0
votes
1answer
32 views

ElGamal in $Z^*_{p^n}$

If $p$ is an odd prime and $n$ natural,it is known that the group $Z^*_{p^n}$ is cyclic.Explain why the selection-choice of the group $Z^*_{{3^{1000}}}$ for the construction of a cryptosystem ElGamal ...
5
votes
3answers
266 views

What are the practical implications of ciphertext distinguishability?

Commonly there are four ways to "break" a secrecy-focused cryptosystem: Recover the secret key Recover the message Distinguish an encryption from random noise Distinguish the encryption of two ...
1
vote
1answer
46 views

How AES treat string input to encrypt data and what will happen if the cipher key is less than that expected?

The official docs of AES have several example of how hexadecimal or byte input can be encrypted. I have some problem about the input text and cipher key. My question is: How can encrypt string input ...
2
votes
2answers
64 views

What is the advantage of AEAD ciphers?

What is the advantage of AEAD ciphers? Why is the TLS working group pushing for them? I thought modern cipher suites require SHA256 for authentication. What advantage is there to including Poly1305? ...
0
votes
0answers
15 views

Cryptanalysis on two time pad ciphers? [duplicate]

One time pad ciphers are unbreakable if the message is encrypted correctly and if only used once. However if used more than once, it becomes decipherable. How come? Also, would it be smart to use one ...
1
vote
2answers
45 views

Let $F$ be a PRF, is the following $G(x)=F_{0…0}(x)∥F_{0…1}(x)|| … ||F_{1…1}(x)$ a PRG?

$F$ is a PRF with $n$ bit key, input, and output length. I know the answer is "NO it isn't!", but I can't understand why. Is that because on any input $x$, the keys for every $F$ in the concatenation ...
0
votes
0answers
34 views

How to verify perfect secrecy of a cryptosystem? [closed]

I’m playing with a self-made encryption algorithm: “a new approach to data encryption” by Suhail Yazji (video available at youtube.com/watch?v=h1kABn5dfXc). How can I prove my algorithm to be ...
2
votes
2answers
83 views

Present an attack for the combination of OTP and textbook RSA

Let $N=p \times q$ where $p$ and $q$ are two primes. Compute $\Phi (N) = (p-1)(q-1)$. Choose $e$ s.t. $1 < e < \Phi(N)$ and $gcd(e,\Phi(N))=1$. Compute $d = e^{-1}(mod \ \Phi(N))$. ...
1
vote
0answers
34 views

Prove that certain amount of data was stored

I'm looking for a way to prove that a certain amount of data was stored, through some easily verifiable piece of information. Similarly to how proof-of-work can prove through a hash that a certain ...
2
votes
2answers
69 views

Can we solve the Hidden Number Problem in $GF(2^n)$?

Is it possible to solve the Hidden Number Problem in extension fields? In particular in $GF(2^n)$? Let's suppose an attacker knows some least/most significant bits of $r_i = a_i \times k$ in a given ...
1
vote
1answer
49 views

Knowing that $G(s)$ is a PRG, is the following construction $G'(s) = G(s||0)$ a PRG?

I know there already is a very similar question. However, I can't understand why $G'(s)$ is not a PRG. If $G(s)$ is a PRG, then why $G(s||0)$ can't also be a PRG? How can the distribution over ...
1
vote
1answer
31 views

For $p=23$, $g=2$, $q=11$ you are given the signature $(18,3)$ in the message $m=2$. Construct a signature in the message $m'=3$

Alice uses an ElGamal signature in group $(Z/pZ)^{*}$ without using hash function. To sign the message $m \in (Z/pZ)^*$ calculates the signature $(r,s)$ as follows: choose random $k \in \{0, 1, ...
5
votes
0answers
83 views

Attacks on elliptic-curve based cryptosystems through solving the Decisional Diffie-Hellman Problem with the Weil Pairing

Are there any examples of practical attacks on cryptosystems set over elliptic curves which utilize the easiness of DDH for certain choices of curves $E(\textbf{F}_q)$, and as such their lack of ...
1
vote
0answers
32 views

What consequences do the plaintext space size has on the performances in the BGV scheme?

In the BGV paper [1], the authors say in §5.4 that you can have $\mathbb{Z}_p$ as plaintext size with a large $p$. What is the impact of the size of $p$ on the ciphertext size and computational work ...
3
votes
2answers
113 views

Is there any such thing as “proof of location”?

