A primitive or protocol with provable security is accompanied by a mathematical proof that shows how to reduce the security claims about the protocol to a set of assumptions.

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What does “Worst-case hardness” mean in lattice-based cryptography?

In the wiki page of Lattice-based Cryptography the "Worst-case hardness" is defined as below: Worst-case hardness of lattice problems means that breaking the cryptographic construction (even with ...
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1answer
1k views

What is it meant by a “hybrid argument”?

Can anyone explain (or point to a reference for) what a hybrid argument is in a security proof, and when it's convenient or preferable to use it? Among some of the places where I've seen it ...
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1answer
129 views

Security based on PRF

I've seen that there is several kinds of PRF, and sometimes people speak about strong PRFs. When proofs of a protocol or algorithm are given based on the assumption of the use of a PRF, are they ...
3
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1answer
351 views

Proofs of security methodologies

I'm looking for course material on the subject of proofs, reductions, and games, as used to prove cryptographic schemes secure. What are the methodologies? What are the preferred ones? In what cases ...
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6answers
549 views

A block cipher with independent keys for each round

I want to modify a standard block cipher in the following way. I replace each round key by a key picked at random. Is this block cipher as secure as the original one ? Thank you. EDIT Some missing ...
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1answer
238 views

Unforgeability and type of adversary

When trying to prove security of asymmetric signature, for instance for existential (or strong) unforgeability against chosen messages attack, do we need to consider the signer as a possible ...
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0answers
62 views

Is it feasible to break an encrypted and later encoded message?

A message is sent from a person to another. The plain message is first encrypted, even with a weak algorithm - say, DES. Then, the encrypted message is encoded with a simple substitution, which is ...
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4answers
386 views

Automated security protocol verification tool for eCK model

I want a tool that (runs on Win7 and) can perform automated verification of a protocol in the eCK security model as described in Microsoft Research's paper "Stronger Security of Authenticated Key ...
3
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3answers
231 views

Chance in cryptography

I was just thinking about my own chance and the way chance can defeat even the most advanced algorithm. My thought was : you can make a strong session id, but what if by chance, a hacker set this ...
3
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1answer
238 views

Is $q(n)=1/n$ a negligible function?

By definition - $q(n)$ is a negligible function if for every positive integer $c>0$ there exist an integer $N_c$ such that for all $x>N_c$ : $q(n)<1/x^c$ So for the function $1/x$, if we ...
3
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1answer
156 views

Is this really the correct way to do an IND-CPA test?

In a description of IND-CPA (indistinguishability under the chosen plaintext attack), I have been reading the following, simple test: The adversary can generate as many messages as he wants. Then, ...
4
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2answers
320 views

Hash function based on block cipher (and proof of security in the PRP model)

Do there exist proofs of security for primitives like hash functions (based on a block cipher) in the PRP model. I often see proofs in the random oracle model (for hash function based on compression ...
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2answers
135 views

Why do PKI schemes need security proofs? [closed]

When it comes to designing new PKI-based key-exchange protocols, why are security proofs needed? Without them, can we show a protocol's security? Does there exist a PKI-based key-exchange protocol ...
3
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1answer
113 views

A confusion about HMQV?

As the full version of HMQV is very long, I will give a graph of it below \begin{array}{@{}l@{}c@{}l@{}} \hat{A} && \hat{B} \\ (a,A=g^a)&&(b,B=g^b) \\ x\in_R[1,q-1],\quad X=g^x ...
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1answer
219 views

Is there proof to the relation between the gap Diffie-Hellman problem and the the Cha-Cheon signature scheme?

I am trying to prove that: "If the gap Diffie-Hellman problem is easy, then the Cha-Cheon signature scheme will be broken." Can you help me to prove it? Is there any proof to the relation between ...
3
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1answer
112 views

Difference between computational and statistical indistinguishabilities

What is the difference between the two notions of computational and statistical indistinguishability?
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1answer
62 views

order between adversaries and type of resources given

We have a game $G0$ for which an adversary $A$ has access to a certain amount of ressources. Let us suppose that the maximum advantage for the adversary to win this game is $Adv_{G0}$. If we modify ...
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3answers
891 views

Hash function based on pseudorandom functions and security

Are there hash functions that make use of pseudorandom functions. Precisely, I'm looking for a specification of a hash function based on PRF (and based on the security of such a primitive).
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2answers
181 views

Acceptable assumptions when proving security

Considering the output of a cryptographic primitive, like an encryption scheme (CBC, ...), a hash function or even the output of any schemes based on number theoretic assumptions, is it reasonable ...
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1answer
64 views

Are those two distributions indistinguishable?

