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What is the difference between the two notions of computational and statistical indistinguishability?
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Is the following scheme private?
By private i mean an untrusted aggregator (UA) cannot reveal anything other then an aggregate function output on plaintext data
Each party holds a secret key $k_i$ and data $d_i$. It sends to the aggregator $d_i H(r)^{k_i}$. $H$ is a hash function that maps elements to a group $N$ in wh... |
I know that, if CBC-MAC is used in such a way that the tag is the concatenation of all the blocks' outputs (and not just the last one), it's insecure under CPA for the simplest case of 2 blocks CBC-MAC where:
the message is $m=m_1\mathbin\|m_2$, where $|m_1|=|m_2|$ equals the block size of the cipher, and
the tag is $... |
The idea of crypto_box API in NaCl library is to shield the programmer away from the technical details and provide easy to use functions for encrypting and encrypting messages.
Given what I've just written, I do not understand why the idea of nonce is exposed in this API. Explaining what nonce is and how to use it take... |
For all $c_0\leftarrow m_0 \oplus k$ there exists a $k'$ such that $c_1 \leftarrow m_1 \oplus k'$, where $m_0 \neq m_1$ and $c_0 = c_1$.
Assuming a truly random $k$, the first assignment is a one-time pad. If we were to repeat the process over all $m \in M$, we would create a Stirling set of the first kind.
To use be... |
I'm reading "An Efficient CCA2-Secure Variant of the McEliece Cryptosystem in the standard model" by Rastaghi which states:
As we know, in hybrid PKE schemes XOR alone cannot perfectly hide
challenge bit to the CCA2 adversary
The author does not define hybrid PKE schemes. What is their definition?
Why is it that X... |
Consider 3 parties, Alice, Bob and Charlie. Suppose
each party has a bit as input, i.e. Alice, Bob and Charlie hold $a, b, c \in \{0, 1\}$ respectively.
Show how construct a scheme with which they can compute the function $f (a, b, c) = a \oplus b \oplus c$
such that the following are satisfied:
(1) All parties... |
I understand and have implemented elliptic curve signatures in Python without the use of libraries like Sage, and would like to implement the MOV attack against certain weak types of elliptic curves.
Even though I understand the mathematical notation and terms of group theory, I'm a programmer by trade, not a mathemati... |
I am having difficulty solving part (ii) of Excercise 5.17 from Becker's Cipher Systems.
Exercise 5.17
$\quad$If $f(x),g(x)$ are any two polynomials over $GF(2)$ with $f(0)=g(0)=1$ show that
(i) $\Omega(f)\cap\Omega(g)=\Omega((f,g))$
(ii) $\Omega(f)+\Omega(g)=\Omega([f,g])$.
It is easy to prove that $\Omega(f)+\Omega... |
When using Curve25519, the private key always seems to have a fixed bit set at position $2^{254}$.
Why is that? Is there any good reason to use a fixed positioned most-significant-bit in the private key?
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I'm reading about Merkle tree signatures, and I would like to know whether the security of that scheme depends on the height of the tree, or does it only depend on the hash function being resistant to collision?
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Assume:
$O$ be a reversible random permutation oracle on a finite set and $O^{-1}$ the inverse permutation (pretty much equivalent to a random permutation: What is the difference between a bijective random oracle and a random permutation?). Here, the attacker can call both $O$ and $O^{-1}$ on any input
$M$ be a fixed-... |
Let the block length 64-bit, 256-bit key, cipher text accordingly - 64 bits. What is the strength of the block cipher, if any unknown attacks, which could reduce its strength. We can only brute force.
Let $M=\{0,1\}^{64}$ be the plaintext space, $C=\{0,1\}^{64}$ be the ciphertext space and $K=\{0,1\}^{256}$ be the key... |
Is it possible to perform RSA decryption if one only knows $N$ and $e$?
Failing that, what is the maximum key length where brute-force is still practically feasible?
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Can someone help me with a Hill cipher?
When do I have to use:
1x3 plain text matrix (p1, p2, p3) * 3x3 key matrix
3x3 key matrix * 3x1 plain text matrix
Or they are both correct?
