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Questions tagged [perfect-secrecy]

Confidentiality in a very strong sense. Ciphers reaching perfect-secrecy can't be broken to disclose informations over the plaintext from the ciphertext, even with unlimited computing power. The most known example cipher reaching perfect screcy is the one-time-pad.

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Shannon's Perfect Security for Asymmetric Encryption

I have the following definition of Shannon's Perfect Security. Assuming messages and keys are drawn randomly from some distribution then: The probability of guessing plaintext m is not enhanced by ...
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Can a perfectly secret scheme have non-uniform ciphertext distribution if the plaintext and ciphertext length is equal?

I've seen this question asking if perfect secrecy implies uniform ciphertext distribution, and I understand that this is not the case. However, all given counterexamples seem to require a construction ...
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Why is perfect secrecy defined under a ciphertext-only threat model?

I recently acquired Katz & Lindell's Introduction to modern cryptography (3d edition). Currently I'm on page 27 where we have the following definition: Definition 2.3: An encryption scheme (Gen, ...
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Katz and Lindell, proof of lemma 2.4

Can someone explain the logic behind the claim that the second equality is because we condition on the event that $M$ is equal to $m$ in the proof of Lemma 2.4 from "Introduction to Modern ...
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Is there a TLS cipher suite with perfect forward secrecy (PFS) but without authentication, i.e. anonymous, ephemeral key exchange?

Is there a TLS cipher suite with perfect forward secrecy (PFS) but without authentication, i.e. anonymous key exchange? I am not asking or wish to discuss the principle question whether an ...
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Can a computationally-unbounded adversary break any cipher which is not perfectly secret?

Imagine we have a cipher defined as $(K, M, C, E, D)$ which is not perfectly secret, namely: $\exists m_0, m_1 \in M, c \in C \text{ s.t. } P[k \leftarrow K; E(k, m_0) = c] \neq P[k \leftarrow K; E(k, ...
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Proving if two samples hides a value?

Given two values $r'-r \mod q$ $i - r \mod q$ Where $r',r$ sampled randomly from $Z_q$ while i is pick arbitrarily from $Z_q$ and a secret Can we claim that this hides $i$? Here is my sketch: ...
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Perfect Secrecy other than One-time Pad

The most known example cipher reaching perfect secrecy is One-time Pad, which employs modulus addition for encryption and decryption. Is there any other well-known cipher no less practical than OTP ...
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Does CCA security imply perfect secrecy?

Can any encryption scheme that is CCA (Chosen Ciphertext Attack) secure be considered to achieve perfect secrecy?
Judge Rhadamanthus's user avatar
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Defining the random variables $K,M,C$ and Perfect Secrecy

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 $...
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prove of disprove the modified shannon's theorem when the correctness requirement is relaxed

Suppose the correctness requirement of private-key encryption scheme is now relaxed to require only that $$ \Pr[Dec_k(Enc_k(m)) = m] \ge \frac{1}{2} + \epsilon. $$ Prove of disprove that if an ...
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Is it necessary keys to have equal propabillities for the system to have perfect secrecy?

Shannon's theorem for perfect secrecy states that $$\forall x \in M, y \in C:\quad P[x|y]=P[x] $$ I know we need $|M|\leq |C| \leq |K|$. If $|Μ|=|C|=|K|$ all keys should have equal probs. If $|Μ|<|...
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why XOR is recommended/Used in every paper I read for encryption and decryption stream cipher?

Stream ciphers use a deceptively simple mechanism: you combine the plaintext data, bit by bit, with “key” bits, using the exclusive or operation. Why can't I use other opeartions such as NAND, AND, ...
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What is the simplest way to implement data encryption for Raspberry PI project that communicate through Bluetooth? [closed]

I have developed a project based on Raspberry Pi that communicates through Bluetooth with Android application, My idea is to enhance its privacy through encryption. So, I've tried ...
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Is 7-Zip Encryption really secure? [duplicate]

Is 7-Zip really a good encryption tool? I wonder what kind of encryption is used in 7-zip. I see most people using 7-Zip. Just curious about what extent it is safe.
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Relation between the size of key space and message for an encryption scheme that is not perfectly secure

I have been trying to solve the following: Given a scheme that is perfectly correct but not perfect secrecy. It satisfies computational security, however, in that, if Q = Pr[Adv wins no query semantic ...
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How can I distribute a set of anonymous tokens digitally among a known limited population to do anonymous voting?

