instruction stringlengths 32 27.2k |
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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.
|
I am really new to cryptography and I have asked a similar question which is about Decisional Diffie-Hellman assumption (What's the meaning of asterisk and PPT in this paper?) and it is already kind of difficult to me.
But this paper Practical Secure Aggregation for Privacy-Preserving Machine Learning (https://eprint.i... |
Basic question: ENT seems to trip up generators that pass NIST 800-22 and maybe even dieharder. How do the latter two test suites miss such an obvious failure?
There are two things I want to mention about the well-known randomness test suite ENT, which is, as far as I understand, considered to be far less rigorous than... |
Consider the DSA digital signature scheme.
Does the intercepted message m||s||r contain all information about the signer’s private key? Please justify your answer carefully.
Please note that the equation $a = αx \mod p$ does give all the information about $x$ in the range $0 ≤ x ≤ p − 2$ when $a$, $p$, and the primitiv... |
Given an one-key cipher such that:
$E[k_1,E(k_2,m)]=E[k_2, E(k_1, m)]$
Is there any key distribution protocol that involves only two parties (Alice and Bob) without the key distribution center?
The protocol should allow Alice to send a session key to Bob with confidentiality using the one-key cipher.
|
I understand that there are symmetric and asymmetric (public-key) cyphers. The first have the same key used for encryption and decryption, while the second use a public key for encryption and a private key for decryption.
I understand that there are block and stream cyphers. The first work on rounds through the various... |
In the knowledge soundness definition page 8 of Groth16, it says: The extractor gets full access to the adversary’s state, including any random coins. My question is why full access? Why we just don't say oracle access to the adversary?
Then in the definition of witness-extended emulation (WEE) in Bulletproof (page 10)... |
Let's suppose I want to do One-Time-Pad but I only have a biased true random number generator (TRNG).
I XOR to the ciphertext block with another with random data got from the TRNG, e repeat the process two or more times with different random blocks.
Will this scheme make the One-Time-Pad more secure? Will this provide ... |
Reference paper: "A CERTIFIED DIGITAL SIGNATURE"
With reference to the image above which is from Page 20 of the attached paper. What is this new protocol that the paper speaks of here? What does "transmitting Yi to B just before signing a message" mean? How does it differ from the default case? How could anyone claim... |
I have a bunch of signatures (1000) signed with ECDSA secp256k1 curve. I can verify all of them with the same public key.
I have studied attacks are performed against ECDSA signatures using known MSB or LSB of the nonce.
Is private key recovery possible if nonce $k$ value is of unknown length? None of the signatures ha... |
I'm currently working on replacing the chacha20 encryption in my app with chacha20poly1305, but I'm running into a few questions that I can't seem to find clear answers to, mainly stemming from the Rust chacha20poly1305 crate:
Why does the chacha20poly1305 crate require a nonce for every message, but chacha20 only req... |
I am looking at wrapping AES keys with RSA. In NIST SP 800-57 Part 1 Recommendation for Key Management, pg 55 it is estimated that the RSA security-strength equivalent of symmetric AES-256 key would be a RSA key with 15360 bits modulus. This RSA key size looks impractical, and mostly not even available due to technical... |
I want to implement a client that generates random 48-bit values and send them as broadcast messages. We assume also there is a legitimate receiver getting those values (so, there is some sort of pre-authentication that has already happened but it is not of importance here. We can also assume the client/receiver share ... |
As far as I understand, a property is computational if it holds in a computationally-bounded context, so for ANY computationally-bounded involved entity (even if an unbounded one could discover the property is actually missing): e.g. any computationally-bounded distinguisher evaluating two transcripts to check CZK, or ... |
I want to use the asymmetric encription offered by a tool to encrypt my files and I would like to know if the following encryption process works, regardless of perhaps not optimal use.
Generate a 32-bytes-random-key inside the browser with window.crypto.getRandomValues
use sjcl crypto library for:
choosing AES algor... |
Various proposals are being explored for X509 V3 certificates in a Post Quantum Cryptography (PQC) world.
Currently, these include just having a certificate for classical and PQ, having a hybrid certificate for classical and PQ using X509 extensions or composite certificates that concatenate as many signatures into one... |
Given the coin flipping protocol:
A chooses $a \in_R \{0,1\}$ and computes $commit(a,r)$. She sends $commit(a,r)$ to B.
B chooses $b \in_R \{0,1\}$ and sends $b$ to A.
A sends $open(a,r)$ and B checks if the opening is valid.
Both output $coin = a \oplus b$
where $commit$ is the commitment scheme used by Alice.