The Decision composite residuosity problem problem states that is impossible two distinguish between those two ensembles: $\{x^N \mod {N^2} | x \in \mathbb{Z^*_{N{^2}}}\}$ and $\{r \in ...
3
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2answers
312 views

Can you help with that definition for a CCA?

The following is a definition taken from Introduction to Modern Cryptography by Katz and Lindell. I'm having a hard time understanding some basic concepts! Can you please help me? ...
0
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1answer
65 views

The real-life meaning of proving over a group that doesn't support the oracle?

If I proved a scheme's security under GDH assumption, in real-life, if this DDH oracle does exist, then it's good, but what about other side ? In real-life, if this DDH oracle doesn't exist, then ...
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2answers
121 views

PPT eavesdroper able to output $m_{0}$ and $m_{1}$ of different lengths

I've read the following two questions and their answers: Messages of different lengths and one-time computationally-secret Why is a non fixed-length encryption scheme worse than a fixed-length one? ...
2
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1answer
293 views

Proof of the standard pseudorandom generator + XOR encryption scheme in Goldreich

Reading Goldreich's Foundations of Cryptography II, I found this proof for the security of the common pseudorandom generator + XOR encryption scheme (Proposition 5.2.12 in the book): Assume you ...
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1answer
115 views

SHA-1 Keyed Hash Function

I know that SHA-1 is an unkeyed cryptographic hash function when used in practice. But, in the theory, all hash function are defined with keys. My question is: How I will be able to formalize the ...
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4answers
313 views

Is there a proof for showing any cryptogram is crackable?

I commonly hear statements along the lines of "all cryptograms are crackable - it's only a matter of time". Is there a proof to show that any cryptogram is "crackable"? The proof may be of a more ...
2
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2answers
171 views

Where does the meaning of reduction to a hard problem lie?

Given you a protocol, if we can reduce breaking the protocol to a hard problem, such as DLP or CDH, then we can say that this protocol is secure. Theoretically speaking, reduction is a good method ...
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1answer
93 views

Sematically Secure McEliece

I am read the Lemma 2 (pp13) in the paper "Kazukuni Kobara and Hideki Imai: Semantically Secure McEliece Public-Key Cryptosystems –Conversions for McEliece PKC– (PKC 2001)". Related to the question ...
0
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1answer
74 views

Hash of multiset of values, which lets me compute the hash of the union

Cryptographic hash functions normally take as input a bitstring. I am looking for a hash function that takes as input a finite multiset of values. In other words, given $S \subset \{0,1\}^*$, I want ...
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2answers
524 views

What is the definition of “security beyond the birthday paradox”?

I'm reading a paper about MACs and I would like to be sure about the meaning of a security beyond the birthday paradox. Is there a definition?
12
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1answer
777 views

Does unbalancing a feistel cipher always improve security? Does it improve security at all?

So according to Wikipedia unbalanced feistel ciphers provide greater provable security. Specifically, they state: The Thorp shuffle is an extreme case of an unbalanced Feistel cipher in which one ...
24
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2answers
6k views

Why does nobody use (or break) the Camellia Cipher?

If Camellia is of equivalent security and speed to AES, concerns arise. First of all, assuming the above, why is Camellia so rarely used in practice? Why aren't there any breaks in Camellia? Does ...
4
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1answer
206 views

Is it safe to assume Salsa20 to be a PRP?

Often in security proofs a certain block cipher is assumed to be a pseudorandom permutation or PRP. I wonder if this goes for stream ciphers as well, and specifically for Salsa20. If limit ourselves ...
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1answer
176 views

Security of cloud computational protocols in UC Framework?

