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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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Show that adversary indistinguishability is equivalent to specific perfect secrecy definition

How can I show that adversary indistinguishability (AI) is equivalent to the following deifinition of perfect secrecy (PS)?: $P[Enc_k(m_0) = c] = P[Enc_k(m_1) = c]$ for all $m_0,m_1 \in \mathcal{M},c ...
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Proof one-time pad is perfectly secret with eavesdropping game definition

I have the following definition of perfect secrecy (please assume that the probabilistic version is not available): If we consider the eavesdropping game given by: $$\begin{array}{|r | r|} \...
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35 views

Shamir Scheme: Whats the problem of not using random x-coordinates?

i would like to know why there is a problem of not using random x-coordinates in shamir secret sharing schemes. I consider that after evaluating the points in a polynomial $f(x)$, the share is ...
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What is perfect secrecy?

I read some similar questions like Simply put, what does “perfect secrecy” mean? (This one defines perfect secrecy as ciphertext conveys no information about the content of the plaintext. Now, ...
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1answer
88 views

In perfectly secret scheme, if key and message space are uniformly distributed, is ciphertext space always uniform as well?

Following up on a similar question, Does perfect secrecy imply uniform ciphertext distribution?, the answer seems to be that in a perfectly secret encryption scheme, the distribution of the ciphertext ...
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2answers
108 views

Why does the key for a one-time pad have to be uniformly distributed? [duplicate]

I would like an intuitive argument for what goes wrong in the proof that that a one-time pad provides perfect secrecy, if the key $K$ is not chosen uniformly at random from the entire key space.
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Non-interactive public sum of private values

Suppose there is a large number of participants each with a secret value. The secret values are very large (e.g. 256-bit integers). Each participant has published a public commitment to their secret ...
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1answer
91 views

For perfect secrecy, does the keyspace need to be uniform?

The definition of perfect security is just that: $Pr(M =m | C=c) = Pr(M=m)$. We can prove that one time pad is perfectly secure for any distribution on a message space $M$, and it happens to be that ...
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1answer
71 views

Please prove distinguishability given a non-perfectly secure cipher

I'm trying to prove that a perfectly secure cipher yields indistinguishability. I already know and can prove that a perfect cipher => indistinguishability by the following proof: \begin{align} \Pr(...
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1answer
108 views

Perfect Indistinguishability in shift cipher

I have the following question: Which of the following attackers can be used to demonstrate that the shift cipher for 3-character messages does not satisfy perfect indistinguishability? ...
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1answer
72 views

How well is it understood mathematically why encryption schemes are hard to crack?

I have read some intro material into cryptography. It mainly goes into the current encryption schemes like AES, but not very deeply into the mathematics of why they are secure. I know that encryption ...
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206 views

Practical perfect security in bitwise XOR vs integer addition/subtraction cipher

XOR already provides perfect security in theory but it's hard to apply it in practice due to strict requirements. I was thinking about whether simple addition/subtraction in integer format would not ...
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Showing that a cipher is not a perfect cipher

I was given this problem: Prove that the following ciphers are not perfect, using as few blocks as you can. There is no need to prove that the number of blocks is indeed minimal. DES AES-128 AES-256 ...
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3answers
125 views

Is perfect forward secrecy (PFS) possible without public key cryptography

I have an understanding of PFS as used in most key agreement algorithms as well as things like TextSecure protocol and ratchets. My undestanding is that PFS is not possible without asymmetric (public ...
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1answer
173 views

Perfect Secrecy prove

There was a question on my final exam, but I could not get a point. I really want to know the right answer. Question is: Suppose a cryptosystem has perfect secrecy. Prove that H(P|C) = H(P) H(...
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Is perfectly secret key exchange provably impossible?

