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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Katz/Lindell Problem 2.2 - Purpose of proof where you redefine the key space?
I am self-studying by using "Introduction to Modern Cryptography: Principles and Protocols" (2nd edition).
I am looking at the following problem.
Prove that, by redefining the key space, we ...
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If a different plaintext may produce the same ciphertext, is the system perfectly secure?
Define the injective map $\phi: \Omega\rightarrow \mathbb{N}$, such that $\Omega=\mathcal{A}^n$ denotes the set of all strings of length $n\in\mathbb{N}^*$ from an alphabet $\mathcal{A}$ of elements $...
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Advantages and possible usages of encryption schemes with probabilistic decryption
We can define deterministic and probabilistic encryption;
Deterministic $c = E(k,m)$, and
Examples are textbook RSA, block ciphers in ECB mode.
Deterministic encryption fails to achieve CPA security....
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Do probabilistic one-way functions imply deterministic one-way functions?
Suppose $f$ is a probabilistic one-way function. Then my question is, does there exist a construction of a deterministic one-way function $g$ based on $f$?
Or is it possible that probabilistic one-...
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Why random number used in RSA padding but not in AES?
I noticed that people use a random number in the RSA-OAEP padding scheme to avoid deterministic encryption. But in pkcs#7 people just use the padding size rather than some random bits. Doesn't it make ...
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Probability of collision when we use a particular part of sha 256 hashed value
So I was supposed to use hash some co-ordinates and I was supposed to use k 3-wise independent hash functions in order for the mathematical explanations behind that algorithm to be hold. But after ...
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1answer
97 views
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 ...
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Understanding why Semantic Security implies Message Recovery Security
I am stuck in the proof where it says $$p_0=\frac{1}{|M|},$$ 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 ...
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1answer
66 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 ...
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1answer
111 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 ...
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81 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 ...
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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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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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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 $a,b,c,d$...
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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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951 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 ...
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556 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 ...
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107 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; ...
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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?
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2answers
447 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, $b-⟨a, s⟩$ would be either 0 or ⌊ q ⌋ depending on the encrypted bit, and decryption would always be ...
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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 ...
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1answer
298 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 ...
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1answer
371 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 ...
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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 ...
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2answers
229 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 ...
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1answer
593 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.
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1answer
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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:
<...
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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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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 ...
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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 ...
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1answer
276 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 ...
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232 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 ...