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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Perfectly secret cipher can leak about the key?

As defined by Shannon, a cipher is perfectly secure if ciphertext leaks no information about the plain text. Under this definition, can ciphertext leak something about the key? Are there any ciphers ...
8
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2answers
134 views

Proof that perfect privacy implies that the number of keys is at least the number of messages

I was reading a proof to the statement: Perfect privacy implies that $|K| = |M|$ where I am pretty sure that $K$ is the set of keys and $M$ is the set of messages. The proof is the following, ...
7
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2answers
2k views

Is perfect-forward secrecy achieved with RSA?

I am new to cryptography and am going through the book Understanding Cryptography by Paar and Pelzl. From what I understand Symmetric key distribution systems like Kerberos do not provide PFS ...
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1answer
419 views

One time pad: why is it useless in practice?

The symmetric cryptosystem One time pad (OTP) seems to be very beautiful since it is perfectly secret according to Shannon. Many books, however, point out that the main drawback is that one must ...
4
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1answer
43 views

Generate a random number $r \in \{1,2, \dots , k\}$, where $k$ is not public and is distributedly held

A set of parties can securely generate a random number $r \in \{1,2,3,\dots, k\}$ when $k$ is publicly known. However, can we generate the random number $r$ if $k$ is not publicly known and is held by ...
4
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1answer
118 views

What does the probability subscript mean in Shannon's secrecy definition?

Shannon's secrecy can be defined as: $$P_M (M=m) = P_{SK,M}(M=m|E(SK,m)=c)$$ What does $P_M$ means? (same question for $P_{SK,M}$) I know that is the probability space M, M being the messages; I do ...
4
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1answer
312 views

Why does a perfect secrecy can be achieved when decryption correctness is not totally required?

By Shanon theorem, a perfect secrecy encryption scheme must use a key space of equal size as the message space. But when the correctness requirement is weakened such that $Pr[Dec_k(Enc_k(m))=m]=1/2$ ...
3
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1answer
66 views

2 party AND computation under passive perfect security

In the book written by Ivan Damagard titled "Secure Multiparty Computation and Secret Sharing", at the end of the third chapter he provides a proof for why it is impossible to securely compute 2 party ...
3
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2answers
251 views

Perfect Forward Secrecy in TLS

I read that TLS does PFS using Diffie Hellman. However, DH can be used even without certificates - so how is DHE-RSA better than plain DHE? Is DHE a insecure algorithm, that DHE-RSA is needed?
3
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2answers
65 views

(Non-) Perfect Secrecy of Vernam Cipher Using $E(m) = m \oplus k \oplus \operatorname{rev}(k)$

Given the cipher $$E(k, m) = m \oplus k \oplus \operatorname{rev}(k)$$ where $\operatorname{rev}(k)$ is the reversed binary of $k$, how would one prove that the cipher is not perfectly secret. I ...
3
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1answer
351 views

Which is better ECDHE with TLS 1.0

I have a webserver which only supports TLS 1.0 and I am not sure about something: Which is the better cipher in this group when aiming for the best security? ...
3
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1answer
95 views

How can recovered 5-letters plain text help me to recover reused OTP key

I have 10 cipher texts ciphered with One Time Pad (OTP) using the same key. I need to recover the key (or in other words, to recover the 11th cipher text which I assumed would require me to recover ...
3
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0answers
60 views

Perfect secrecy is maintained for other plaintext prob distributions?

Suppose a cryptosystem achieves perfect secrecy for a particular plaintext probability distribution. Prove that perfect secrecy is maintained for any other plaintext probability distribution. Having ...
2
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1answer
316 views

An example of of an information theoretically secure protocol that is not cryptographically secure

Does there exist a protocol $\pi$ for some functionality $F$ which is information theoretically secure protocol that is not cryptographically secure for some threshold number of corrupt parties? ...
2
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2answers
83 views

How to prove a symmetric encryption scheme provides perfect secrecy?