I am ... |
I've know that a PRF Xored with its key is not a secure PRF. Then I wonder that what if the Xored (or multiplied) item is another random number. The formal expression is as belows:
Let $F_k(x):\{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}^n$ be a PRF.
"$<<$" operation indicates left rotation, "$\cdot$" operation indic... |
Summary. Given some dimension $n$ (say $n=50$), is it possible to describe explicitly a lattice $L$ and a basis $B$ of $L$ such that
$$ \frac{ \| LLL(B)_1 \| }{ \lambda_1(L) } > 1.02^n $$
where $LLL(B)_1$ is the first vector of the LLL-reduced basis of $B$ (for $\delta=1$ say)? The constant 1.02 is the one given in "LL... |
Alice has an ElGamal public key $y=g^x$. Bob encrypts a value $g^b$ based on Alice's Elgamal public key and he ends up with a ciphertext $(g^by^r, g^r)$. Can Bob prove that the value $b$ is in some range without revealing it or do you need to be the "owner" of the ElGamal secret key $x$ to create such proofs?
If $g^b$... |
I'm trying to understand the GF theory, but every time I come across information about AES it all makes no sense.
In my opinion $GF(2^8)$ defines any polynomial of the form:
$a_{7} x^7 + a_{6} x^6 + a_{5} x^5 + a_{4} x^4 + a_{3} x^3 + a_{2} x^2 + a_{1} x^1 + a_{0}$
Where $a_{i}$ can be 0 or 1. And everywhere I come acr... |
skinny cipher has been lately considered as ISO/IEC standard while is still competing as building block of Romulus AEAD in NIST LWC finalists.
what is the difference between the two ISO and NIST processes? which is higher hand in the industry adoption ?
|
I implemented carry-less multiplciation using the CLMUL instruction set. This is similarly fast to simple modulo multiplication. But computating the result mod some polynomial is still very slow. I do it this way:
for (unsigned int i = 32; i-- > 0; )
{
if (c & (1L << (i + 32)))
{
c ^= 1L << (i + 32);
... |
I am wondering if there is any available threshold crypto library that is well-audited and ready to be used in production.
Any pointer is appreciated.
|
Leaving memory-hardness assumptions aside, some slow hash functions are iterated salted hash-chain versions of regular cryptographic hashes. This is usually defined by a round parameter i.e., in PBKDF2. Is there any cryptography paper that addresses security-bits definition based on the factor of rounds of linear succe... |
Certificates are used very often in crypto. From the search, I am a bit confused what exactly is the "public key" inside a certificate essentially? Is it always a signature verification key, or could it also be the encryption key?
In my understanding, for root and intermediate CA certificates, the public key is always ... |
Assume two end-points $A, B$. $A$ sends to $B$ a $Hash(pv||key)$, where $pv$ is a public value that can be intercepted by attackers. The $key$ is a common secure shared key in both end-points, and $||$ denotes concatenation. Obviously, end-point $B$ has all the info required to check the received hash. I was wondering ... |
Let's consider for simplicity Middle-Square Weyl Sequence RNG:
https://arxiv.org/pdf/1704.00358.pdf
We can choose there parameter for independent stream generation, we can call it key. Let's consider we would use it as a stream cipher, so stream is xored with plaintext.
But what it mean to broke such a cipher? Even if ... |
So I was casually practicing RSA on paper for an exam, I did the whole process I wrote bellow, and when I tried the encryption and decryption I got distracted and instead of doing $m^e \mod n$
I did $m^e \mod {\phi(n)}$ and both the decryption and encryption worked.
Is this normal?
Here are the numbers:
$$
p = 11\\
q =... |
I read here:
https://www.researchgate.net/publication/220335697_GCM_GHASH_and_Weak_Keys
how GHASH works. So we have $m$ 128-bit blocks $X_{i}$ and we compute in $GF(2^{128})$:
$Y_{m} = \sum_{i=1}^{m} X_{i} \times H^{m-i+1}$
$H$ is a key. Am I see right there that $H$ is raised to the power? Is there method to do it fas... |
I'm a bit confused on how to validate the authentication tag between two different AES GCM implementations.
One implementation (on my part) is in Java. The other, I don't know.
In my implementation, the plaintext is encrypted with the doFinal function. I prepend the initialization vector to the result.
