instruction stringlengths 32 27.2k |
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JSON Web Tokens (JWTs) (RFC, introduction) are digitally signed using a secret key (which can be symmetric, but for distributed use cases will typically be asymmetric). The signature forms the third and final part of the JWT, and can be verified from the JWT recipient side using the same secret key (for symmetric signi... |
Some interpretations say "By masking a secret value with a uniformly random zero sharing, the masked value appears to be a random value drawn from a uniform distribution. This randomness helps protect the privacy of the original secret value, as it becomes indistinguishable from other random values. Using zero sharings... |
I am currently working on Side Channel Attacks (SCA) on Kyber and Dilithium. I have found myself quite confused with side channel, because so much is mentionned all the time.
For instance, I don't understand when to use distinguishers, when to use tools like the t-test, when you need to work with key guesses, etc... In... |
When recovering the public key from ECDSA signature (r, s), the first step is recovering the point R.
You do this by plugging in (r + xn) into the curve equation where n is the order of the basepoint and x is some integer
my question is how do you find this x value, say for secp256k1 but also the general case
I have a ... |
I have seen various papers discussing the security of the Learning with Errors problem with very small uniform secrets and errors but I have not found any papers on the general LWE problem with uniform secrets and errors within (-b,b) range where b < the LWE modulus q but not so small as to be binary or ternary. Is th... |
I am studying the Dilithium signature from Ducas et al's CRYSTALS-Dilithium: A Lattice-Based Digital Signature Scheme.
Wanting to understand how the supporting algorithms work together, I am trying to work out and visualize an example by hand. If I understand correctly we have the HighBits and LowBits algorithms calli... |
There is a common term used in cryptography called a hash collision. If I am reading the definition correctly on Wikipedia, this can occur if two different data values give rise to the same hash value.
Duplicate hash, different input:
text1 encoded = hash1
text2 encoded = hash1
The first code block is a binary value... |
In an online community, you sometimes have to ban certain IP addresses or even entire IP ranges due to abuse. You may hire moderators to help you with this, but you might not trust them enough to show them everybody’s plain IP address.
The question is: Is there a scheme to encrypt or hash IP addresses in a way that pre... |
KZG poly-commitment & QAP linear PCP can be proved sound under Knowledge of Exponent assumption or Generic Group Model (I take it for granted from lecture 6 and 9 of ZK-MOOC https://zk-learning.org/), and it seems to me GGM is the preferred one because it permits less trusted setup parameters.
If I have understood corr... |
Assume we have a hash table using the function h(x) = x mod 32. h(x) = x mod 33. Also assume it dynamically resizes by doubling the amount of buckets and rehashing. If I was able to provide inputs for the hash table it would be really easy to flood with colliding entries to slow lookups to O(n).
However, say we were to... |
I have been unable to find any mathematical explanations on how TrueCrypt's plausible deniability encryption works, when using TC containers.
Would someone be able to provide a mathematical walkthrough of how it works?
Other encryption systems implementing things in a similar way is outside the scope of my question. Al... |
In short what are the differences (pros & cons) between multiplying by powers of Tau
(from this lecture https://youtu.be/tAdLHQVW)
and raising to powers of Tau
(from this lecture https://youtu.be/xuGQYEvytxk)
I know pairing is used by the verifier in both, and that they deferred the pairing details to the next lectur... |
I am relatively new to cryptography and am curious what cryptographers would say about what I think is a beautiful one-way hash function described in a paper I found here https://arxiv.org/abs/1801.05079
To summarize the hash function, the Collatz function $f: \mathbb N \rightarrow \mathbb N$, is defined as $f(n)=(3n+1... |
I read somewhere that ike1 does not support asymmetric authentication. Does that mean that it does nit support PKI authentication (digital certs)?
Thanks
Champ
|
I read this in the documentation of HighwayHash:
By contrast, 'strong' hashes such as SipHash or HighwayHash require
infeasible attacker effort to find a hash collision (an expected 2^32
guesses of m per the birthday paradox) or recover the seed (2^63
requests). These security claims assume the seed is secret. It is
r... |
I'm implementing impossible differential cryptanalysis on mini-AES using Raphael phan's paper.
I've coded mini-AES using Raphael phan's first paper on the structure of mini-AES, where he only mentions 2-round mini-AES.