I tried to search the internet, but found nothing useful.
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I am studying differential analysis and have a question.
Consider the following simple cipher:
$$c_1 = S(m_1 \oplus k_1) \oplus k_2$$
(Plaintext $m_1$ xor with key $K_1$, then result goes into an S-BOX, the output of which is xor'd with $K_2$). This case is very simple. Using the main property of XOR we can get differe... |
Dan Boneh's courersa lecture on format preserving encryption at 5.50 mins , talks about truncating a PRF on $n$ bits to PRF on $t$ bits.
The approach is by appending $(n-t)$ zeros to input $t$ bits then applying AES on $n$ bits and truncating it back to $t$ bits . He says there are better ways to do it but does not me... |
I have a web-software project which needs a bit of protection in form of authencitation…
This web based software runs on an intranet. There is no access to the internet from these terminal machines. Nevertheless, I want to stop anybody who copies the (PHP-based) software and tries to run that software on another machin... |
Informally, Private Information Retrieval (PIR) is a protocol between a user $U$ and a Server $S$, that meets the following conditions:
$U$ obtains enough information about a database hosted by $S$, to decide which record $i$ in the database to request from $S$.
$U$ initiates the PIR protocol with $S$ and retrieves al... |
I've been reading Brakerski and Vaikuntanathan's Efficient Fully Homomorphic Encryption from (Standard) LWE.
When the authors discuss a small modulus p used for the transition from (n, log q) to (k, log p), how 'small' are they talking about?
If a database has two data types - TEXT (character arrays) and INTEGER (4 or ... |
I'm looking for a function or set of functions that can produce a pseudo-random permutation on an input set of arbitrary size.
Given a set of $M$ values in range $0..M-1$, where $M$ is positive integer,
I need a function $I' = F(K,M,I)$, where $I$ is a value in range $0..M-1$, $K$ a key (to be determined) and $I'$ a va... |
I'd like some advice on cryptography best practices. I need to store on my web app the users' credentials (login & password) for 3rd-party sites.
I'm using AES-256 with random key and initialization vector (provided by the Net 4.5 framework, if that's relevant), and store the encrypted data in completely different syst... |
I am wondering if it's possible to have a scheme as follows.
Here is the scenario:
we have a set of objects (e.g. strings) {O1, O2, ..., On}
we have a set of users {U1, U2, ..., Um}
each user asks to compute a special function f over a subset of the objects
we have an intermediate (trusted) component A that must be ab... |
I am a bit confused about the expected running times of brute force attacks on different cryptosystems.
So let's assume a key size of $2^n$ bits.
Symmetric key cryptography:
$E(brute)$ = $2^{n-1}\cdot$ comparisons time
So if I understood correctly I need to generate all the possible $2^n$ keys to find the "right" key ... |
For a padded message, M, using the El Gamal encryption schema, how can we determine the random number $r$, when we are given $p$, the prime number, $g$ which is the primitive root of $p$, $b$ and $x$ which is the private key.
So the public key is $(g,b,p)$ where $b=g^x$ $mod$ $p$.
To encrypt, we compute: $y_1 = g^r$ m... |
I'm doing a code review for a crypto solution that reuses the same key with a constant IV. I want to demonstrate that this is not the right way to do things by figuring out the key and decrypting all of their test data.
I have access to lots of ciphertext.
I know the same key is used.
I know the same IV is used.
Ciph... |
Suppose we are given $p$, the large prime, $g$ which is the primitive root for $p$, $b$ which is calculated as $b=g^x$ mod $p$ where $x$ is the private key and $0<x<p-1$.
Also suppose we know $y=g^r$ mod $p$ where $r$ is some random number and $0<r<p-1$ and is the discrete log of $y$. We also know $s=(M-xy)(r^{-1})$ mo... |
Merkle signature (pag. 40) use than public key (verification key) the root of the Merkle Tree and than private key (to sign) the set of pre-images of the $g(Y_i)$ where $Y_i$ is the verification key of a choose One Time Signature. My question is What's is a trapdoor between these two keys?