I'm looking for a way for someone to prove to me their geographical location without a trusted third-party. Imagine wanting to prove to someone you're actually physically in a specific place. I'd ...
1
vote
0answers
51 views

ElGamal signatures systems

Let $p$ prime number $q/p-1$ prime and $g\in (Z/pZ)^*$ element of order $q$.Also $a\in \{1,...,q-1\}$ the private key and $y\equiv g^a\pmod p$ the correspoding public key.For each of the following ...
2
votes
3answers
91 views

Attack on Double Encryption Scheme

In this protocol: A → B : { <[A, {K}pk(B)]> }pk(B) B → A : { <[B, {K}pk(A)]> }pk(A) I'd like to determine why this is insecure. How can the attacker learn the key K if A and B are both ...
-2
votes
1answer
36 views

In which step does AES use the key to encrypt data?

AES has the following steps in encryption: SubBytes, ShiftRows, MixColumns, and AddRoundKey and the following steps in decryption: InvSubBytes, InvShiftRows, InvMixColumns, and Inverse of AddRoundKey. ...
4
votes
2answers
154 views

Signature and hash function properties

I understand the need for the hash function to be collision resistant and second pre-image resistant. For what reason, exactly, does a hash function need to be pre-image resistant? If this property ...
1
vote
1answer
54 views

Playfair Cipher + Vigenere Cipher?

I'm researching cryptography for a school project, came across the above two ciphers, and something occurred to me. Would combining these two schemes give a considerably stronger encryption than ...
1
vote
0answers
61 views

Library to find an addition chain for a large number? [closed]

I need a short addition chain for a number $n>2^{100}$ in order to implement a fast exponentiation. The memory footprint is not important. Finding an optimal chain for a large number $n$ is ...
2
votes
1answer
63 views

Permuting Small Sized Set in Practice

Imagine we have a set $S$ of $m$ elements and we wants to permutes the set elements. Thus the original position of each element should be unknown after permuting. If we define a permutation function ...
0
votes
1answer
42 views

Reduction to cdp,dl or cdh?

Assuming a randomize encoding scheme that takes as input a secret key $\mathsf{sk} \in \mathbb{Z}_p$ for a large prime number $p$. Then the algorithm outputs $g^{\mathsf{sk}x}, x \in \mathbb{Z}_p^*$. ...
1
vote
1answer
34 views

Ephemeral key is held constant in ElGamal

Is there a known algorithm to recover the sender's messages in ElGamal $\mathbb{F}_p^*$ if the ephemeral key is held constant in two or more transmissions, assuming the messages are always distinct? ...
0
votes
0answers
30 views

CPA-security of a pseudorandom permutation encryption scheme

Let $F$ be a pseudorandom permutation, and define a fixed-length encryption scheme $(Gen, Enc, Dec)$ as follows: on input $m \in$ $\{0,1\}^{n/2}$ and key $k \in \{0,1\}^n$, algorithm Enc ...
0
votes
1answer
93 views

Point addition in NaCl/libsodium (Curve25519)

In NaCl and libsodium, the crypto_scalarmult function implements the operation $Q = kP$ (scalar/point multiplication). There doesn't seem to be a function for point ...
2
votes
0answers
58 views

Words having weight near to minimum distance

I am studying the NP-Problem of the codes Syndrome Decoding. The formulation is show below. Input: a binary matrix $H$ of dimension $r \times n$ and a bit string $S$ of length $r$. Property: there ...
1
vote
1answer
65 views

Simulation Based Proof: What Can / Can not Simulator Do?

I have seen some examples in "Foundation of cryptography" and "Efficient two party computation", in which simulator can do some things that in the real world model the parties cannot do, for instance: ...
4
votes
2answers
72 views

Is there a signature scheme for the Cramer-Shoup cryptosystem?

I have a project that I have to use cryptosystem and signature scheme for it. I've read about Cramer-Shoup cryptosystem and I want to use it since it is more secure the ElGamal cryptosystem, but, I ...
2
votes
1answer
67 views

Is the ring of octonions “commonly” used in Cryptography?

I've recently read "Fully Homomorphic Encryption on Octonion Ring" by Yagisawa, which is based on octonion rings over finite fields. Personally I've never encountered octonion rings in cryptography ...
3
votes
0answers
65 views

Example: pre-image resistance to second pre-image resistance

It is possible to convert a pre-image resistant function $f:\{0,1\}^{n}\rightarrow \{0,1\}^{n}$ to a second-preimage resistant function? I am thinking to use a pseudo-random generator and construct ...
5
votes
1answer
92 views

Why is the whole initial state used in the final addition of Salsa20 and ChaCha?