But in the impossible differential paper we're attacking 5-round mini-AES so I need to extend the key... |
Is there a list of all the (most) assumptions (such as RSA and DDH assumptions) used in cryptography and the corresponding properties?
|
Why was the dimension of A doubled in kyber?
LWE encryption uses a public matrix A of dimension K but kyber uses a double matrix A resulting in $A ^{ k * k * n }$
When deriving the results of the definition of gen, enc en dec this results in:
$$
RA_0 S + RA_1 S + RE + E_3 + \frac{q}{2}m - RA_0 S + RA_1 S + ES \\
$$
Whi... |
I am studying the zerocoin paper‡. More precisely I am stuck at page 6, on the Spend function (in paragraph "B. Our construction").
I am not understanding how the ZKSoK is computed.
Let's consider the Pedersen commitment as
$$C\gets g^Sh^r\bmod p$$
I've found a lot of examples online but they all refer to a case where ... |
I am reading the Wikipedia page for Interactive proof systems and am having trouble understand the notation in the definition of soundness, many of which is left unspecified.
Given a formal language of strings $L$, a verifier $\mathcal{V}$ for this language satisfies the soundness property if for every prover $(\tilde{... |
The conventional and simple wisdom is to combine head with /dev/urandom to create the amount of pseudo-random data that is needed.
But that is slow.
I found a faster method - cryptsetup FAQ suggests to use its mechanism.
See 2.19 at:
https://gitlab.com/cryptsetup/cryptsetup/-/wikis/FrequentlyAskedQuestions
But the issu... |
I don't understand why relinearization is so significant. I understand the equations in the paper (in this post I'll be using notation from BV but I would it applies to BGV+BFV) but if anything it seems like it would be less efficient. We go from:
$$h_0+\sum_ih_ix_i+\sum_{i,j}h_{i,j}x_ix_j$$ to utilizing t and getting... |
In "Efficient reductions among lattice problems" by Micciancio (2007) it is said, that
SVP reduces to SIVP in their exact versions.
I did not found anything about this fact, is a reduction that trivial?
Does the same hold for their approximation versions?
|
I think I understand the value of using ZKP's for proving things about data in isolated systems, like for privacy and computation roll-ups in blockchains L2's.
But I hear a lot about real-world use-cases, a classic example is proving your age is above a certain number, or proving your income to a mortgage lender, witho... |
I have an AES encrypted data and the key, but I am not able to tell the block cipher mode [ECB|CBC|CTR] used in encryption or know the key length.
Below is the encrypted data output in java.
{"encrypt_data":"GorwlI4cdifSjaKM0Uu4v24DewQqsaN3VTkZMmtDZkttVdoUEV23mBYlYhbcB/oN","encrypt_aes_key":"VRkSYqtGUBr4Zzt7ET8kMw2dvrQ... |
I am trying to understand how this ciphertext length is calculated from a signcryption scheme to analyze the communication cost. I understand, we consider the key length and the message length to calculate the ciphertext length. But don't understand at what step and what parameters we actually consider. For example, in... |
Intuitively, if we can invert a PRG, then we can easily distinguish it with random distribution by checking g(inverse(y)) = y. So every PRG is a OWF?
Unlike the problem "Is every pseudorandom generator a one way function?", i can prove that if the output length is large enough (for example |g(x)| >= 2|x|) then the PRG ... |
Consider a variant of the Paillier encryption scheme where the message space is restricted to $\mathbb{Z}_q$ such that the RSA modulus $N$ of the Paillier cryptosystem satisfies $N > q + q^2$. I am interested in the following variant of the CCA security game where the decryption oracle answers with not a complete decry... |
RFC 5869 for HKDF says "an application needs to make sure that salt values are not chosen or manipulated by an attacker".1 Soatok also discusses some nuances in choosing salts for HKDF.2 This question also discusses a situation where it led to a vulnerability.3
While these sources all indicate that salts should not be ... |
I am going through Dan Boneh's video tutorial on PLONK Polynomial IOPs - https://www.youtube.com/watch?v=vxyoPM2m7Yg
He describes 3 type of proof gadgets he will use
He gives a proof of the Zero Test which I understood.
However, he doesn't cover the proof for the Sum Check & Product Check in his video.
