Questions tagged [probabilistic-encryption]
Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts.
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1answer
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Laplace Inequality
I am trying to prove that if $r_i \sim Lap(0,1/\varepsilon)$ where $\varepsilon >0$ then:
$$Pr[r_i \geq 1+r^*] \geq e^{-\varepsilon}Pr[r_i \geq r^{*}]$$.
I know that for $r*>0$ it satisfies ...
2
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1answer
50 views
Understanding why Semantic Security implies Message Recovery Security
I am stuck in the proof where it says $$p_0=1/|M|$$ , I just do not understand how we can infer this equality.
Also, am I right in understanding that B is defined as choosing his two messages at ...
0
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1answer
58 views
Is it possible to construct dataset for only another party to consult?
Is it possible to construct a dataset made of some kind of probabilistic encrypted indexes such that anyone can update the information contained in the set but only the one with a secret key could be ...
2
votes
1answer
78 views
Standard deviation of gaussian noise in FHEW scheme
I've got two questions regarding the paper FHEW: Bootstrapping Homomorphic Encryption
in less than a second.
First, the final error of a ciphertext after the refresh procedure is stated as following ...
1
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0answers
60 views
Question on nCPA Security and Uniform Permutations
I feel I am misunderstanding the idea of nCPA security and its relation to uniform permutations. In particular I've been reading the paper "Hoang, Morris Rogaway; An Enciphering Scheme Based on a Card ...
0
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1answer
93 views
Challenging Question for the Build a Secure MAC with Special Properties
We would like to ask you to give a construction for requested scheme which provides those properties or give a proof that is not achievable.
[Note that unsuccessful attempts to build such a scheme ...
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0answers
145 views
Leak information (new setting)
This question is similar to Leak Information?, but with new settings.
Let $a,b,c,d,e,f$ be selected at random from $\mathbb Z^*_q$. Also, let $r_1,r_2,r_3,z_1,z_2,z_3,p_1,p_2,p_3$ be selected at ...
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2answers
195 views
Leak Information?
Let a,b,c,d be selected at random from $\mathbb Z^*_q$. We pick values $r_1,r_2,r_3,z_1,z_2,z_3 \gets \mathbb Z^*_q$.
Do $u_1,u_2$ that are computed as follows, leak information about values $a,b,c,d$...
4
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0answers
172 views
computational indistinguishable/distinguishable?
Let $a,b,c,d$ be selected at random from $Z_q$. Consider the following two distributions $X_1$ and $Y_1$:
$X_1={(r_1\cdot a, r_2\cdot b, r_3\cdot c, (r_1+r_2-r_3)\cdot d)}$ where $r_1,r_2,r_3$ ...
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votes
2answers
638 views
If a probabilistic encryption algorithm is used, how does decryption return the correct message?
Given a key $k$ and a plaintext $p$, a deterministic encryption algorithm will return a ciphertext $c_1$. In a second trial, I run the same key and plaintext $p$ through the encryption algorithm and ...
5
votes
1answer
404 views
Katz/Lindell Problem 2.2
2.2 Prove that, by redefining the key space, we may assume that $\text{Enc}$ is deterministic without changing $\text{Pr}[\text{Enc}_k(m)=c]$ for any $m, c$.
After banging my head against this ...
0
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1answer
93 views
What is the advantage of a probabilistic PKC over a traditional PKC?
While reading through a textbook, I came across the idea of a probabilistic public key cryptosystem, which uses a probabilistic TM to generate the public encryption and private decryption algorithm; ...
4
votes
0answers
158 views
What's the difference between game-based and simulation-based security? [duplicate]
What's the difference between game-based and simulation-based security? When we use the simulation-based, how to construct the simulator based on the adversary?
7
votes
2answers
342 views
Understand LWE(Learning With Error) negligible error probability
According to Regev's paper, p15
Correctness. Note that if not for the error in the LWE samples, $b-āØa, sā©$ would be either 0 or ā q ā depending on the encrypted bit, and decryption would always be ...