Both Salsa20 and ChaCha basically work like this: Put the key, the nonce, the sequence number and a constant into a 4x4 matrix of 32-bit words. Transform the matrix invertibly with a number of ARX ...
-2
votes
1answer
79 views

Show How to Efficiently Solve the Computational Diffie-Hellman Assumption given an Algorithm that Solves the Square-DH Problem

Let $q$ prime number, $G$ a cyclic group with order $q$ and let $g \in G$ be a generator of $G$. Suppose that you have an algorithm $A$ who takes input the element $g^a$ of $G$ and gives as output the ...
2
votes
0answers
41 views

search of patterns in key schedules

I am developing a new key schedule, and there is this article (Enhanced Key Expansion for AES-256 by Using Even-Odd Method) where the authors also propose a new algorithm and one of the objectives is ...
0
votes
1answer
40 views

Algorithm for factoring a number $n$ of a specific form given $n$ and $\varphi(n)$

Given the natural number $n$, which is in the form $p^2 \cdot q^2$ with $p$,$q$ prime numbers. Also $\varphi(n)$ is given. Describe a fast algorithm (polynomial time) that calculates $p$ and $q$. ...
1
vote
2answers
40 views

Simulator in Private Outsourced Computation over Outsourced Datasets

Please, consider two honest parties $A$ and $B$ outsourced their private data to a malicious server $S$. So the parties store their data in the server. Then at a later point in time they want to ask ...
2
votes
1answer
106 views

How to prove that a function is not pseudorandom?

I am currently enrolled in a cryptography course, which uses the book by Katz and Lindell. I'm struggling with the exercies which ask for proofs, like the following one: Let G(k) be a PRG with ...
3
votes
0answers
29 views

Blinding to mask private key operations

Blinding is often used to mask private key operations when the underlying problem is integer factorization. For example, its used in both RSA and Rabin-Williams signature schemes. This presumes ...
1
vote
2answers
40 views

El-Gamal signature with two messages

Alice uses an ElGamal signature with base the group $Z^*_{107}$ and parameter $g=3$ of order $q=53$.The private key of Alice is some $x \in \{0,1,.....,52\}$ and the public key of her is $y=10$. To ...
4
votes
2answers
184 views

Can a 1 byte difference in AES 128 bit keys make huge difference in output?

If we take some randomly generated key of AES-128 and we change any random 1 byte of that 16 byte key, will this make huge difference in the AES cipher text generated over same input string? Does ...
10
votes
2answers
319 views

Terminology: differences between the terms “pre-master secret”, “master secret”, “private key”, and “shared secret”?

Both crypto.SE and security.SE have excellent Q&As about how TLS generates session keys (I have linked some at the bottom). In reading these threads I'm having troubles with terminology since the ...
1
vote
2answers
119 views

Transforming Gaussian random $[0,1] $ numbers to uniform $[0,255] $

I am not exactly sure if this is for math stackexchange or crypto: A TRNG outputs numbers in $[0,1]$ in a Gaussian distribution. I would like to convert them into uniform random bytes ($[0,255] $) to ...
3
votes
0answers
28 views

Proving existence of an encryption scheme that has indistinghuishable multiple encryptions in the presence of an eavesdropper, but is not CPA-secure [duplicate]

I got stuck in trying to find a solution to the 3.7 exercise of the Katz-Lindell book. The exercise also assumes the existence of a pseudorandom function. The problem is that a multiple messages ...
3
votes
1answer
105 views

How can I generate a good password from a SHA512 hash?

I have to change local administrator passwords on machines. I don't want to store password in a database. I have to generate a password that I can find later to connect to the machine again. So I ...
1
vote
1answer
60 views

What is k in RSA?

I am currently learning about RSA since I didn't understand the public-key-system but now I am… kind of. So I am writing the numbers as follows: $p = prime\ number\\ q = prime\ number\\ N = ...
0
votes
0answers
20 views

Implementation of digit serial rotators for SIMON cipher?

I am working on architecture of SIMON cipher where I have to use either bit serial, parallel or digit serial to implement the algorithm for each round function and also for sub-key generation. So I ...
2
votes
1answer
47 views

Using AES for smaller blocks in a Feistel network

I was wondering how decryption would work for FPE in the case of cycled Feistel ciphers. I understand that simply reiterating through the networks with reversed key order will generate the ciphertext ...
3
votes
2answers
314 views

What are the implications of a birthday attack on a HMAC?

After collecting approximately $2^{n/2}$ message-tag pairs a collision can be observed. So two different messages (m1 and m2) will have the same tag. This paper states: Then, for any string x, ...
0
votes
1answer
46 views

Execution speed of AES_128 GMAC operation

I have read about the speed performance of AES_128_GCM on specific processors Intel and AMD that support AES New Instruction set. As compared with CMAC and HMAC is it relatively slow for other ...
3
votes
2answers
32 views

Why is Rabin encryption equivalent to factoring?

I don't understand the proof of equivalence I've read everywhere (e.g., in Rabin's paper or on Wikipedia). Here's my objection: let's say you have a Rabin decryption oracle that takes ...

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