The universal composability allows one to the analyze security of cryptographic protocols . But it does have some gaps when it comes to analyzing few protocols especially two party cases when there is ...
5
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1answer
190 views

Proof that MACing a hash of the message is also a secure MAC

I found a theorem that says: Let $MAC = (S,V)$ be a MAC for short messages over $(K,M,T)$. Let $H: M^{big} → M$. Define $MAC^{big} = (S^{big},V^{big})$ over $(K,M^{big},T)$ as: $S^{big}(k,m) = ...
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1answer
70 views

Safety when disclosing hashes of secrets used to calculate other secrets

In my application, I am generating a big random number and publishing a SHA256 hash of it. After the hash it published (but not the secret), anyone can submit any number, and the system will calculate ...
2
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1answer
160 views

The Goldreich-Goldwasser-Micali Construction with bad PRGS

I understand that if we have a secure PRG then the Goldreich-Goldwasser-Micali construction gives us a secure PRF. However, what I've not been able to find much material on is how will the GGM ...
2
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1answer
460 views

Why is proof-by-reduction needed (for Elgamal proof of security, for example)?

The textbook proof for Elgamal encryption basically reduces to the Decisional Diffie-Hellman assumption (DDH). Elgamal: $Gen(.): x \xleftarrow{R} \mathbb{Z}_p$; $Enc(m,g^x): r \xleftarrow{R} ...
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2answers
336 views

Is this a structural weakness of Feistel networks?

I'm doing a lot of reading about Feistel networks. Something occurred to me a bit ago that I hadn't realized previously, namely that in any Feistel construction there are bits of the plaintext that ...
5
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1answer
109 views

Is there any existing analysis for this construction to turn a tweakable blockcipher into a PRF?

I'm basically looking at this construction to turn a tweakable blockcipher $E_c(x)$ taking a key $k$, nonce $n$, counter $c$ (forming tweak $t = c||n$) and an input $x$ into a PRF on an ...
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1answer
360 views

Is my understanding of CPA indistinguishability experiment correct?

Following are steps to conduct Chosen Plaintext Attack (CPA) indistinguishibility experiment $PrivK_\mathcal{A,E}^{eav}(n)$. $\mathcal{A}$ is the adversary $\mathcal{E}$ is the encryption scheme ...
3
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1answer
870 views

Proof that IND$-CPA implies IND-CPA?

I've read a few papers recently that used a notion of security called "indistinguishability from random bits/strings" under chosen plaintext attack, also called IND\$-CPA. See e.g. ...
3
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1answer
348 views

some of my confusions about DDH assumption

The wiki defines the decisional Diffie–Hellman assumption as follows: Decisional Diffie–Hellman assumption Consider a (multiplicative) cyclic group $G$ of order $q$, and with generator $g$. The DDH ...
12
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3answers
2k views

What is the ideal cipher model?

What is the ideal cipher model? What assumptions does it make about a block cipher? How does it relate to assuming that my block cipher is a pseudo-random permutation (PRP)? When is the ideal ...
2
votes
1answer
159 views

Can you help me understand PFS and wPFS?

Every time I encounter the concepts of PFS (perfect forward secrecy) and wPFS (weak perfect forward secrecy), I feel uncertain about them. My understanding is that: PFS ensures that, if the ...
6
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1answer
180 views

Is there a security proof for the Triple-DES construction in the ideal cipher model?

Suppose one has an ideal block cipher $E \: : \: \{0,\hspace{-0.04 in}1\hspace{-0.03 in}\}^k \times \{0,\hspace{-0.04 in}1\hspace{-0.03 in}\}^w \: \to \: \{0,\hspace{-0.04 in}1\hspace{-0.03 in}\}^w ...
3
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1answer
120 views

Does there exist a two-pass AKE protocol that is secure in eCK model and also has PFS?

As we can know that the best two-pass AKE protocols with DH message can achieve is the weak form of perfect forward security (wPFS) which guarantees security against the passive adversary. But ...
4
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1answer
200 views

Questions about the ideal cipher model

I've read that we can study the security of modes of operation by assuming the use of an ideal block cipher. I've also seen a paper suggesting that the ideal cipher model could be something else than ...
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49 views

Conditions for proving that a signcryption scheme is secure

If I'm able to prove that any scheme satisfies confidentiality ad unforgeability conditions, will it be a valid signcryption scheme, without explicit signature and encryption parts ?
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2answers
293 views

Perfect Secrecy, two Definitions

I'm reading the proof of the implication "Def 2.1 $\Rightarrow$ Def 2.4" in these slides about Adversarial Indistinguishability and Perfectly-Secret Encryption. I have a doubt in the slide 10. Here it ...