Prod Check
Prov... |
Let $f_k$ be a PRF. We claim that $f_k$ is a OWF. PROOF let $f_k$ is not a OWF, there exists a $PPT$ algorithm $A$ that can invert $f_k$ with non-negligible advantage. Even if we know the input $x$ for given $f_k(x)$ with a non-negligible advantage, how can we claim that we can distinguish $f_k(x)$ from random with non... |
For a public-key encryption scheme (Gen,Enc,Dec), the textbook definition of IND-CPA security is the following:
The challenger runs (pk,sk)←Gen and sends pk to the adversary.
The adversary performs some computation, chooses (m0,m1) and sends them to the challenger.
The challenger runs ct←$Enc(pk,mb) , b←${0,1}, and... |
I'm trying to design an encryption system for a new mobile app and am thinking of using Shamir's Secret Sharing Scheme in a way which I have not seen before. Does this seem possible or does it violate some mathematical concept I'm not understanding in SSS?
I want to split a key generated on the user's mobile device whe... |
I am currently studying the proof of the Dilithium signature in the quantum random oracle model (QROM). I am curious to hear if anyone have any thoughts on the importance of having proofs in the QROM or if proofs in the standard random oracle model should be sufficient?
Have been exploring the topic briefly with some m... |
I have found similar question for PIV (and not PGP)
I assume PIV and OpenPGP would work in similar ways. I also assumes that the GPG private key never leaves the Yubikey.
If these assumptions are correct then:
at encryption: a symmetric key is generated and encrypted on the sending computer using the GPG public key, t... |
A signature system applies textbook RSA to a $b$-bit hash of the message. What's the cost (preferably, as CPU time on common hardware) of existential forgery assuming known signature of $r$ random messages? How much is that reduced if public exponent is very small ($e\le7$)?
We assume
Safe RSA public key $(n,e)$ and m... |
Sorry in advance if I'm asking a stupid question:
I thought the role of "IV" in encryption is to avoid having identical ciphertext for identical plaintext.
So one could use some random IV.
Writing some Perl code I'm confused, however.
Consider this test code:
use Crypt::Rijndael;
my $cipher = Crypt::Rijndael->new('x' x... |
Let's suppose I encrypt two blocks of 1MiB with AES-256 in CBC mode, each one using different keys, XOR the resulting ciphertexts and send this XORed block to an adversary. Remembering that the adversary will not have access to resulting ciphertexts, only the XOR of them.
What could he/she do with the XORed block? Can ... |
Let $E\!: y^2 = f(x)$ be an elliptic curve over a finite field $\mathbb{F}_{q}$ of odd characteristic. Consider an $\mathbb{F}_{q}$-point $P = (x,y)$ on $E$. Suppose that we only have the $x$-coordinate (with one auxiliary bit) and we want to recover $P$, that is, the value $y = \sqrt{f(x)}$.
Assume that the field $\ma... |
Is there modification to LWE public key crypto-system which makes the decryption process is totally deterministic and does not affect security?
|
Given a message $m$, how can I prove that $m$ lies between 0 and 31 without revealing the message using a Sigma protocol?
The message is encrypted as:
$$c = a^{\beta} \cdot g^m ,$$
where:
$a$ is the public key of the receiver,
$\beta$ is the secret key of the sender, and
$g$ is a generator of a cyclic group $G$ of pri... |
Let's say a device has 2 private keys and service has the 2 corresponding public keys.
Is there an efficient way to encrypt a symmetric key from the service side utilizing the 2 public keys, such that on the client, it requires both private keys in order to decrypt?
I.e if I only have private key 1, I am unable to decr... |
While using ECDH key exchange, we can choose to use different kind of elliptic curve, e.g. P224, P256 or P384 etc. (btw, I am using go).
