resulting in $H(m) = \sigma^e \mod N$ if all goes well.
Why do we have to use RSA for this instead of something else, for exam... |
I need a lightweight cryptographic hash function which is additive but not reversible, however I'm not sure such a function exists! (it would be better if it works in multisets as well)
By additive I mean:
given such function f, another function g must exist, having the property g(f(X),f(Y))=f(X||Y), where || denotes c... |
Are there any examples of a cryptographic scheme based on (an average-case form of) a #P-complete problem?
|
Very short question.
Is it possible to encrypt a sequence of numbers with FPE in a range 10 000 to n where the possible encrypted values are offset and can only fall within the range 10 000 to n?
Eg. A sequence number with a maximum of 10 digits will be zero padded (0000 0532 12) and encrypted into the IAN part of a PA... |
Why if $q$ is a power-of-two integer, then doing arithmetic modulo $q$ (addition and multiplication) is very efficient and straightforward?
|
I'm self-studying cryptography from A Graduate Course in Applied Cryptography by Boneh and Shoup (version 0.5), and I'm having trouble seeing the result in Exercise 6.7.
In the book a secure MAC system is defined in terms of an attack game where an adversary can perform signing queries on arbitrary messages to receive ... |
Basically this post was about a cipher with a trailing "="
Any idea is welcome :)
|
The proof of Theorem 5.2.13 : For semantic security, the author wrote "$m_1 \leftarrow {\rm Sim_1}(1^\lambda)$". I think it may contradict with the security requirement defined in Definition 5.2.11 and Definition 5.2.12 where it is required that the outputs of ${\rm Sim_1}(1^\lambda)$ and ${\rm SFE1_F}(1^\lambda, x)$... |
Currently I am facing a situation in which Ed448 key pairs (private + public key) are available and the system should be extended by a Diffie-Hellman (ECDH) operation. First of let me summarize what I have understand so far.
Ed448: Is the digital signature algorithm on edwards448.
X448: Is the Diffie-Hellman function b... |
I'm studying ECDSA, and almost all somewhat detailed articles talk about using Strauss-Shamir trick on the verification step.
Then I searched, and found this explanation (more like a stating) for the algorithm, and then this other pdf (page 7) that explains it a bit more in detail. But none of them provide an explanati... |
$\text{CBC-MAC}$ is defined as follows:
$\text{CBC-MAC}_k() = IV $
$\text{CBC-MAC}_k(m_1, . . . , m_n) = E_k(m_n \oplus \text{CBC-MAC}_k(m_1, . . . , m_{n−1}))$
My lecture notes say that this is secure for fixed-length messages but forgeries are possible with arbitrary-length messages. I'm trying to come up with a ... |
I was wondering whether there exists a symmetric encryption scheme such that
there is 1 sender and n receivers. Each receiver has 1 random and independent symmetric key. The sender knows the symmetric keys of all receivers in advance.
the sender can encrypt one message using the above n keys and produce a ciphertext. ... |
In the following paper: https://eprint.iacr.org/2018/056.pdf, the random oracle is defined as follows:
$ H: *\xrightarrow{} \{ \mathbf{v} | \mathbf{v} \in R_{q,[1]}, || \mathbf{v}||_{1}=\omega\}$
Where $R_{q,[1]}$ stands for those elements that belong to the ring $R_{q}=Z_{q}/<x^n+1>$ and have coefficients between [-1,... |
I'm trying to stop a server using Diffie Hellman algorithms of less than 2048 bits ..but I'm getting confusing results
I've run
Get-TlsCipherSuite | Format-Table Name, Exchange, Cipher, Hash, Certificate
and I can see
TLS_DHE_RSA_WITH_AES_256_GCM_SHA384
TLS_DHE_RSA_WITH_AES_128_GCM_SHA256
TLS_DHE_RSA_WITH_AES_256_CBC_... |
Assume an architecture with fast 60-bit native words (a close example would be Ocaml, which has unboxed 63-bit numbers, and only boxed 64-bit numbers). We're looking for the fastest hash function in that architecture. Keccak is great, but our best bet, so far, is to port it from implementations that use 32-bit numbers,... |
Show that if two different RSA public keys $p_k$s are known to an attacker for the same secret key $s_k$, then $s_k$ can be broken
I've deduced that that if the 2 public key exponents are $e_1,e_2$ then they have the same remainder modulo $\phi$, but that still doesn't help me determine $d$.
|
In the Section 3.12 of book writen by Boneh and Shoup, a Bit commitment from secure PRGs is presented as follow:
Bob commits to bit $b_0\in_R\{0,1\}$:
Step 1: Alice chooses a random $r\in R$ and sends $r$ to Bob.