1
vote
0answers
232 views
Thorp-Shuffle Coupling
My question is regarding the coupling of the Thorp-Shuffle, as described in Morris/Rogaway/Stegers, Thorp-Shuffle Encryption. On pages 7 to 9, they describe and implement a coupling. It's all fairly ...
1
vote
1answer
261 views
Using High Level Probability Theory (eg Markov Chain Mixing) in Cryptography/Cryptanalysis [closed]
I'm currently doing a PhD in probability theory, specifically (discrete space) Markov chains and their mixing properties. As well as my current main project, I'm looking to have a side project, eg to ...
1
vote
1answer
235 views
Probability of collision in PRF
My question is related to this:
Collision-resistant Pseudorandom function
Assume we have a pseudorandom function as follows: $PRF: \{0,1\}^{l}\times\{0,1\}^{t}\rightarrow\{0,1\}^{m}$, where $l$ is ...
1
vote
2answers
118 views
How can the identity $\textbf{Pr}[\textbf{y}=y|\textbf{x}=x] = \sum_{\lbrace K:x=d_K(y)\rbrace}\textbf{Pr}[\textbf{K}=K]$ be verified to hold?
How can the identity $\textbf{Pr}[\textbf{y}=y|\textbf{x}=x] = \sum_{\lbrace K:x=d_K(y)\rbrace}\textbf{Pr}[\textbf{K}=K]$ be verified to hold for any cryptosystem?
In his book Cryptography, Theory ...
2
votes
2answers
181 views
How to sign low-entropy messages?
Suppose you would like to prove authenticity of messages where the message space is small. Suppose the meaning of the message depends highly on the context, e.g. on time but also on events that are ...
1
vote
1answer
513 views
Is there an additive homomorphic encryption that supports exponentation
For example say we have two numbers a and b. Now is there any partial homomorphic encryption scheme that allows to compute (a-b)^2 over the ciphertexts of a and b without round trips.
2
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1answer
855 views
setting the MGF hash to a different value other than the regular hash with openssl for PSS signatures
In PKCS1's Probabilistic Signature Mode you have the Hash and the MGF Hash. Both appear to be, by default, sha1, with the OpenSSL CLI client, however, I can change it to sha256 with the following:
<...
4
votes
2answers
2k views
Why is Paillier Cryptosystem called probabilistic?
The definition of Paillier Cryptosystem says that it is a probabilistic asymmetric key algorithm for public key cryptography. Can some body explain why it is called "probabilistic"?
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3answers
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What is the meaning of “probabilistic encryption algorithm”?
I am learning cryptography by myself, and I am not able to understand the meaning of "probabilistic encryption algorithm".
How is it different from "deterministic encryption algorithm"? How can ...
5
votes
2answers
93 views
Does $(u_1=r_1\cdot x,\ \ w_1=r_1\cdot z, \ \ u_2=r_2\cdot x,\ \ w_2=r_2\cdot z)$ Leak Information?
Consider we have a fixed value $x$. We pick values $ r_1,r_2,z\leftarrow \mathbb{F}_p$, where $p$ is a large prime number, and it is public. So $r_1,r_2,z$ are uniformly random values.
We compute ...
2
votes
1answer
225 views
Weakening of Paillier cryptosystem due to ciphertext equivalence and order in CryptDB
The Paillier cryptosystem is probabilistic in nature and IND-CPA secure. By design given two ciphertexts one cannot distinguish whether decrypting those two ciphertexts will result in same or ...
1
vote
1answer
221 views
Partial Homomorphic Schemes that are probabilistic
As mentioned in wikipedia there are many Partial Homomorphic Encryption(PHE) scheme like RSA, Elgamal, Pailler etc.
Pailler encryption scheme seems to be probabilistic
Are there any other PHE ...
