Questions tagged [security-definition]

Questions about formal definitions of "security" for various cryptographic schemes (e.g. perfect secrecy, semantic security, ciphertext indistinguishability, etc.)

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35
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3answers
31k views

What are preimage resistance and collision resistance, and how can the lack thereof be exploited?

What is "preimage resistance", and how can the lack thereof be exploited? How is this different from collision resistance, and are there any known preimage attacks that would be considered feasible?
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8answers
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Simply put, what does “perfect secrecy” mean?

I would like to ask for a clear (but maybe not so deep) explanation of what the term "perfect secrecy" means. As far as I have researched and understood, it has to do with probabilities of assuming ...
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2answers
819 views

Uniform vs discrete Gaussian sampling in Ring learning with errors

The Wikipedia article on RLWE mentions two methods of sampling "small" polynomials namely uniform sampling and discrete Gaussian sampling. Uniform sampling is clearly the simplest, involving simply ...
19
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1answer
4k views

What do the signature security abbreviations like EUF-CMA mean?

From time to time, one stumbles across formal security definitions. This includes security definitions for signature schemes. The most common ones are the *UF-* ...
19
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2answers
4k views

What stops the Multiply-With-Carry RNG from being a Cryptographically Secure PRNG?

Despite the fact that Marsaglia's MWC PRNG (multiply-with-carry random number generator) is considered to be "the mother of all RNGs", it does not seem to be considered to be a CSPRNG (...
17
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2answers
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Why is AES considered to be secure?

The security of RSA is based on the integer factorization problem, which is a very well defined and understood mathematical problem. This problem must be solved in order to fundamentally break RSA. ...
16
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6answers
3k views

How exactly is “true randomness” defined in the realms of cryptography?

Especially in relation to stream ciphers, I frequently read about (sometimes theoretical, sometimes practical) attacks that are able to "distinguish a ciphertext from a truly random stream". What's ...
14
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2answers
507 views

Does GCM (or GHASH) only provide 64-bit security against forgeries?

In a recent comment a doubt was voiced about my answer, which claims GCM to requires $2^{128}$ for a successful forgery. The doubt was that the square root needs to be taken meaning the security would ...
13
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3answers
20k views

What is the difference between uniformly and at random in crypto definitions?

Very often in the description and analysis of a cryptographic protocol there is a need for a an element $k$ that is sampled uniformly AND at random. Is there a redundancy in the definition with ...
13
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1answer
4k 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 ...
12
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4answers
3k views

Is the one-time-pad a secure system according to modern definitions?

Occasionally I hear people say that one-time pads are "useless" or even "broken". "modern cryptography knows more security definitions, under some of which the one-time pad is completely broken." ...
11
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3answers
2k views

How small is negligible?

When proving theorems in crypto we often make use of the concept of negligible functions or, more simply, negligible parameters. As a rule of thumb, given today (2018) computational power, what is ...
11
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2answers
1k views

Definition of a CSPRNG

I am interested in what conditions are necessary and sufficient to define a cryptographically secure pseudo-random number generator (CSPRNG). Wikipedia lists two defining characteristics: It ...
10
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2answers
720 views

Key Size for Symmetric Homomorphic Encryption Over the Integers

In the paper Fully Homomorphic Encryption over the Integers, it mentions a symmetric key scheme on page 1 and 2. Key Generation: Pick a random odd number $p \epsilon [2^{N-1},2^N)$ Encrypt A Bit m: $...
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3answers
1k views

How to prove the security of block ciphers

I see very often proofs of security for asymmetric crypto algorithms, for instance, using reductions to known hard problems, or game based proofs... In the field of protocols (like authentication) it ...
9
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2answers
2k views

Example of a PRP that is not a strong PRP

The exact definition of security for a pseudorandom permutation is straightforward - for some encryption scheme $E\,\colon\,\mathcal{K}\times\mathcal{D}\rightarrow\mathcal{D}$, it must be the case ...
9
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1answer
4k 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. http://pdf.aminer....
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2answers
197 views

Confusion about definition of homomorphic encryption

I am trying to better understand homomorphic encryption, but I feel like I keep getting inconsistent information in the papers that I am reading. One of the papers I am reading says the following: ...
7
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1answer
2k 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 ...
7
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1answer
3k views

What does it mean for an adversary to run in PPT?