I learned in class that in order to achieve perfect secrecy, the source of the plaintext $\mathcal{P}$ needs to be independent from the source of the encryption key $\mathcal{K}$. We also learned that ...
2
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3answers
333 views

If a cipher has key length shorter than plaintext, then it is not perfectly secure

I am trying to verify the statement above. So far I only know that a One-Time-Pad is the only “perfectly secure” cipher. It has a key length which is exactly the same as the plaintext. I think the ...
2
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2answers
122 views

Shannon theorem of perfect secrecy

From the class: Shannon Theorem: For a perfect encryption scheme, the number of keys is at least the size of the message space (number of messages that have a non-zero probability). Proof: ...
2
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3answers
133 views

How do I create a secure encryption scheme using addition?

You have a 4 number long PIN code with each number ranging from 0 to 9 which you wish to encrypt. You are then given a random 4 digit number ranging from 0 to 9999, which when added to the original ...
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1answer
47 views

Optimal threshold for passive and perfect security

The authors of the book titled "Secure Multiparty Computation and Secret Sharing" claim that there exist functions which cannot be computed with passive perfect security for $t \geq n/2$ corrupt ...
1
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2answers
92 views

Does a stream cipher provide perfect secrecy?

From WAR10CK here: If I actually do create a machine using RC4 or AES-CTR and have a TRNG continually feed it a constant steady stream of random bits. Provided that the stream of bits is purged ...
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2answers
100 views

What do these notations mean in the definition of Perfect Secrecy, if we read those in English?

If m: message, M: message space, k: key, K: keyspace, c: cipher, C: cipher space and $E_k$: encryption function, such that $E_k(m) = c,\ m,m^* \in M,\ k\in K,\ c\in C.$ Then, what do the following ...
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3answers
319 views

Does perfect secrecy imply uniform ciphertext distribution?

I suspect the answer is no, but I am not able to either prove it, or provide an example. In Katz and Lindell's book, it is only said that with a perfectly secret encryption scheme, the plain and ...
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2answers
3k views

How can a cryptosystem be unconditionally secure?

The definition of an unconditionally secure cryptosystem states that the cryptosystem cannot be broken even with infinitely computational ressources and time. However, since most books define the ...
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1answer
49 views

Lower bound of key space size with relaxed perfect secrecy

My apologies, I'm quite new to cryptography. If we relax the definition of perfect secrecy such that for cyphertext $c$, messages $m_0$ and $m_1$, and constant $E$: $P[c|m_0] \le E * P[c|m_1]$ ...
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2answers
115 views

Perfect secrecy with n-time key

How can you encrypt $n$ messages with the same key, and have the same theoretical security you'd have encrypting a single message with a one time pad? For example, how can you encrypt two messages ...
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1answer
110 views

Is one-time-pad still secure if the number of 1's in the key is revealed to the attacker?

For example, if $m = 10011$, $k = 11001$, $n=3$ (which is the number of 1's in k), $c = m \oplus k = 01010$. If $c$ and $n$ are revealed to the attacker, is this scheme still secure?
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1answer
601 views

Can a monoalphabetic substitution cipher attain perfect secrecy?

Can a monoalphabetic substitution cipher attain perfect secrecy? Definition of perfect secrecy: $${\rm Pr}[\,{\rm Enc}_k(m_1) = c\,] = {\rm Pr}[\,{\rm Enc}_k(m_2) = c\,]$$
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1answer
480 views

Hill cipher is not perfectly secure

I am on cryptography course and there is a homework question to show that Hill cipher doesn't have perfect security. So assume we have an cryptosystem $(P,C,K)$, where $P = C = \mathbb Z_{26}^N$ and $...
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1answer
75 views

Rationale of “r” AES key use in OTR version 3 AKE protocol?

I just tried to review & understand AKE (Authenticated Key Exchange) protocol as defined in OTR secure messaging protocol version 3 here , and aiming to achieve Perfect Forward Secrecy I am a ...
1
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1answer
880 views

One-time pad, zero key and Shannon

I'm supposed to prove that OTP without the zero key $k=0^n$ is not perfectly secret anymore. I understand that it's not because an attacker learns something by looking at the plaintext and ciphertext. ...
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1answer
47 views

One time pad (OTP) perfect secrecy with different key space

Let say $K_{0} = \left \{ 0,1\right \}^n$ $K_{1} = K=\left \{ 0,1\right \}^n$ \ $0^n$ $[b\leftarrow \left \{0,1 \right\}, k \leftarrow K_{b}:b=1|k \neq 0^n]$ --- (1) Key is chosen using ...
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2answers
68 views

Can one construct OTPs without using XOR?