My question is, what is the criteria to choose different kind of elliptic curve? Is it related to desired security level? If yes, what is the "rule of thumb" to choose between the cur... |
"Factoring integers with sublinear resources on a superconducting quantum processor" seems to indicate the end is getting closer for RSA - much faster than anticipated earlier:
We proceed by estimating the quantum resources required to factor RSA-2048. We find that a quantum circuit with 372 physical qubits and a dept... |
In the official documentation of the X3DH Algorithm (link) is made an analysis about the forward secrecy. Forward secrecy would be an uselful property if we would repeat the protocol multiple times. But in the Signal-Protocol it is always used only once, to initialize the Double Ratchet Algorithm (which then on its own... |
Content and Informal Problem
Suppose a protocol $\pi$ doing an arbitrary task between two users A and B. I only know that $\pi$ relies on a IND-CPA symmetric encryption scheme $\mathcal{E} = $(KeyGen, Enc, Dec). In details, A holds a key $k$ in $\pi$ computes encryptions of $n$ messages $m_1, \dots, m_n$, providing to ... |
So I went ahead an wrote this little program. What it does is it takes a password for a seed and generates a (pseudo-random) bit-pattern using rule 30 from cellular automata. It then XORs our input file with the same-length pattern. In theory this should be secure, given I would start padding the plaintext and only use... |
As I understand it, in WPA2, the shared key (for encryption) is derived from the password, plus nonces and identities used in the initial 4-way exchange. An attacker who was able to sniff the initial exchange could perform an offline dictionary attack on the AP password.
I've also learned about PAKE protocols that also... |
I think my understanding on initialization vector (IV) might be lacking, but as I understand it, an IV is used to create randomness to an encrypted message so that the message is difficult to crack from an attacker. The randomness part I can see the importance of.
The part I can’t get my head around is why use the IV. ... |
I am trying to solve a puzzle, and I think have to solve a cipher. But I'm not actually sure what I have to do ... Example :
The diu uff i dve. lleive pi he bl hle f he mi Nw ie d hiie d eve me Biie ide hi i. Ti Bii imli Vili Buei G Bii Ti imli, Gee li bei ipped el be ie EL lvd ie Nvz d ell u h u. lle Re Ve Bl ize ... |
A hacker goes into a database and downloads a bunch of hashes and salts of users with knowledge of the hashing method. Say this is one entry that got downloaded:
cbc0a790b2f28fc72ca43eb749028b9f:21022011
(hash:salt)
Without the salt, the hacker simply computes 100M common passwords and their hashes and find matches. Wi... |
There are two algorithms in my framework, $E_1(\cdot)$ and $E_2(\cdot)$.
In particular, executing $E_1(\cdot)$ on a specific input $x$ (i.e., $E_1(x)$) is equivalent to executing $E_2(y)$ for some input $y$.
Suppose the security model of this framework allows an adversary $\mathcal{A}$ to query $E_1(\cdot)$ with any in... |
Let $E$ be an elliptic curve over a finite field $\mathbb{F}_q$. For simplicity, let the group $E(\mathbb{F}_q)$ be of prime order.
Assume that I know how to construct an efficiently computable permutation of $E(\mathbb{F}_q)$ as a set, that is, just a bijective map $\phi: E(\mathbb{F}_q) \to E(\mathbb{F}_q)$ rather th... |
In pairing based cryptography (PBC) we restrict the pairing domains to be subgroups of the $r$-torsion group $E[r]$. This arises two questions to me:
Why do we restrict them to subgroups of $E[r]$? Couldn't we use, for instance, the whole group of points $E$? Or a mixture between various torsion groups? (As long as t... |
I wrote code that solves the subset sum problem via the LLL algorithm, as given in chapter three of the Handbook of Applied Cryptography https://cacr.uwaterloo.ca/hac/
I ran the code on ten random sets, each with positive integers from one to $2^n$, each with a random subset adding up to a target integer. The code foun... |
In GCM, GMAC, the additional associated data (AAD) (as well as outputs of subsequent blocks) is multiplied by a polynomial H in GF(2^128). This appears to be doing some secure hashing.
Is that what's happening, and if so, is this a general hashing method that's used elsewhere?
|
I am going through Dan Boneh's video on PLONK - https://www.youtube.com/watch?v=LbpPCN-f_XA&t=952s
At around 19 minutes, he gets to the Prod Check Gadget.
Background:
$\omega \in \mathbb F_p$ is the primitive $k$th root of unity (i.e. $\omega^{k} = 1$)
$\Omega = \{1, \omega, \omega^{2}, ..., \omega^{k-1}\}$
Let $t(1) =... |
Say I have some message like "Hello World" that I want to encrypt, I get that Hello World is the Plain Text and the output from the encryption is called Cipher Text.