I've been reading this question where a detailed description of mine is given, I've understood that a polynomial-time adversary is an adversary for which the only feasible strategy are those that take ...
7
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1answer
1k views

Understanding Twist Security with respect to short Weierstrass curves

I'm trying to understand the "Invalid-curve attacks against ladders" section of SafeCurves Twist Security page and I have difficulties to apply it to short Weierstrass curves. That section claims ...
7
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3answers
309 views

Is there a cryptographic approach to availability

Background Cryptography can be said to provide the tools used to fulfill the goals of information security. The three pillars of information security are confidentiality, integrity, and ...
7
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2answers
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Difference left-or-right CPA security, IND-CPA security

I am trying to understand the notion of left-or-right-CPA (LOR-CPA) security for private-key encryption schemes introduced in my lecture. If I understood it correctly so far, the only difference to ...
7
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1answer
123 views

Definition of secure computation with more that two parties

In Definition of secure computation in m-party case with respect to semi-honest adversary (Definition 7.5.1 in Foundations of Cryptography: Volume 2, Basic Applications by Oded Goldriech) we say ...
7
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1answer
497 views

The notion of sub-exponential security

I have been reading a paper where they construct probabilistic IO (indistinguishability obfuscation) from sub exponential IO. I want to know if the following two notions of sub-exponential security ...
6
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2answers
1k views

What is a q-type assumption?

I've seen the term "$q$-type assumption" used in a few papers without a definition. A Google search doesn't seem to come up with anything useful either (except the same papers without a definition). ...
6
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1answer
2k views

An unpredictable PRG is secure (Theorem Yao'82)

in the Mr Boneh's online course is stated the following theorem: Let $G:K \to \{0,1\}^n$ be a PRG. “Thm”: if $\forall i \in \{0, … ,n-1\}$ the PRG $G$ is unpredictable at pos. $i$, then $G$ ...
6
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1answer
762 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 ...
6
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1answer
548 views

What is the difference between RCCA and CCA2?

Well, I know it's easy to tell CCA1 from CCA2, but I failed to find the difference between RCCA and CCA2. What is the difference?
6
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1answer
1k views

Public-Key Deterministic Encryption : Why does not provide perfect security?

I've got a question about an assignment . The question is "Why a Public-Key Deterministic Encryption Algorithm does not provide perfect security ?" . I suppose it means according to Shannon . Any ...
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5answers
1k views

Effective security of block cipher – equal the key size, or half the key size?

The Wikipedia “Key Size” article states: The security of an algorithm cannot exceed its key length (since any algorithm can be cracked by brute force), but it can be smaller. … … … Most symmetric-...
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2answers
2k views

Block Ciphers and (Non-)Generic Attacks

I am currently reading through Cryptography Engineering and came across this definition of block cipher security: Definition 2 An attack on a block cipher is a non-generic method of ...
5
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1answer
171 views

“Power of one” as input to functions of a cryptosystem

What does $1^\lambda$ mean when you pass it as a parameter to the functions of a cryptosystem. The cryptosystem in question is this and a picture reference is this. I have been told it signifies the ...
5
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2answers
595 views

What is the difference between information-theoretic and perfect types of security?

I'm having a hard time pinning down an exact definition of the difference between information-theoretic and perfect types of security. A rigorous definition seems elusive... A. Wikipedia puts the ...
5
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1answer
990 views

IND-CPA security of CTR mode

Let's suppose CTR mode is instantiated such that the input to the block-cipher is $\langle \mathrm{IV}+\mathrm{ctr}\rangle$ instead of $\mathrm{IV}\mathbin\|\langle \mathrm{ctr}\rangle$, where $\...
5
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2answers
274 views

What is the relationship between entropy conditioning and final output bias in a TRNG?