TL:DR How can I give a population of N people the chance to randomly pick one token each person guaranteeing those: Nobody knows noone else's token. Noone can pick more than one token. Every person ...
Xavi Montero's user avatar
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Information Theoretic Security for Public Key Encryption

Do there exist information theoretic secure public key crypto-systems? Are they useful in any way, or are they just mathematical curiosities?
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What is the Work Factor of the one time pad?

Work Factor is defined as the minimum amount of work (can be the length of the key) to determine the secret key of an cryptosystem (HAC, Menezes, Alfred J. et al). And One time pad have unconditional ...
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Proving two definitions of perfect security are equivalent

I'm trying to prove that the following two definitions are equivalent: $\forall m\in M $ and $c\in C$ $\Pr[C=c \mid M=m]=\Pr[C=c]$ $\forall m_1,m_2 \in M $, $E_k(m_1)=E_k(m_2)$, where $E_k(m_i)$ ...
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Perfect security - is this definition correct?

I have this definition: each ciphertext is equally probable for a given plaintext and key chosen at random I know that perfect security can be defined as $$\forall c \in \mathcal{C} \ \forall m_1,...
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Ideal cipher vs Ideal encryption scheme

Ideal cipher is a random permutation for every key in its key space. And, ideal encryption scheme is the one which has perfect secrecy/indistinguishability. For an encryption scheme, random ...
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difference between unconditionally sure, perfect confidentiality, and semantically sure, adversary-wise and advatnage-wise?

can anyone please tell me the difference between unconditionally secure, perfect confidentiality and semantically secure? I know that for perfect confidentiality, we have an adversary A that has an ...
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Katz/Lindell - 2.10: Is exhaustive search over the key-space allowed in perfect indistinguishability?

I am self studying using "Introduction to Modern Cryptography (2nd edition)" I am trying to understand how the solution to the following problem is valid: Prove that a scheme satisfying ...
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Katz/Lindell 2.4 - Generalizing from 2 messages to any message space?

I'm trying to solve problem 2.4 in "Introduction to Modern Cryptography" (2nd edition) for self-study. The problem asks to prove that perfect secrecy $$ Pr[M = m | C = c] = Pr[M = m] $$ ...
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Perfect Secrecy for Shift Cipher

I've read the definition of perfect secrecy as the following: A cryptosystem has perfect secrecy if $\Pr(x | y) = \Pr(x)$, for all $x \in P$ and $y \in C$, where $P,C$ are respectively the set of ...
João Víctor Melo's user avatar
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Why are stream ciphers computationally secure?

In case multiple stream ciphers exist, I'm refering to this specific instance in which you generate a key that is just as long as the msg, M, as a function of a nonce and a smaller key K. My textbook ...
Sebastian Nielsen's user avatar
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Secret sharing is based in random variables that are uniformly distributed?

In Rabin and Ben-Or, their basic assumption is that each participant can broadcast a message to all other participants and that each pair of participants can communicate secretly. Hence, they design a ...
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Equivalent conditions for perfect secrecy of a symmetric crypto system

I've been reading about perfect secrecy in crypto systems and I've ran across two definitions which turn out to be equivalent. The first is Shannon secrecy: A crypto system $(\cal K, \cal M$, $\text{...
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One-time pad without zero: proof check

I started learning cryptography and tried to work through this problem: consider one-time pad where $\mathcal{M}=\mathcal{C}=\{0,1\}^n$ and $\mathcal{K}=\{0,1\}^n\setminus 0^n$ (call this scheme $\Pi$)...
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An exercise from a textbook

Let $\varepsilon>0$ be a constant. Say an encryption scheme is $\varepsilon$-perfectly secret if for every adversary $\mathcal{A}$ it holds that $$ \operatorname{Pr}\left[\operatorname{PrivK}_{\...
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Is OTP still perfectly secure if we limit message and key space

If we have a message space M {0,1,2,3,4,5,6} and likewise keyspace is K = {0,1,2,3,4,5,6} (generator choosen uniform keys k) We define our encryption to be the XOR of their bitwise rep on K and M ...
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Question on double-asymmetric encryption and split knowledge