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In his writeup of the Solitaire keystream generator algorithm, Bruce Schneier warns not to use the same key for two different messages:
The first rule of an output-feedback mode stream cipher, any of them,
is that you should never use the same key to encrypt two different
messages. Repeat after me: NEVER USE THE S... |
I started to implement some MAC since last week with the specifications given here. I'm currently testing the OMAC (one-key CBC) with test vectors. In the OMAC specifications at page 4, they explain how the padding works. Just below that, they said :
[...] Where the empty string counts as one block.
This is strange, ... |
I'm doing research about "Cryptographic attack methods in Web Application" so I have some questions to ask you guys:
Block Cipher vs Stream Cipher, which is more common used in Web Application?
How and Where is Stream Cipher implemented in Web Application?
Hope to get your response soon :)
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I know it sounds strange.. but, are there any ways in practice to put the hash of a PDF file in the PDF file? And after geting the hash in the PDF file - if someone would do a hash check of the PDF file, the hash would be the same as the one that is already in the PDF file? :) maybe with MD5, since it's known to have w... |
Imagine that your lecturer and the undergraduate office have conducted a key exchange protocol after which both of them hold the string $X$. Yet, it is possible that a curious student sitting next to the lecturer in the bus may have gained some information $E$ about $X$. (Un)fortunately, the student eavesdropper Eve ha... |
Simple question: we have AES 128 encryption and a key. How can we calculate the key check value (KCV)?
One example: key is 48C3B4286FF421A4A328E68AD9E542A4 and KCV should be 77DC84.
I am trying it out in C#, but there are just to many 'unknowns' for a newbie in cryptography...
Edit: there was a question why I need it ... |
Assume the sender wants to share their ephemeral/long-term public key with intended receiver only and both share symmetric key.
Is it secure to encrypt the (full/partial) public key (of RSA, ECC) with the shared symmetric key?
Is there any chance of finding symmetric key from encrypted public key?
If not why?
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In the past year or so we have seen production of ASIC devices designed for mining of cryptocurrencies. These devices can perform SHA256 hashing at rates much higher than was seen in the past and are continually advancing in power. Can such devices be used to perform cryptanalysis instead of mining? Does this develop... |
There has been lately a question on KCV (key check value), value provided by many CRYPTOKI (PKCS#11) implementations. I don't particularly like KCV, but I decided to ask about proper use of KCV.
This "KCV" (also known as CKA_CHECK_VALUE object attribute) value is derived as follows:
For most objects: first three byte... |
I'm looking for a cryptographic technique that instead of permuting a cleartext, would add noise to the cleartext to obfuscate the true text among a bunch of garbage. For example, a list of 10 numbers would be combined with a list of 90 random ones with the goal of making the true set of numbers difficult to recover.... |
Assume
$S$ be a finite set
$O$ be a random oracle from $S$ to $S$, such that $O$ is bijective
$f$ be a random permutation of $S$
Is there any difference between $O$ and $f$?
Does it makes any difference if $S$ is not finite?
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By definition - $q(n)$ is a negligible function if for every positive integer $c>0$ there exist an integer $N_c$ such that for all $x>N_c$ :
$q(n)<1/x^c$
So for the function $1/x$, if we take the positive integer $c=1$ then we need to find some $N_c$ such that for every $x>N_c$:
$1/x<1/x$
$=>$ Definitely such $N_c... |
What is the impact of the distinguisher for the high-rate Goppa codes (as published in "A Distinguisher for High Rate McEliece Cryptosystems") on the CFS signature scheme and the McEliece/Niederreiter cryptosystems?
It seems that the distinguisher strongly affects the CFS scheme, forcing its parameters to increase (if ... |
When implementing a XOR cipher with a pseudo-random key equal in length to the plaintext, Is there a significant difference in potential key strength between keys drawn from a pool of either 1000 or 5000 possible characters? (that is, each character in the key may be any one of up to five thousand possible characters) ... |
Is this MAC secure:
To authenticate a message $m=m_1||\ldots||m_l$ where $m_i \in
\{0,1\}^{n/2}$, choose $r \leftarrow \{0,1\}^n$ at random, compute
$$t:=F_k(r)\oplus F_k(\langle 1\rangle || m_1) \oplus \ldots \oplus
F_k(\langle l\rangle ||m_l)$$
(where $\langle i \rangle$ is $\frac{n}{2}$ bit encoding of the in... |
Do I pronounce it as a word or letter-by-letter, i.e., "R-I-P-E-M-D"?