The typical version of the one-time-pad (OTP) uses XOR to combine a key pad and a message. ($c=m\oplus k$) Now let's assume some other scenarios which have the practical application of blinding. Do ...
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1answer
65 views

Unconditional authentication

I have a few questions regarding universal-hash functions: Is there a way universal hash functions can be used to provide unconditional authentication in the way the OTP provides unconditional ...
1
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1answer
107 views

Perfect secrecy of a crypto system

Suppose we have the following crypto system: $P = C = K = \{0, 1, . . . , n − 1\}$, $E_k(x) = (x + k) \bmod n$ and $D_k(y) = (y − k) \bmod n$. Prove that the crytosystem has perfect secrecy. Perfect ...
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1answer
151 views

Is there an asymmetric One-Time-Pad? [duplicate]

Is there something like a perfect asymmetric crypto-algo? Is there proof that there must be one or not. From a logical point of view it seems to be possible to design such algorithm if your keysize is ...
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0answers
97 views

How we can said a crypto system have perfect secrecy?

For example: I have 3 plaintexts ($a$, $b$, $c$) and 4 keys ($K_1$, $K_2$, $K_3$, $K_4$), making a table map to the cipher text, key as row and plaintext as column $\begin{matrix} \ \ \ \ \ \ \ \ \ \ ...
1
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1answer
148 views

Perfect secrecy over Stirling numbers

For all $c_0\leftarrow m_0 \oplus k$ there exists a $k'$ such that $c_1 \leftarrow m_1 \oplus k'$, where $m_0 \neq m_1$ and $c_0 = c_1$. Assuming a truly random $k$, the first assignment is a one-...
0
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1answer
72 views

What is the meaning of the overlapping region on OTP-perfect secrecy diagram?

I'm new to cryptography. I want to ask about OTP-perfect secrecy diagram like figure below: On the overlapping region (middle), notated by R(X;Y;Z). R can be calculated by I(X;Y) - I(X;Y|Z). ...
0
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1answer
68 views

How can I turn this cipher into a perfect cipher by altering only its encryption algorithm?

Given a toy cipher that picks a key, k, from the key space of {00,01,10} and a message,m, from the same set {00,01,10} and encrypts using E = m ⊕ k. How can I change the encryption function E in ...
0
votes
1answer
636 views

Why cant Public Key Encryption be perfectly secure? [duplicate]

I would be very grateful for any help. I cant figure out why (probabilistic) public key encryption schemes can never provide perfect secrecy? Any Ideas? Excerpt: In contrast to the private-key ...
0
votes
1answer
68 views

Why perfect secrecy can be ensured when a plain message and a cipher-text based on one-time pad are correlated?

First, some well-known results are as follows. For random variables $X$ and $Y$, we have $$H(X,Y) \leq H(X) + H(Y).$$ The equality is achieved when $X$ and $Y$ are independent. Second, in one-time ...
0
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1answer
150 views

Definition of perfect secrecy using ciphertext

This week my professor in class taught us the definition of perfect secrecy. He said that for any ciphertext the probability that it might have come from any message in the message space should be ...
0
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0answers
80 views

Perfect Secrecy of AES file Encryption

Why does AES file encryption not ensure perfect secrecy? I understand that $\Pr[E(K,M_1)=C_1] = \Pr[E(K,M_2)=C_2]$ given $M1\neq M2$ holds for perfect secrecy of a scheme. However, this seems to hold ...
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1answer
470 views

Prove that the affine cipher over Z26 has perfect secrecy if every key is used with equal probability of 1/312

Prove that the affine cipher over Z26 has perfect secrecy if every key is used with equal probability of 1/312. Just some guidance/help with this problem would be greatly appreciated not sure how to ...
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2answers
60 views

Is the one-time pad secure?

I have read about one-time pads (OTP) on Wikipedia. Is this secure? Can I actually use modular addition as ecryption like it said in Wikipedia? And the plaintext is as long as the OTP, so when I send ...