This question concerns the conditioning and output of true random number generators. It refers to NIST Special Publication 800-90C, Recommendation for Random Bit Generator (RBG) Constructions. It ...
5
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1answer
145 views

Parameterizing adversaries with security parameters

In many cryptographic games, the adversary doesn't seem to be parameterized by the security parameter.‡ Are such games equivalent to variants in which the adversary is parameterized by the security ...
4
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2answers
161 views

What is the security concept in printer cartridge?

Based on this datasheet or this patent, one of the usage of PUF is printer cartridge identification and authentication. I was wondering why printer cartridge needs identification and authentication. ...
4
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3answers
421 views

Is it possible to exactly reverse engineer an unknown cipher inside a black box?

Consider the following arrangement:- There is an unknown cipher algorithm operating inside the black box. You can enter infinite key /plain text pairs, and observe all of the outputs. The box might ...
4
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1answer
347 views

Is the practice of “security through obscurity” violating Kerckhoffs's second principle?

Security through obscurity is the reliance on the secrecy of the design or implementation as the main method of providing security for a system or component of a system. Kerckhoffs's second principle:...
4
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1answer
2k views

What exactly is a “security parameter”?

I often encounter the term “security parameter” when I read crypto related stuff. My basic understanding is that it just denotes some bit-length however, I'm not so sure. For example, when it says ...
4
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1answer
395 views

Strong One-Way Function

In the book "Foundations of cryptography-Oded Goldreich-Page 33", if we use the deterministic polynomial-time algorithm instead of the probabilistic polynomial-time algorithm for case 2 (Hard to ...
4
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1answer
162 views

How to determine the security in bits of a scheme?

This may be a stupid question. But how would we determine the security bit of a crypto scheme? For example, SHA2-256 offers 128 bit security due to birthday paradox, so do they measure the security ...
4
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2answers
257 views

On the security definition of password-authenticated key exchange

I found in all PAKE papers, the security is defined as something like this: Let $Succ(A)$ be the probability that an attacker $A$ successfully distinguished the session key from a random string. Then ...
4
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1answer
312 views

Do Curtmola et al.'s IND-CKA1/2 security definitions protect against search pattern leakage?

In the article Searchable Symmetric Encryption: Improved Definitions and Efficient Constructions, Curtmola et al. propose adaptive and non-adaptive (indistinguishability and simulator-based) security ...
4
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1answer
767 views

Indistinguishable encryptions in the presence of an eavesdropper equivalence

I'm trying to prove that definition 5 and definition 6 in this document are equivalent. This is what I've done at the moment: Asume that the scheme has Indistinguishable encryptions in the presence of ...
4
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2answers
3k views

Perfect security definitions

In my notes, there are 2 definitions of perfect security: "For $M \in \{0,1\}^m$, define the distribution $D_M$ on strings as follows: to choose a random member of $D_M$, choose a random $K \in \...
4
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1answer
2k views

Difference between semi-honest and malicious adversary using Ideal Real Model Paradigm

Would you please explain to me why in the security definition of ideal/real model paradigm which is described in the efficient secure two-party protocol book(Hazay, Lindell), the simulator tries to ...
4
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2answers
179 views

Is there a computational security of public-key encryption which is similar to the one of symmetric key encryption

We say a symmetric key encryption scheme $\Pi_{1} = (\mathrm{Gen}, \mathrm{Enc}, \mathrm{Dec})$ is computational security if for every PPT algorithm $A$ and every $x_{0}, x_{1}$ ($|x_{0}| = |x_{1}|$), ...
4
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1answer
165 views

Is there an example of a “robust, yet not private” SMC protocol?

I have been trying to understand the interplay between robustness and privacy of an SMC protocol. It is easy to come up with a protocol that is private but not robust. Can someone provide an example ...