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I'm reading Collision-Resistant Hashing: Towards Making UOWHFs Practical, and they
say that its formalization is non-asymptotic. Why is the formalization non-asymptotic?
What is an example of hash function with an asymptotic formlization?
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I know a protocol for bit commitment using regular OT (Bob has 1/2
chance of learning the bit Alice transferred to him) which goes like this:
COMMITMENT PHASE
Alice chooses a bit $b$
For $i=0$ to $i=n^2$
$\;\;\;$Alice chooses $x_{ij}$ for $1\leq j\leq n^2$ randomly so that $(\sum_jx_{ij}) \equiv b \pmod 2$
... |
From what I can remember, RSA is something like this:
Generate 2 distinct prime numbers $p$ and $q$ that have similar bit length.
Compute $n=pq$ and $\phi(n)=(p-1)(q-1)$
Compute $e$ such that $1<e<\phi(n)$ and $\gcd(\phi(n),e)=1$. It is optimal for $e$ to be prime
Compute $d$ such that $ed\equiv1\pmod{\phi(n)}$
To enc... |
I am trying to solve the example of algorithms of Certificateless Signature by manually and solving the mathematics of Algorithms but not succeed while doing mathematical calculations.
Please provide any solved example and some website which provides examples on these algorithms to learn manaully how it executes... |
I have two keys (K1 and K2) at both the client and the server. I hope to use HKDF in both client and server side to concatenate the keys.
I will use the same salt value at both the client ad the server. Then will I be able to arrive at the same key by applying HKDF at both the client and the server to K1 and K2?
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I need a secure protocol to authenticate client side users with my server which has an API. I am devising something more secure particularly to resist active MITM attacks where an attacker may modify the request and perform some damaging function on the server. The general username/password model doesn't suit my purpos... |
I'm in search of the correct definition of a stateful authenticated encryption scheme (sAE), and its related security notion. This has been treated several times in the academic literature, however, all the papers I've read contains a discrepancy between how they state the security goal in informal English and their fo... |
Let's say A wants to send a message, so everyone who gets the message, can be assured that it's from A. A then sends a message message|timestamp|E(A_private_key, Hash(message|timestamp))
What are the benefits of timestamp? How can a person who gets the message know that it's the correct timestamp? Why just not send mes... |
In this paper on pg. 1241 the authors discuss bullet point on Adaptive Zero-Knowledge :
I am new to Zero-Knowledge and I am having trouble understanding what they are saying.
I think they are saying the probability an adversary A in the real world wins and the probability an adversary in the ideal world wins are cl... |
Suppose $E_k$$(a, b, c)$ is encryption of values $a, b$ and $c$ with key $k$ through encryption algorithm AES (AES-128) and each $a, b$ and $c$ are 300 bits integer values.
Also Suppose this algorithm in my question situation work in CBC mode.
If $V_1= E_k(a, b, c)$ and $V_2= E_k(c, a, b)$, my questions is: are the... |
Does any of you know what is the difference between the Pedersen commitment and the commitment that uses the ElGamal encryption scheme?
For the sake of completeness, I recall what both of them look like.
Given two public and large primes $p$ and $q$ such that $q∣(p−1)$, and a (also public) generator $g$ of the order-$... |
Can you help me to finding some papers that shows AES is secure against known-plaintext attack?
|
In SSSS, if you recreate the original secret with one of the decoder inputs being slightly damaged (e.g. one or two chars incorrect), you receive a slightly damaged version of the original secret. So if the original secret was "Abraham Lincoln", decoding using a slightly damaged input might still get you "Ab%aham Linco... |
For fun, I'm learning more about cryptography and hashing. I'm implementing the MD2 hash function following RFC 1319 (https://www.rfc-editor.org/rfc/rfc1319). I'll preface by saying I know there are libraries, I know this is an old hash, and I do not intend to use this in anything real-world, so don't anyone freak out.... |
I have blinded $m = 16$ with $r= 13$, $e = 7$ and $n = 209$.
