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.

learn more… | top users | synonyms

3
votes
1answer
377 views

Perfect Secrecy -> One Time Semantic Security -> Secure PRG

I think I have some sense of what Perfect Security means, and even Semantic Security, but I am struggling with randomness, so I'm going to ask a question about CSPRG's (Cryptographically Secure PRG's) ...
3
votes
1answer
221 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 ...
3
votes
2answers
165 views

Security model for privacy-preserving aggregation scheme.

Suppose that $S=(E,D)$ is an additively homomorphic encryption scheme. Now I want to design a protocol $P$ such that given inputs $x_1,x_2,..,x_n$, the adversary $A$ (who can decrypt) can only learn ...
3
votes
1answer
122 views

Proofs by reduction and times of adversaries

I have some difficulties to understand, when we construct a reduction, how we determine the time for the constructed adversary to break a target security property. In general these details are not ...
3
votes
1answer
95 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 ...
3
votes
1answer
125 views

CDH problem and Square-DH problem

CDH problem roughly says that choose $U=g^u, V=g^v$ uniformly at random from cyclic group $G$, it's hard to compute $CDH(U,V)=g^{uv}$. Square-DH problem roughly says choose $U=g^u$ uniformly at ...
3
votes
1answer
131 views

Flaw in the security definition of *Stateful* Authenticated Encryption?

I'm in search of the correct definition of a stateful authenticated encryption scheme (sAE), and its related security notion. This has been treated several times in the academic literature, however, ...
3
votes
1answer
451 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
votes
1answer
172 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 ...
2
votes
1answer
188 views

Randomized stream cipher using multivariant quadratic equations

This is an idea I had for cipher that I thought might reduce to a known hard problem. It is efficient (compared to something like BBS) in terms of time but not in terms of space. Here's the ...
2
votes
2answers
171 views

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 ...
2
votes
1answer
522 views

Question about the definition of a secure PRF

I'm taking a cryptography introduction course, and we're covering the definition of a secure PRF. I understand the test goes as follows: A challenger picks a function $f$ such that $f \leftarrow ...
2
votes
2answers
103 views

Reductionist proofs of decisional problems to computational

Are they any reductionist proofs where an attacker $\mathcal{I}$ for a well established computationally "hard" problem $\mathsf{Π}$ is employing an attacker $\mathcal{A}$ who we assume is able to ...
2
votes
1answer
104 views

Security proof of FO(Fujisaki-Okamoto) hybrid encryption

The proof of FO hybrid encryption is hard to understand. $\:$ Especially, how does the challenger respond to the decryption queries when the challenger can only have some encryption queries? Can ...
2
votes
1answer
137 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 ...
2
votes
1answer
199 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 ...
2
votes
2answers
410 views

What are the differences between proofs based on simulation and proofs based on games?

what are the main pros and cons of proving the "security" of a crypto scheme under simulation proofs instead of game based proofs?
2
votes
2answers
144 views

how much trust can we place in protocol verifiers? [closed]

I read many papers on authenticated key exchange protocols, and most security proofs are done by the authors. In this method, you can imagine that the efficiency is low. Moreover, even if you have ...
2
votes
2answers
141 views

What are the cryptographic assumptions in the Dolev Yao model?

In the Dolev Yao model for interactive protocols, the cryptographic primitive (encryption, for example) is considered as a blackbox. Does blackbox here mean that the primitive is to be considered CPA ...
2
votes
1answer
254 views

Why are protocols often proven secure under the random oracle model instead of a hash assumption?

Is this true that whenever you design a protocol using a hash function, you must prove its security under the random oracle? I mean, is it possible to devise a protocol $P$ using a function $H$, and ...
2
votes
1answer
321 views

server side Javascript security

It is accepted that the javascript library lacks the ability to create an adequate PRNG. My understanding that this was mainly due to the limits of a sandboxed browser enviroment that javascript ...
2
votes
1answer
25 views

Is the CONF key sharing Problem equivalent to discrete log problem?

If there a proof in the literature which says the CONF Problem is equivalent to solving the discrete log ? Let $g$ be a generator of a cyclic group $\mathbb{G}$ of prime order $q$ CONF problem: ...
2
votes
1answer
108 views

Is this EAX extension weakening the (provable) security of EAX?