I understand tha... |
I'm trying to understand that scheme:
https://xilinx.github.io/Vitis_Libraries/security/2019.2/guide_L1/internals/gcm.html
Here on page 11 it looks like GHASH gives only one value "Return $Y_m$":
https://web.cs.ucdavis.edu/~rogaway/ocb/gcm.pdf
After hashing several subsequent blocks. It make no sense to me. If I under... |
According to wikipedia:
https://en.wikipedia.org/wiki/Rijndael_S-box
AES is doing interesting thing (where $<<<$ is circular shift):
$s = b \oplus (b \lll 1) \oplus (b \lll 2) \oplus (b \lll 3) \oplus (b \lll 4)$
and this is equal to ($\times$ is multiplication in $GF(2^8)$):
$s = b \times 31 \mod 257$
This provides a ... |
The goal is for Alice to send an encrypted message to Bob. Neither Bob nor anyone else should be able to decode the message. Alice should be be able to decode it, when all data is shown to her. However, Alice cannot store anything related to the message.
Private keys:
X1 - random bits
X2 - random bits
M - large pri... |
Given that CBC mode encryption is vulnerable to padding oracle attacks, what is the next best alternative ?
a) Include a hash check in the API scheme, validate the hash and then proceed with CBC. If hash check fails then return error indicating same. Eg: Include HMACSHA256(AES256(plaintext)) checksum that is required t... |
Looking at https://crypto.stackexchange.com/a/30616/16548 and all the ways I generate RSA keys (code, SSL) the MSB is always 1 and so when DER encoded has 0x00 prefix.
I think it is always so when the RSA key length is a power of two (e.g. 2048 or 4096).
But the question I'm wondering now before going to bed: is it so?... |
Consider a scenario：data owners $C$ sends a $l$ bits value $x$ to parties $P_0$ and $P_1$ via additively secret sharing scheme, for example, $C$ randomly selects $r \in_R \{0, 1\}^l$, and sends $r$ to $P_0$ and $x-r$ to $P_1$. In insecure channel, adversary $\mathcal{A}$ could obtain $r$ and $x-r$ to construct secret $... |
I know AES-GCM and AES-CCM but what is the difference between AES-CCM8 mode and AES-CCM mode ? Is it the length of the cipher?
|
I am trying to find a reduction for the following DLOG problem in generic groups. It is a simple generalization but I'm not finding any reference (the closest being the Chaum-Pedersen signature scheme sec 3.2, and BLS signatures without the hashing).
Let $G$ be a cyclic group, and $g, h$ generators. The problem is to f... |
Any body can explain, what are the key differences between Shannon entropy and Guessing Entropy? In some research I got entropy uses binary search or balanced Huffman tree. Guesswork uses linear and unbalances Huffman tree?
Also guesswork can calculate unlimited guessing?
|
I'm reading Understanding Cryptography by Christof Paar and Jan Pelzl. In chapter 2 (Stream Ciphers) there's a question that goes like this:
Assume we have a stream cipher whose period is quite short. We happen to
know that the period is 150–200 bit in length. We assume that we do not know
anything else about the inte... |
Let's consider this definition of computational indistinguishability.
Computational indistinguishability. A probability ensemble $X=\{X(a, n)\}_{a \in\{0,1\}^{*} ; n \in \mathbb{N}}$ is an infinite sequence of random variables indexed by $a \in\{0,1\}^{*}$ and $n \in \mathbb{N}$. In the context of secure computation, t... |
In Hebrew language there is the term tzophen (צופן) which means cipher.
There is also a term "maphtech hatzpana" (מפתח הצפנה) which means "ciphering key".
What is a ciphering key?
Cipher, as far as I know, is a matter of resorting characters to get a meaningful message, so what "key" is needed to do so?
It might be th... |
I need to design a Σ-protocol ZKP using Pedersen commitment scheme that proves knowledge of a, y such that statement A = h^y * g^a only holds for even y (y=2x).
Of course, the protocol needs to be sound, special-sound, and honest-verifier zero-knowledge.
Any suggestions?
|
Is it possible for an attacker on a Diffie-Hellman key exchange to manipulate both sides in a way so that the secret generated on each side is identical?
Or put differently, would it be possible to detect an attack via MITM if we can detect via a different channel that the secrets of both parties do not match?
|
Why I care: I want to implement some secure sessions for communicating over internet and since I am a complete amateur in this and don't want to spend a lot of time learning about cryptography or about specific libraries (as I am doing this only for fun), I want to have minimal preparation from programming side. From m... |
Let $E$ be a known, "secure" curve, defined over a field $\mathbb{F}_q$ where $q$ is either a prime $\geq 5$ or a power of $2$. Denote by $n$ the amount of rational points of $E$.