Step 2: Bob chooses a random $s\in S$ and computes $c=com(s,r,b_0)$, where $com(s,r,b_0)$ is the ollowing f... |
In the final step of verifying an EdDSA signature, 4[S]B is compared to [4]R + [4][k]A.
Because I'm using the XYTZ - extended twisted Edwards coordinates, I want to, for efficiency reasons, do:
$$ Y(\text{Left}) \cdot Z(\text{Right}) = Y(\text{Right}) \cdot Z(\text{Left})$$,
But that leaves the X coordinates unchecked.... |
I read some papers that mention the von Neumann corrector. They always assume that for the von Neumann corrector, the input bits are independent of each other and same bias
Why does the von Neumann corrector only work when the input bits are independent of each other and same bias?
|
I am trying to prove the following:
Given an ensemble $\{p_n, g_n\}$ ($p_n$ is an $n$-bit prime and $g_n \in \mathbb{Z}^*_{p_n}$ is a generator), if $A$ is a deterministic polynomial time algorithm such that:
$$ \Pr_{x \leftarrow \mathbb{Z}^*_{p_n}} [A(a)=x \text{ where }
g_n^x=a]=\frac{1}{poly(n)}$$
then there is a... |
Work Factor is defined as the minimum amount of work (can be the length of the key) to determine the secret key of an cryptosystem (HAC, Menezes, Alfred J. et al).
And One time pad have unconditional security or is perfectly secure, it means it is impossible to break even with unlimited processing power and memory (whe... |
Consider the following protocol:
$A\rightarrow B: \{N_A,A\}_{pk(B)}$
$B\rightarrow A: \{N_B,N_A\}_{pk(A)}$
$A\rightarrow B: hash(N_B, A, B)$
where it is intended that when either $A$ or $B$ has completed their own role in the protocol, they are assured that the other has participated in the protocol with them and... |
Let $E$ be an elliptic curve over a prime or a binary extension field $GF(2^m)$, and let $G(x_g,y_g)$ be a generator point on the curve. Let $Q$ be an arbitrary point $Q = r*G$, with $r$ scalar, and $Q$ an element from the group of generator $G$ of order $n$.
I have read in some sources (e.g. here for curves over binar... |
Me and my friend would like to login to an SSH server using the same private RSA key.
However, we don't want to transmit the key over the internet, for security.
I am thinking if it's possible to generate the same RSA key pair using a mutual secret from the Diffie–Hellman Algorithm (or other key exchange algorithms).
S... |
From the wiki, we know that to encrypt a message $M$ using Elgmal encryption, one should firstly map the message $M$ to an element $m$ of G using a reversible mapping function, then run the ElGamal encryption algorithm to get the ciphertext $C$. To decrypt $C$, one should run the decryption algorithm to get $m$, and fi... |
Referenced paper here.
The above excerpt is from Page 19 of attached paper. I have a few questions.
y = F^9(x) is equivalent of F(F(F(F(F(F(F(F(F(x))))))))) ?
The excerpt says that this allows us to sign 4 bits of information. Shouldn't it allow a person to sign any size message(ex: 100 bits) not just 4 bits by just ... |
Here I use a Threefish kernel module with CBC mode. But there is no hash function that can supply a IV with Threefish block size (1024-bits), so I use a 64-bit random IV inserted in the dm-crypt with cryptsetup --skip option.
I know that the ideal size for an IV in CBC encryption is the same size of the block, but, wha... |
I generate a random message m sent to a device that calculates sig(m, privKey) with secp256k1. It then performs an HTTP GET call to share both pubKey and sig with the purpose of authentication.