But, let's say I want to encrypt the data again, so I feed in the cipher Text from first round back into the encryption algorithm and then get the new cip... |
Is it possible to adapt the Chaum-Pedersen protocol for using elliptic curves by simply replacing the exponentiation with scalar products?
For example, if g is a point in the curve, then g^k is the scalar multiplication k*g as defined for elliptic curves. Would that still work?
I took the diagram from here.
Update:
In... |
A custom file format has a header encrypted with a 2048-bit RSA public key. I need to decrypt it using a 2048-bit RSA private key. The header has 48 bytes, and according to the scheme I got for the task, after decryption I should get a 48 bytes of "plaintext" payload.
However, this scheme does not make any sense to me.... |
Suppose someone has a black box, which is running some program. This box has some internal states, and we can observe the outputs it produces. Now someone comes along and claims the release the source code of the program running on that black box. Is there a way to verify that claim, without also requiring the disclosu... |
I am going through Dan Boneh's video on PLONK - https://www.youtube.com/watch?v=LbpPCN-f_XA&t=952s
At around 19 minutes, he gets to the Prod Check Gadget.
Background:
$\omega \in \mathbb F_p$ is the primitive $k$th root of unity (i.e. $\omega^{k} = 1$)
$\Omega = \{1, \omega, \omega^{2}, ..., \omega^{k-1}\}$
Let $t(1) =... |
I understand that FIDO2/WebAuthn generates a separate key-pair for each web-site (domain), and only allows a specific key-pair to be used for authentication on the same web-site (domain) who originally generated/registered that key-pair with the browser/authenticator. Also, I'm aware that this is done in order to preve... |
Given that there are two parties, and a process has been conducted by which both parties are knowledgeable of a shared value p, how could two parties communicate with each other over a public channel using the value p as a seed for a random number generator?
|
I have a checksum scheme that uses a simple polynomial summation as described here.
Basically I'll take a random value $R$ and a set of inputs $[v_0, v_1, v_2]$ and checksum it like $v_0*R + v_1*R^2 + v_2*R^3$. This was designed to get simple collision resistance with incremental checksumming.
I'm trying to change this... |
In a message exchange with RSA, an unusual public exponent $e = 65536$ is used.
Since $N$ is easily factored, I am able to derive $p$ and $q$. Consequently $ \phi(N) = (p-1)*(q-1)$.
However, since $2^3$ is present among the factors of $ \phi(N), \gcd(e,\phi(N)) = 8$. It is not possible to compute the private exponent d... |
Just started learning about RSA cryptography so forgive me if I made any mistakes or misunderstandings.
n = 1024-bit integer (product of two large primes p*q)
e = 65537 (standard exponent)
However I also have some ciphertext all encrypted with the same keys.
c1 = m1e MOD n c2 =
m2e MOD n ... ck =
mke MOD n
Among the... |
GPUs or dedicated hardware can calculate most things much much faster than regular computers ever could. There are password hashing algorithms such as scrypt and argon2 that make the difference smaller, but a powerful dedicated argon2 machine/cluster is still much more efficient than an old budget smartphone is.
My tho... |
I am working through a textbook on crypto, currently on DES section. What bothers me is that there was no explanation about where do we get initial 64-bit key from. This question is also very hard to google, because you get straight away redirected to all sorts of articles about key schedule, where the existance of the... |
I am looking at some secret encryption method that apparently uses CBC and a block size of 256 bytes. I can do a chosen-ciphertext-attack. When I modify a single byte in the ciphertext a complete block of 256 bytes in the plaintext is corrupted, plus a single byte at the same offset in the following block. That leads m... |
I've spent some time learning about DIDs but have some questions about key rotation:
The way I understand it is that a DID and DID doc are generated from a public key derived from a private key.
Subsequently, if the owner wants to rotate the keys (the private key really), they can make a new DID doc which will include ... |
Let's suppose I hash a 384-bits message with a cryptographic hash function and generate a hash digest of 128-bits. I know that due to the pigeonhole principle, many inputs of same size will result in the same 128-bits hash digest.