Moin moin, Let‘s assume there are two keypairs (d1,e1) and (d2,e2), where d1 and ...
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Proving that a scheme is $\epsilon$-perfectly secret

I am currently trying to solve the following problem (2.18) from the book "Introduction to Modern Cryptography (3rd edition)" by Katz and Lindell: Let $\epsilon > 0$ be a constant. Say an ...
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AKE using Noise_NNpsk2 vs Noise_NKpsk2

I am working on an implementation based on the Disco library, which itself is based on Noise and strobe framework. The goal is to do bilaterally entity-authenticated key agreement with perfect forward ...
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perfectly secret with key chosen uniformly

Prove or refute: Every encryption scheme for which the size of the keyspace equals the size of the message space, and for which the key is chosen uniformly from the keyspace, is perfectly secret. My ...
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How to solve this decryption algorithm given the encryption algorithm?

Consider the following cryptosystem with plaintexts from the set $M$ and ciphertexts from the set $S$ with $M = S = \{0, 1\}^4$ . A plaintext $P = (P_1, P_2, P_3, P_4)$ is encrypted to a ciphertext $C ...
Joshua Leung's user avatar
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Advantage of existing Cryptosystems

I have read about the concept of perfect secrecy and statistical distance. The perfect secrecy is impossible to be implemented on real world scenario. So the cryptosystems used at various websites ...
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2 answers
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Perfect Secrecy and Message distribution

I have been trying to come up with a proof of the following statement, Suppose a cryptosystem achieves perfect secrecy for a particular plaintext probability distribution then Prove that perfect ...
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Formal proof that the following definitions of perfect secrecy are equivalent

I've seen the following two definitions of perfect secrecy for an encryption scheme (Gen, Enc, Dec). ...
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4 votes
3 answers
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Can you have perfect secrecy with countable message/key spaces by dropping countable additivity?

This classic paper by Chor and Kushilevitz shows that if the key space and the message space are both countably infinite, then it is impossible to have a perfectly secure private-key encryption scheme....
Keshav Srinivasan's user avatar
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3 answers
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Is it possible to have perfectly secure public-key cryptography with oracles?

It is a basic theorem of cryptography that it is impossible to have a perfectly secure public-key encryption scheme. That’s because the adversary can search through all possible private keys. But I’m ...
Keshav Srinivasan's user avatar
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1 answer
643 views

Why don't most encryption algorithms use perfect secrecy?

Isn't it possible to make algorithms that are both computationally complex and have many possible answers if you try to crack them without knowing the password? Why aren't many popular algorithms like ...
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Using HMAC with AES modes that do NOT require padding [closed]

I'm trying to use HMAC with AES modes that do not require any sort of padding. Although I am aware that modes like AES-GCM and ...
arunanshub's user avatar
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1 answer
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A generalisation of Shannon's theorem of perfect secrecy

The proof I'm struggling with is the following: Let $\mathcal{E}$ be a cipher defined over $(K, M, C)$. Suppose that $SSadv[A, \mathcal{E}] ≤ \epsilon$ for all adversaries $A$, even including ...
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Perfect secrecy and block ciphers

Consider a block cipher that encrypts bit strings of length $n$, where the key-space of the block cipher is of size $2^{kn}$, $k \geq 1$. My understanding of perfect secrecy is that a system is ...
user918212's user avatar
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How many perfect secrecy systems are there?

How many non-trivial*, interesting perfect secrecy systems are there other than the one-time-pad? Does it seem that the one-time-pad and perfect secrecy are synonymous, but are there any other ...
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Proving equivalency of two security definitions of symmetric encryption schemes

how to prove definition 3.8 and 3.9 are equivalence ? picture is from book an introduction to modern cryptography (2nd edition) by j. katz and y. lindell pdf and https://repo.zenk-security.com/...
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Adding the same noise to all element of a vector is Differential privacy

In Differential privacy, if we add a $N$-dimension private vector with $N$-dimension Laplace or Gauss noise, we obtain differential privacy. However, if we only generate a 1-dimension noise to add it ...
eclipse140790's user avatar
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Perfectly secure cryptosystem as many keys as plaintexts

Is a cryptosystem perfectly secure if there are at least as many keys as there are plaintexts? My guess is yes but I am not sure, new to cyptosystems
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