(m remains private to me and is randomly generated for every new authentication request. EDIT: it crypto terms it might be cal... |
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA supports forward secrecy but it doesn't use GCM mode and use SHA1 TLS_RSA_WITH_AES_256_GCM_SHA384 uses GCM mode and SHA2 but it doesn't support forward secrecy. Which one is more secure?
|
In many NTRU material it is said that with our choice of the polynomial $f$, it will almost always have an inverse. Maybe it's a stupid question, but why will it almost always have an inverse element? And why is it recommended to take the polynomial $1 + pF$ in order to have the inverse?
And one more question: why is i... |
I'm very new to cryptography. I'm required to read a paper.
I totally don't understand. First, what's the meaning of the asterisk in $H:\{0,1\}^*\rightarrow \{0,1\}^k ?$.
Second, what does PPT mean here? (I searched the Internet but didn't get satisfying answer.)
Third, why if $b=1, s\leftarrow H(g^{ab})$, else $s\le... |
I am working on a system to transfer short messages while obfuscating the intended recipient.
In essence, it combines many messages encrypted using PGP, and periodically publishes a file containing those messages. The recipients would then download that file and try all messages against their secret key.
Given a messag... |
I'm reading Understanding Cryptography by Christof Paar and Jan Pelzl. In chapter 2 (Stream Ciphers). There is a section talking about "Bulding Key Streams from PRNGs".
They assume a PRNG based on the linear congruential generator:
$$S_0 = seed $$
$$S_{i+1} \equiv AS_i + B\mod m, i=0,1,...$$
where we choose m to be 1... |
I received an answer in one of my questions saying that multiple-encryption with CTR mode of operation is vulnerable to a sort of meet-in-the-middle attack if the IVs are public. The same user said that keeping the IVs secret such attack not applies and that the cost of breaking a double-encryption with brute-force for... |
I have question regarding DLP in GF(p^m)
I know we can use CADO-NFS to solve the DLP in GF(p).
But what if we move into the GF(p^m) and are working with polynomials? Does the Cado tools can calculate it still? If so, how to use it when the domain is GF(P^2) with polynomials?
Anyone with some experience with this tool c... |
The definition of zk-SNARK involves not leaking any information from the prover-verifier interaction, but what about leaking information from the circuit itself? e.g., could there be a circuit to demonstrate that I know the preimage to s, where s is a signature generate by secret x and signing algorithm HMAC(x, plainte... |
I was reading intro to modern cryptography and didn't understand how did they calculate the probability:
Say we have a cryptographic scheme in which an honest parties run for $10^6 \cdot n^2$ cycles and for which an adversary running for $10^8 \cdot n^4$ cycles can succeed in breaking the scheme with probability at le... |
I was reading the following:
The functions $2^{-n}, 2^{-\sqrt{n}}$ are negligible. However they approach zero at different rates. For example, we can look at the minimum value of $n$ for which each function is smaller than $\frac{1}{n^5}$
Solving $2^{-n} < n^{-5}$ we get $n>5\cdot log(n)$. The smallest
integer value ... |
Consider for example this set of encrypted values under the Elgamal keys $y_0$,$y_1$,$y_2$: $$
Enc_{y0}(g^0),Enc_{y1}(g^{-20}),Enc_{y2}(g^{-10})
$$
Can I prove that one value is $g^0$ and the others are $g^b$ where b is negative without revealing which one is who?
|
I've been wondering about this paragraph for some time:
Multiplication is a great mixing function. If you work out what multiplication looks like in terms of ANDs and XORs it becomes apparent how elaborate a 64bit multiply is. The amount of transistors required to implement it in hardware prohibits multiplication from... |
Let me try to reformulate the problem, as it might help a bit. The requirements are the following:
At the beginning of their connection, the two end-points perform a Diffie-Hellman to derive with a common key $K$.
Then EP1 needs to generate a random 48-bit value $R$ and send it to EP2. This random value needs to have ... |
I have read again and again this paper from A. May, but, probably because I am new to this field, I don't succeed in understanding the MEET-LWE part.
In particular, in part 5 it states to choose a "randomly chosen target vector" $t ∈ \mathbb{Z}_r^q$. Later, is is said that a value of $s1$ satisfying $π_r (As1 + e1) = t... |
I am looking for a hash function that uses a timestamp as salt, and produces an output that when run through another function only returns the timestamp used.
What would this be called? It's not a one-way hash and it's not a fully reversible hash function.
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