How is the estimated number of 384-bits messages that will produce the same 128-bits dige... |
If we look at the WebAuthn specification, then, during the "registration" ceremony, the authenticator generates a new key-pair and a unique user-id. Then the public-key and the unique user-id are sent to the relying party (server), together with some attestation statement. The relying party will store the public-key an... |
I've recently heard about coding based cryptography and it seems very close to the LWE assumption in that it is based on the idea that the error is hard to identify. They are both post-quantum schemes too.
Is there a direct link between the two? (e.g., coding based can be seen as an instance of LWE under certain assump... |
Some statements are expensive to prove. If I need to make a proof for such kind of statement repeatedly (generate new proof $\pi$ for each new verifier), I think it might be a waste of time (as well as computation resources).
If there is a proof $\pi$ that I generated in a non-interactive way, can I reuse it?
What pro... |
As asked, I suppose this must have been answered before, even if not in the form asked here. The most notable AEAD schemes GCM-AES and ChaCha20-Poly1305 do this. Also, even outside AEAD, ad-hoc constructs such as CBC+HMAC also require separate keys. So:
Q1: Why use separate keys in authenticated encryption? As in
what... |
Rotational Cryptanalysis of ARX show that rotational probability of an ARX primitive can be computed by $p^q$ where $p$ is rotational probability of modular addition and $q$ is number of modular additions in ARX primitive.
Similarly, Rotational Cryptanalysis of ARX Revisited extends it to chained additions.
How to calc... |
Having recently learned of coding based cryptography, it seems that they key size for post-quantum security might be a lot larger than what is required by Regev PKE (in the former keys include several large matrices), which is also post-quantum secure. Is this a correct observation? Ether way - what are the pros and co... |
I have done some research on HKDF but I am still not sure about the security properties in different scenarios.
Which properties are fullfilled, when IKM and the salt are random and secret, but not uniformly random? Are the output keys uniformly random?
Which guarantees does HKDF give, if (a.) IKM or (b.) salt got leak... |
In GlobalPlatform specification for smartcards, I came accross this rather strange scheme* ISO/IEC ISO/IEC 9797-1 MAC Algorithm 3:
To calculate the Message Authentication Code, we take some original data (a host cryptogram and a padding), then we apply multiple chained DES calculations, as shown in the image attached.
... |
I have a cypher text with I know encrypted two times with Autokey Cipher with same lengths of keys. I am following the statistical cryptanalysis in here when it is ciphered with one time with Autokey and it works but I could not come up with any cryptanalysis solution when I cipher the text with Autokey cipher but two ... |
Suppose we have an RSA-Oracle that can encrypt and decrypt our input. The the decryption output is equal to: $ (C^d \mod N) \mod 2^n $.
How can I extend the LSB oracle attack, using the using knowledge about the last n-bits of the plaintext?
|
Suppose we have intercepted a public key exchange (via Diffie-Hellman protocol). In addition to the keys A and B, the generator g and the module p are known.
Assuming that it is possible to exchange keys with client B, once it has finished the conversation with A, how can I obtain the private exponent of B?
I had thoug... |
In many books on Cryptography, we refer to probability distributions over the key space $\mathcal{K}$, over the plaintext space $\mathcal{M}$ and over the ciphertext space $\mathcal{C}$.
Then, we let $K$ be the random variable denoting the value of the key output by $\mathsf{Gen}$, so for any $k\in \mathcal K$, then $\... |
We say two states $\sigma, \rho$ are computationally indistinguishable, if for efficient quantum algorithm $\mathbf{A}$, $|P(\mathbf{A}(\rho)=1)-P(\mathbf{A}(\sigma)=1)|$ is negligible. I want to show if the trace distance between above states are negligible then they are computationally indistinguishable.
In the class... |
If i store sensitive stuff (e.g passwords, salted passwords, Internet protacel adresss(so i know its not tamperd with), private keys(the keys are using a portion of the key on multiple disks in diffrent places for security and i want to make sure there in th write order y storing the hash insecurely(eg on ipfs)) *)
*s... |
Recently I started implementing basic skeleton of crystal kyber. Right now I got stuck at NTT, where I am not able to understand how values has to be fed (twiddle factor, actual data which has to be converted into NTT form).I am referring ntthelper.py from python implementation and parametric ntt from HDL implementatio... |
Since NFS runs in essentially $n^{1/3}$ time, and RSA-240 is a composite of two 120-digit primes, shouldn't this have taken at least $10^{40}$ operations, not including any overhead? Even if you could do say $10^{20}$ ops / s as modern supercomputers can almost do, this still should have taken essentially $\infty$ year... |
Reading another user's question, a doubt came to me.