This resulted in $m' = 464$, which led to a $s' = 8$.
Now, I want to unblind this $s'$ by using $s = s' \times r^{-1}$ but im stuck at filling in the $r^{-1}$?
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We consider a large $n$-bit number $N$. We want to find a factor, if it admits any.
For $m$ taking values from $1$ to $n$, perform the following three steps (actually, for each $m$, perform many cycles, as described below).
Generate a random $m$-bit $x$.
If $x$ is a divisor of $N$, return $x$.
If ~$x$ is a divisor of... |
It is clear that when we have any output stream $x_0,x_1,...$ produced by linear-feedback shift register, then this output has to be periodic.
Now I was wondering if we can find an upper bound for the period of the output sequence from a linear-feedback shift register with $R$ registers over $\mathbb F_q$?
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In short:
Is it cryptographically stronger to have a known length password of the maximum length allowed, or a random length password somewhere in the range of the longest length possible?
Does the answer change depending on the max length? For instance my credit union (still!) forces a maximum length of 10 characters... |
I don't seem to grasp why is the handshake for PTK in WPA2-PSK 4-way and not 2-way. Isn't it enough to just have these two steps:
First party sends Nonce1 to the other party
Second party sends to first party Nonce2 and the HMAC(Nonce1, Nonce2, other parameters) using KCK.
I don't understand why does first party have ... |
I want to be able to detect tampering in a log file that is under the control of an untrusted party. I am not interested in secrecy, only the integrity of the contents in the file - so I want to detect if entries have been removed/changed. The solution that I seem to have found from a short google search is to use hash... |
I've been reading about bcrypt and scrypt, and it seems that the general consensus is that bcrypt is more "tried and true", but scrypt is better in theory.
Couldn't you just hash something with bcrypt, then with scrypt? If it has a layer of scrypt to use resources, and a layer of bcrypt, shouldn't that give you the ben... |
Can someone explain, how $a^x \mod N$ can be speeded up, when $a$ and $N$ are known constants? How big is the gain and what resources are needed?
https://www.imperialviolet.org/2013/05/10/fastercurve25519.html
Just to mention: it can speed up SRP hashes bruteforce, which is calculated as $v = g^x \mod N$ where $x = h... |
I'm reading a notion Any Collision Resistance for Hash Functions. In the lecture define a collision finder CF.
CF is said to $(t,\epsilon)$-break the family of hash functions $F_K$
if the running time is at most $t$, and the probability that CF, on
input K, outputs a collision $M,M'$ for $F_K$ is at least $\epsil... |
I have been reading about Shamir's secret sharing, and maybe i completely misunderstand something, but the field is meant to be a prime. However, when i look at the implementations of this algorithm, they all use GF(256).
I do understand the beauty of such field, since that's the best compromise between the size of the... |
Suppose one is implementing a cryptographic scheme over a group where one needs the discrete logarithm to be hard - what is the recommended group to use? I'm looking for a group where calculations are simple but it doesn't need to be extremely efficient. I would therefore prefer some type of multiplicative group mod n.... |
I am actually preparing for a cryptography exam, and I found a question asked by the professor in the class, below are the lines that I copied from the slide :
Example: Let $Ek$ be the encryption transformation of one-key cipher and
$h$ be a hash function. Then $hk := Ek ◦ h$ is a keyed hash function, where $◦$
de... |
In this paper on pg. 1248 in the "preprocessing phase" section the authors say:
In the preprocessing phase, the parties run a (standard) MPC to
collectively generate a key pair (pk,sk) for the FHE scheme, and to
secret share sk in such a way that (a) learning the shares of
corrupted parties, and leakage on each... |
In the paper "Multiparty Computation Secure Against Continual Memory Leakage" on pg. 1239 the footnote at the bottom points out the difference between $joint$ leakage and $disjoint$ leakage. The authors say the weakly leakage resilient protocol of BGG+11 cannot be directly used because it only applies to $joint$ leaka... |
Does it make sense to reuse some of the keys from my PGP (GnuPG, GPG) key block when generating my own SSL Certificate Authority (a toy one for myself and a few web services of mine)?