Consider $E/\mathbb{F}_{q^2}$, the same curve but defined over the 2-degree extension field. It is clear that any $E(\mathbb{F}_q)$ is a sub... |
I had a brief look at "On Defining Proofs of Knowledge" by Bellare and Goldreich and I am a little confused by their definitions.
I was under the impression a negligible function $f$ was defined as something like
$$\forall\ polynomials\ p\ \exists k\ s.t.\ \forall x > k: f(x) < \frac{1}{p(x)}$$
And that non-negligible ... |
I am trying to figure out when to use a new IV for an AES-CBC communication and whether my approach is safe.
Here is a quote from Thomas Pornin from a similar question:
So, to sum up: you must choose a new, random IV (with a
cryptographically strong generator) whenever you are about to encrypt
plaintext data which was... |
I am currently reading about Trapdoor Permutations (TDP). While I can totally understand and think of examples of TDP. I cannot think of any examples of Enhanced TDP. The definition of both TDP and Enhanced TDP is given below :
Standard Trapdoor Permutations Collection : It is a collection of finite permutations, denot... |
A collection of hash functions $H=\{h:\{0,1\}^n \to \{0,1\}^m\}$ is pairwise independent if for every $x_1 \neq x_2 \in \{0,1\}^n$ and $y_1, y_2 \in \{0,1\}^m$:
$$ \Pr_{h \leftarrow H}[h(x_1)=y_1 \wedge h(x_2)=y_2]=\frac{1}{2^{2m}} $$
Given a finite field $\mathbb{F}$ of size $2^n$ I've been able to prove for the set o... |
I'm trying to implement the RSA algorithm with some random (valid as far as I know) generated values but for this combination, encryption/decryption doesn't work.
message = 324
p = 3
q = 29
n = 87
e = 15
d = 15
Which give both and encrypted and decrypted answer of 63
I'm guessing I made and error while generating the ... |
Suppose that we have a block cipher such that the last round of the cipher depends on half of the key and the penultimate round uses the other half.
Suppose also that I attacked the last round using differential cryptanalysis and reduced my search space from 2^8 to 2 choices for each byte of that half of the key.
One w... |
RFC 4880 section 5.2.3.16, "Notation Data," describes how arbitrary additional notations in the form of name-value pairs can be included in an OpenPGP signature packet. Regarding names, it says the following:
Notation names are arbitrary strings encoded in UTF-8. They reside in two namespaces: The IETF namespace and ... |
Let's say that I have a password. And it's secure. But it's a 10-character string.
So If I wanted to create an AES key for the 128-bit version of the algorithm I would just hash it using MD5. Or If I wanted the 256 version of the algorithm I would hash it with any of the 256 length hash functions such as Sha_256. But I... |
Using SHA-256 as a stream cipher appears to bear cryptographic weaknesses, however, I am not quite sure how to implement them in decryption.
Assume that I have an encryption function using 64-byte blocks.
I encrypt each of the blocks with the hash of the previous to produce my ciphertext.
The weak link here is, that I ... |
assume Bob and Alice use Elgamal encryption scheme. Alice wants to send Bob a message, but does not know Bobs public key. Is there a way for Alice to find out Bobs public key by receiving multiple message pairs C1 (ephemeral key) and C2 (message) from Bob? Alice can easily decrypt Bobs messages, as from Bob to Alice th... |
While implementing a protocol in Scyther, I need help with the following questions -
How do we split a particular message/variable into two parts in Scyther?
(For eg. if I have value R in my protocol that I need to divide into two parts say K1 and K2, how do I go about doing it in Scyther. I tried R=CONCAT(K1, K2) whe... |
In RLWE,
we often choose the following polynomial ring,
where q is a prime,
and n is a power of 2, e.g. $2^k$
$$\mathbb Z_q[X]/(X^n + 1)$$
We know that ${X^{2^k}} + 1$ is an irreducible polynomial under $Z$,
because of Cyclotomic Polynomial,
but in this question,
Considering $$\mathbb Z_{17}[X]/(X^4 + 1)$$
$(X^4 + 1)$ ... |
I've been trying to make an algorithm work like the real Enigma machine, fully customizable. I use two online emulators to check that my encoded message is correct :
https://cryptii.com/pipes/enigma-machine
https://www.101computing.net/enigma-machine-emulator/
Currently, without the plugboard, it seems that it works ... |
The purpose of a block cipher is to act like a random permutation, and indeed a common security definition is one in which the block cipher is taken to be indistinguishable from a random permutation (see Wikipedia). So then why not use a random permutation as a block cipher? That is, the secret key could just be a li... |
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