Suppose an RSA oracle exists, with which it is possible to interact to encrypt and decrypt some text. The oracle output is not the decrypted text of the sent ciphertext, but the last n-bits.
The decryption takes place according to the law $ (C^e\bmod N)\bmod 2^n$, ... |
I'm trying to implement an IV that won't need to be stored on it's own.
I'm considering 3 options:
Since I'm using PBKDF to generate a key I could use some bytes from the generated hash
I could use some bytes from the randomly generated salt and split it somehow
I could generate a random separate IV, and stick it to t... |
After thinking a lot about 64-bit block ciphers, I ask a question here.
Most proposed block ciphers these days seem to have a block size of at least 128-bits.
Also, I know that when using a 64-bit block cipher with an operating mode (e.g. CBC or CTR), there is a high probability of a collision when about $2^{32}$ block... |
In Dan Boneh's PLONK Video - https://www.youtube.com/watch?v=vxyoPM2m7Yg he refers to the Prod Check Gadget
$\omega \in F_p$ is a primitive $k$-th root of unity ($\omega^{k-1} = 1$)
$H = \{1, \omega, \omega^2, ..., \omega^{k-1}\} \subseteq F_p$
Prod Check Gadget is used to prove that $\prod_{a \in H} f(a) = c$
I was tr... |
In the Kyber specification the parse function (algorithm 1 on page 6) takes as input a non-terminating byte stream. Although unlikely, an unlimited number of bytes from this stream can be used in this function.
In Kyber.CPAPKE.KeyGen (algorithm 4 on page 8) the parse function is called on line 6 using the output of an ... |
Suppose we have a function $F = f_{s}(x)$ with a key $s \gets \mathbb{Z}_q$ that on input $x$ outputs modular exponentiation $x^s$, where $\mathbb{G}$ is a cyclic group of order $q$ where DDH is hard. If $x$ is selected uniformly at random from $\mathbb{G}$, then modular exponentiation $F$ behaves like a weak PRF (Naor... |
I'm trying to create some test cases for a TLS library for the Key Derivation outlined in RFC 8446 7.1.
I tried to get this information from openssl using the following:
# Generate a ECDH private key
# generate the key to pem format
openssl genpkey -algorithm X25519 -out x25519.pem
# Connect using the private key and... |
I've been trying to understand the multiple keys thing in RSA.
I'm quite sure that multiples private keys are possible:
In RSA, why are there multiple possible private keys, and even the public key itself that can be used to decrypt the message?
More than one private key for RSA
Do equivalent RSA keys exist?
Will publ... |
[Say I want to outsource the computation of $y=f(x)$ without revealing information about $x$, $y$, or $f$. I thought I'd have to combine homomorphic encryption with some obfuscation $\mathcal{O}$, passing along encrypted data $\mathsf{enc}(x)$ and obfuscated program $\mathcal{O}(f)$ to be homomorphically evaluated $\m... |
I want to put some personal info like name and email in e.g. some program that I release to the public but I don't want anybody be able to retrieve those personal info and only when I want they can verify that.
The first and simplest way is to hash my personal info and put the hash in the project, like:
sha265('my_emai... |
The statement is false. We show this by providing a counter-example.
Define
M = {a, b},
K = {k1, k2},
C = {0, 1}.
Let Enc(k, a) = 0 and Enc(k, b) = 1 for k = k1, k2.
Dec algorithm will return an on input ciphertext 0 and b on input ciphertext 1. Clearly, the scheme is correct.
Pr[C = 1∣M = a] = 1 ≠ 0 = Pr[C = 1∣M = b... |
$\vec{u_0} + \vec{u_1} = (M_0 + M_1)\cdot (\vec{v_0} + \vec{v_1})$
$P_i$ gets $(\vec{u_i}, M_i, \vec{v_i})$ where $M_i$ is a matrix , $\vec{u_i},\vec{v_i}$ are vectors, with all entries uniformly distributed over $\mathbb{Z}_{2^k}$
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