In an ideal world people would have one key pair in a trustworthy hardware device, and they could use it to certify everything, e.g. the... |
I have doubts for the definition of the decryption algorithm $D(.)$. I think I've already seen that the decryption returns a plaintext $M$ on input the key $K$ and $C=E_K(M)$.
I have also seen that the decryption algorithm returns either $M$ or the special symbol $\bot$.
Is the first definition valid in the case of sym... |
I have a task to find a the message for which the SHA-1 hash's last 11 symbols in hexadecimal presentation corresponds to an 11-digit number.
I have been given the following example solution:
For the code 38607310235, a solution is a513b8c4507ea2891fb34cd4612e038607301235, which is the hash of $y$
How can I find $y$?... |
I sometimes see, in discussions of symmetric ciphers, reference to the 'key agility' of a particular algorithm. It seems to be related to the difficulty of switching encryption keys, but I don't understand more than that.
Can anyone give a good explanation of 'key agility' and some contexts in which it is important?
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After studying philosophy and being a philosophy teacher, I took back studies 4 years ago and I did a bachelor in maths. I'm in maths grad school now (I'm 32), and I would like to work in cryptography. (I took as many algebra and arithmetic and logic courses as I could, and I'm studying Galois theory this semester.)
I ... |
I've been reading Brakerski and Vaikuntanathan's "Efficient Fully Homomorphic Encryption from (Standard) LWE" and I'm still digesting pieces at a time.
Under section 1.1, "Re-Linearization: Somewhat Homomorphic Encryption without Ideals", they state they mask the plain text with noise. The noise is created with multipl... |
Often in articles homomorphic encryption is praised as the holy grail of encryption for cloud storage. This is done by suggesting that it can do any computation, and as such could be used for encrypted databases.
Performance issues aside, this makes me very sceptical. If such a database is to be any useful you need to ... |
I'm reading Collision-Resistant Hashing: Towards Making UOWHFs Practical (pag. 10 and 11) and here say
The most direct way to construct a TCR hash function is to key a function like MD5 or SHA-1.
...
A safer approach might be to incorporate key bits throughout the
message being hashed. For example, with $|K| = 12... |
Suppose I have two hash functions, of which neither (or only one) is collision resistant, and I want to create a new hash function by taking the bitwise exclusive or (XOR) of the results of those two functions.
Is it possible for this new function to be collision resistant? I suppose not, but I'm not sure why.
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I'm part of a team designing a system where a user have to be able to read a certain package, if he has preformed an action or series of actions that makes it legal for him to do so.
The tricky part is that the user contacts the server, receives the data he needs to work with, along with the package he might have to op... |
In certificateless cryptography, how can a user preserve his privacy from Key Generation Center? If the KGC becomes malicious, how can the user's privacy be preserved?
I read "Privacy-Preserving Decentralized Key-Policy Attribute-Based Encryption, IEEE transaction on distributed system."
In a privacy-preserving decent... |
Let $m = 6$, and let $\mathbb{Z}_m$ denote the set $\{0,…,m-1\}$. Let $X \mod m$ denote the remainder obtained when dividing $X$ by $m$.
(a) Consider the symmetric encryption scheme in which the encryption of message $M \in \mathbb{Z}_m$ under key $K \in \mathbb{Z}_m$ is $M+K \mod m$. Is this encryption scheme perfec... |
Encrypting a very small message using public key cryptography always result in larger encrypted messages. Is it possible to deduce the algorithm used, key length, etc just by looking at the minimum encrypted message length?
More specifically, if I have black box system and when I input a small number of characters to e... |
I have rather simplistic understanding of cryptography, so I have to beg a pardon in advance if the question has internal contradictions.
Imagine data $A$ with a hash $hashA$. This data is encrypted with private key $K$ to get data $E$ and the hash of the encrypted data is $hashE$.
Are there encryption method and hash... |
Why is Lamport-Diffie secure? I note that there is a demonstration based on onewayness (in the book postquantum cryptography). But a one way function is not sufficient to ensure that it can not infer some bits or any feature of the key signature.