I would like to insert a key deriving function into EAX mode, in order to hamper brute-force attacks for a key-size restricted cipher (56 bits). The modification inserts an identical multi-block ...
2
votes
2answers
156 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 ...
2
votes
1answer
320 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} ...
2
votes
1answer
255 views

Exact mathematical definition of simulation based security?

I've been trying to understand cryptographic protocols and how to define their security. The problem is that while I can understand what the intuitive definition says, I have trouble understanding how ...
2
votes
1answer
343 views

Security analysis of a “one-time pad” type hill cipher

Suppose the Hill cipher were modified to something like a one-time pad cipher, where Alice wants to send a message to Bob, and she chooses a key matrix randomly everytime a new message is sent (and ...
2
votes
1answer
102 views

Hamiltonicity proof of knowledge

I'm learning the POK notion and definitions and as a self exercise I wante to prove the statement that the Hamiltonicity protocol is a POK system with knowledge error $1/2$. So the question will be ...
2
votes
1answer
88 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 ...
2
votes
1answer
132 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
votes
1answer
201 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 ...
2
votes
1answer
117 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 ...
2
votes
1answer
136 views

Is Guillou-Quisquater existentially unforgeable against adaptive message attack under a random oracle model?

First of all, the Guillou-Quisquater digital signature scheme is: Note everything is $\bmod n$. Message is denoted by $m$. Private key: $s$ Public key: Hash function $H$, $e$, ...
2
votes
0answers
80 views

Looking for a detailed example of proof by reduction

I'm looking for a very detailed example of proof by reduction. Say we have two or three protocols (that have been proven secure) and we construct a new protocol. We want to provide a proof of security ...
2
votes
0answers
57 views

Protocol/algorithms based on a variable-length input PRF

Are the proofs based on a PRF assumption still valid when using a variable-length input PRF ? The answer might be obvious, but I have a doubt.
2
votes
0answers
119 views

Ideal system for an encryption scheme

What is the ideal system for an encryption scheme? For a pseudorandom permutation the ideal one is a random permutation, for a pseudorandom function the ideal one is a random function. For an ...
2
votes
2answers
293 views

The security proof for Key Policy Attribute Based Encryption

My question relates to the original KP-ABE paper: http://research.microsoft.com/en-us/um/people/vipul/abe.pdf I'm having trouble understanding the proof (pages 10–13) that the scheme is secure in ...
1
vote
2answers
437 views

Tools for modelling and analysis of cryptographic protocols

I am designing some cryptographic protocols and I am new to it. Are there any well-known tools that can be used to model and design these protocols? And also verify or analyze their validity? If not ...
1
vote
1answer
177 views

Indistinguishability attack example

I want solve the next exercise. The author defined the experiment for the cryptosystem $\Pi$, the adversary $A$ and the security parameter $n$ as follows $\mathsf{PRIV_{EAV}}(\Pi,A,n)$ The ...
1
vote
1answer
72 views

Exchanging Keyspace and Message space in PRF

Suppose there is a secure PRF $F: K \times X \to Y$. Then is $F': X \times K \to Y$, defined by $F'(x,k):=F(k,x)$, a secure PRF? In my opinion it should be because exchanging the keyspace with ...
1
vote
1answer
103 views

Rock-paper-scissors over network, how to protect from cheating server?

I'm trying to design cryptographic protocol to play Rock-Paper-Scissors with two parties, neither trusting each other, nor trusting server they use for communication, so game is 'provably fair'. So ...
1
vote
1answer
80 views

Modular protocol design

What does modular protocol design mean? Why does TLS not have modular protocol design? What protocols have modular design? (IPSec, SSH)
1
vote
1answer
56 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 ...
1
vote
1answer
53 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 ...
1
vote
2answers
116 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? ...
1
vote
1answer
66 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 ...
1
vote
3answers
554 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).
1
vote
1answer
50 views

Showing that security of a elgamal invariant is insecure

Original Elgamal signature is defined $S(m, \alpha) = (r, s)$, where $$r = g^k \bmod p$$ $$s = (m – r*α)k^{-1} \bmod (p – 1)$$ more information on Elgamal signature can be found here. Variant ...
1
vote
1answer
90 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 ...
1
vote
1answer
96 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 ...