We know that perfect secrecy in encryption is possible (one-time pad). Now, the concept of key exchange like Diffie-Hellman is that we can establish a shared key without an interceptor knowing, and ...
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1answer
86 views

(Im)perfect Secrecy: |K| < |M|

I have a basic understanding of perfect secrecy. In the case where |K| == |M|, I see that there is only one key to encrypt a given m to a given c. Therefore each m is equally likely with same ...
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Necessity of Randomness when Privately Computing a Sum

I want to show that no 1-private deterministic protocol exists for calculating a sum of $n \geq 3$ parties (within the realms of Perfect rather than Computational Security). I'm having trouble showing ...
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1answer
168 views

Proving one time pad is perfectly secret

I'm reading about one-time pad in "Introduction to Modern Cryptography" by Katz and Lindell. I can understand the definition of perfect secrecy. However, how is OTP proven to be perfectly secure ? I'm ...
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1answer
236 views

Proving that there is no scheme which would be perfectly CPA-secure

A private-key encryption scheme Π = (Gen, Enc, Dec) has perfectly indistinguishable encryptions under a chosen-plaintext attack, if for all probabilistic polynomial-time adversaries A it holds that Pr[...
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Perfect secrecy of OTP [duplicate]

When using the one-time pad with the key k = 0l, we have Enck(m) = k ⊕ m = m and the message is sent in the clear! It has therefore been suggested to modify the one-time pad by only encrypting with k ...
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1answer
198 views

Is the one-time pad still perfectly secret if all-zero keys are excluded?

I'm trying to solve this question related to one-time pads and perfect secrecy: My solution is: I assumed that the current message space is $M = \left\{ 0,1 \right\}^l$ and the new keyspace after ...
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77 views

Perfect Secrecy for some distribution implies perfect secrecy for any distribution

I'm quite thrilled about this question I got for homework, even though we were given the answer to the problem. It goes like this: Let $\mathcal{M}$ be the set of plaintexts of a symmetric encryption ...
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1answer
64 views

One-time pad and Perfect secrecy

Consider the following property of one-time symmetric encryption scheme $(\mathsf{Enc}, \mathsf{Dec}, \mathsf{K})$. For Every message distribution $M$, every pair of messages $m_0,m_1$ belonging to $M$...
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1answer
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Question on probability distribution

I computed $\Pr[\mathsf{CT} = 1] = \Pr[\mathsf{CT} = 2] = \Pr[\mathsf{CT} = 4] = 2/9$ and $\Pr[\mathsf{CT} = 3] = 1/3$. When I calculate the first entry in the table, I get 1/2 not 1/9. Is my ...
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Perfectly secret scheme for two distinct messages

Following the same definition in this question for perfect secrecy for two messages $m,m' \in \mathcal{M}$. I don't understand how the accepted answer produces a secure system? I mean The adversary ...
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157 views

Epsilon Perfect Secrecy: Size of Key Space

I am solving a homework problem which defines $(1-\epsilon)$-perfect secrecy as the secrecy satisfied by the encryption scheme when the following inequality holds $\Pr[M=m\mathrel|C=c]\leq (1+\...
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48 views

On computing probability of some cipher text

One presentation shows how one could compute probability of some cipher text occurring: Which I understand. However, also for computing probability that a plain text occurs given a ciphertext occured,...
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2answers
140 views

clarify perfect secrecy definition

One of the notes defined perfect secrecy (PS) as Let E = (E,D) be a Shannon cipher defined over (K,M, C). Consider a ...
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2answers
2k views

Can one claim that AES has perfect secrecy for a key size and message size of 128 bits?

While looking at this question I discovered the following here (question 5), and wanted to ask it as a separate question. Alice knows that she will want to send a single 128-bit message to Bob ...
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1answer
155 views

How Shannon’s concept of perfect secrecy is linked with mutual information?

For a system to be unconditionally secure $H(K) \geq H(M)$, i.e entropy of the secret key must be at least as great as the entropy of the plaintext The mutual information is: $I(X;Y)=H(X)-H(X\...
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1answer
128 views

Secure multiparty sum computation corruption bound

In Section 3.4 of the book Secure Multiparty Computation and Secret Sharing, it is claimed that for a secure multiparty computation problem with $n$ parties, the optimal corruption bound (concerning ...
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secure system in the perfect sense

a secure system in the perfect sense verifies the definition of perfect security. My question is as follows: There is always a way to check for perfect security by solving the first degree equation by ...
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330 views

Manual secret sharing?