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In the paper “Multiparty Computation Secure Against Continual Memory Leakage” on pg. 1237, the footnote #1 discuss why it is not possible to construct a leakage resilient two-party protocol. But I'm confused about the 2nd half.
Assume the adversary controls party $P_1$. In this case, he knows the
entire secret stat... |
Would exposing a cryptographic hash function's digest (e.g. SHA-3) of RSA private key data compromise the key? If so, what are the possible (cryptanalysis-) vectors for attacking the key if an attacker had knowledge of this hash?
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Hi I have a stream cipher which uses a keystream of:
F(r) || F(r+1) || F(r+2) || ...
Suppose F(r) is the RSA encryption algorithm:
F(r) = r^e mod p where e and p are known , e = 3
My question is:
If we know F(r), F(r+1) and F(r+2), how can we calculate the subsequent key sequence?
Is there some obvious relation betwe... |
According to this document the padded message has the following structure:
$EM \;= \; 0x00 \; || \; 0x02 \; || \; PS \; || \; 0x00 \; || \; M$
What is the purpose of this null byte at the beginning of the message?
After OS2IP decoding (also described in the document) to convert the message to a "bignum" I would expect... |
The title is asking the question in layman terms, but what I really mean to ask is this:
Let $x \in \lbrace 0,1 \rbrace^{128}$ (an arbitrary input block) and let $K \in \lbrace 0, 1 \rbrace^{128}$ (an arbitrary key for 128-bit AES). Let's mark AES decryption with $AES_K^{-1}$. My questions are:
Is $AES^{-1}_K$ defined... |
I'm reading Multivariate Cryptography and would like to know why we use two affine transformations to scramble the central map?
Why not use only one?
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While reading some papers, I found that sometimes $Z_p$ was used but sometimes $F_p$ was used ($p$ is prime). Usually, the author will only use their subgroups like this: choose a big prime factor of $p-1$ , denote $q$, and set $G=\langle g \rangle$.
My questions are :
Why do we only use the subgroup while $Z_p$ OR $... |
I have been reading Bernstein’s “Quantum attacks against Blue Midnight Wish, ECHO, Fugue, Grøstl, Hamsi, JH, Keccak, Shabal, SHAvite-3, SIMD, and Skein” paper from 2010…
This document disproves the claims of preimage resistance for Blue Midnight Wish,
ECHO, Fugue, Grøstl, Hamsi, JH, Keccak, Shabal, SHAvite-3, SIMD, ... |
Poly1305-AES uses two per-connection keys $k$ (for AES) and $r$ (for Poly1305's compression function) and a per-message nonce n to execute. I've read the original paper on the implementation, and I think I understand what it does, but not how it works. In particular, if the security of the MAC is dominated by the sec... |
I was reading “An Efficient Protocol for Yao’s Millionaires’ Problem” (Ioannidis and Grama 2003). In the proposed protocol in section three, it is written:
(Step 4) For every $i$, $1 \le i \le d$, Bob obliviously transfers $A^\prime_{il}$ where $l = b_i + 1$.
(Some context: $d$ is a security parameter, $A^{\prime}$ i... |
I am using a AutoSeededRNG from Crypto++ to generate IVs for use in CBC encryption.
I am encoding the IVs using Base64 for future use (decryption).
I notice that all the Base64 encoded IVs end with gB. Why is this? Is it a security problem?
Here is the code:
for (int i = 0; i < 10; i++) {
CryptoPP::AutoSeededX917R... |
I'm designing a function f that should be moderately hard to invert and very fast to evaluate in a modern CPU. The function will be used in a proof-of-work function.
I've read that the middle-bits of multiplication are the harder bits to obtain, so I suspect that they are the hardest to invert.
Let $f(x) = ((x^2) >> 16... |
I have two-factor authentication enabled on my Google account, and I have this app on my phone which generates a number I have to type when I'm logging in to Google-Mail.
But I don't understand how this number is validated on Google's side. My bank has a similar approach: they gave me this little gadget which also gene... |
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