What are feasible options for an equivalent of Shamir Secret Sharing using small tables, preferably usable with pen-and-paper? We want to share a secret $K$ into $n\ge2$ shares, so that $m$ shares ($2\...
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2answers
307 views

Is there such a thing as perfect CPA security?

Consider the following experiment. If we require that $$\operatorname{P}\left( \mathcal A \text{ succeeds} \right) = \frac{1}{2}$$ for any adversary $\mathcal A$ in order to call the scheme $\Pi$ ...
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1answer
156 views

Perfect secrecy of block ciphers

Is it right that all block ciphers don't provide perfect secrecy like AES? If it's true, how can we prove that? If it's not true can you tell me a sample? Any reference or guidance would be ...
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161 views

Generating OTP using Digital Dead Drop

I've had a thought and I'm wondering if this would be a useful way to devise and distribute a one-time pad. It relies on a digital dead drop and a hash function. The digital dead drop could take a ...
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1answer
762 views

Understanding how to proof an encryption scheme is perfectly secret

Consider each of the following encryption schemes and state whether the scheme is perfectly secret or not. Justify your answer by giving a detailed proof if your answer is Yes, and a ...
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1answer
105 views

Corruption bound of MPC when n>2

In the book titled "Secure Multiparty Computation and Secret Sharing" stated that MPC protocol is not secure when the adversary $t>n/2$. This was proved by using a 2 party protocol, but I can't ...
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1answer
106 views

Multi-Embedded Xor for Perfect OTP

I am looking for a perfect OTP design, so let's see if this design is good. There are 2 issues when it comes to a good OTP system, the key and the plaintext, we will use XOR as cypher: If the ...
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Does High Frequency Randomisation of valid and dummy messages in a high volume channel add security?

This was originally posed as this question: "Does randomisation of valid and dummy messages in a high volume channel add security?" But due to the reformulation based on answers provided, Tylo (https:...
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1answer
279 views

Perfect secrecy with some considerartion

According to eavesdropping indistinguishability experiment $PrivK_{A,\Pi}^{eav}$ from page 34 of this book, I define $\varepsilon$-perfect secrecy as this($\varepsilon>0)$: For every adversary $A$ ...
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What is different between Strictly Ideal and Perfect Secure?

Consider a Cipher $C = (X, Y, Z, \Pr[X], \Pr[Z], E, D)$. $X$ is the plaintext, $Y$ is the ciphertext, $Z$ is a set of keys, $E$ is the encryption function, $D$ is the decryption function. $\Pr[X]$ is ...
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1answer
306 views

What are the vulnerabilities of XOR in the following scenario?

What are the security vulnerabilities of the XOR operator in the following scenario: The Key, The Cyphertext and the Plaintext are the same size in bits. The Key is only used once and it's secret The ...
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1answer
41 views

Equivalance Operator - Perfect Secrecy

The equivalance operator is the inverse of the XOR operator, it's symmetric. Would this mean that it would also provide theoretical perfect secrecy just like XOR? XOR ...
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Are one-time pads crackable in theory?

I've been taught that one-time pads are the only perfect encryption, since the only way to recover the message is by knowing the key. For example, for a target bitstring of 100 bits, I cannot scan ...
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Perfect Secrecy with 1 Time Complex Secret Cypher

Is it possible to achieve perfect secrecy, unbreakable, unguessable, uncrackable by using a totally secret cypher? The following conditions must apply: Using the secret cypher only 1 time, so that ...
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60 views

Interpretation of message space distribution in the definition of perfect secrecy of encryption schemes

I am a beginner to cryptography, and have started reading Katz and Lindell's book titled "Introduction to Modern Cryptography". I'm unable to understand what the probability distribution over the ...
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2answers
508 views

Perfect secrecy with XOR & SHIFT?

I have read that XOR provides perfect secrecy, when the key is perfectly random. However it's technically hard to generate truly random numbers, especially on computers, so that is why people use AES, ...