A model used in cryptographic security proofs, in which concrete primitives such as hash functions are replaced with a "random oracle": a hypothetical black box that maps its inputs to truly random outputs, but in such a way that the same input always yields the same output.

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105 views

What does “learnable with oracle queries” mean?

I came across the following quotes in reading papers on obfuscation (1, ibid, and 2): The next result follows from the fact that point functions are not exactly learnable (since a uniformly chosen ...
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46 views

Forward Secrecy with pseudorandom functions

Let $H_1$, $H_2$ be keyed hash functions (e.g. $H_i(x) = SHA_{256}(s_i||x)$ for pseudorandom $s_1$, $s_2$). Let $s_n = H_1^k(s_0)$, $k_n = H_2(s_n)$, where $s_0$ is a secret (pseudorandomly chosen ...
2
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1answer
112 views

Is this modified Schnorr signature scheme secure?

Signing Let y = g^x, which is your public/private keypair. Let r = g^v, for random v Let c = H(M) Let z = (v + cx) mod q The signature is the pair (r,z) Verifying g^z = ry^c mod p We further ...
4
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1answer
216 views

How does Random Oracle and Standard Model differ? [duplicate]

I am new to Crypto field. Many papers are boasting of not using Random Oracle model. Instead, those prove security in Standard Model. I am surprised how do these models differ. Can anyone please ...
5
votes
1answer
77 views

Length-preserving all-or-nothing transform

Is there any known way to construct a length-preserving all-or-nothing transform? In other words, a secure all-or-nothing transform where the length of the output is the same as the length of the ...
1
vote
1answer
59 views

On modeling a random oracle hash function which maps $\mathbb{G}_1 \rightarrow \mathbb{G}_2$

How can one model a random oracle hash function which maps $\mathbb{G}_1 \rightarrow \mathbb{G}_2$? (Assume $\mathbb{G}_1$ and $\mathbb{G}_2 $ to be additive and multiplicative groups of prime order ...
3
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2answers
195 views

Is a random oracle controled by the challenger?

When proving a Crypto scheme security under random oracle model, is the random oracle always controlled by the challenger? What if the Hash is only used by the adversary?
4
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1answer
168 views

Entropy when iterating cryptographic hash functions

Consider a cryptographic hash function that maps $n$-bit strings to $n$-bit strings: $$ \DeclareMathOperator{\H}{H} \DeclareMathOperator{\SHA}{SHA-256} \H(x) : \left\{0,1\right\}^{n} \mapsto ...
2
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0answers
66 views

Obfuscating point-like functions

There are standard schemes for obfuscating a point function; I'm wondering if we know how to obfuscate a slight generalization of a point function. I'll elaborate more precisely. Definition 1. A ...
1
vote
1answer
75 views

What is the difference between a bijective random oracle and a random permutation?

Assume $S$ be a finite set $O$ be a random oracle from $S$ to $S$, such that $O$ is bijective $f$ be a random permutation of $S$ Is there any difference between $O$ and $f$? Does it makes any ...
4
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2answers
218 views

Is the following symmetric design secure?

Assume: $O$ be a reversible random permutation oracle on a finite set and $O^{-1}$ the inverse permutation (pretty much equivalent to a random permutation: What is the difference between a bijective ...
4
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2answers
274 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 ...
8
votes
4answers
341 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 ...
6
votes
1answer
163 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 ...
7
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1answer
357 views

understanding forking lemma

Every time when I read a paper that has digital signature, when it comes to prove the security of a digital signature scheme, many chances that the author will use the forking lemma. The forking ...
6
votes
1answer
360 views

How random is the shared secret in the Diffie Hellman key agreement

How random is the value $ZZ$ in the DH protocol? This question was triggered by this somewhat naïve implementation in I2P shown by Sergei at Stackoverflow. Obviously $ZZ$ is distinguishable from a ...
1
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0answers
137 views

Hash function with values in a multiplicative group of prime order [closed]

I have to implement a cryptographic protocol which involves a cryptographic hash function $H: \{0,1\}^* \to G$. It is viewed as random oracle. $G$ is a multiplicative group of prime order. I want to ...
1
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2answers
158 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 ...
2
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0answers
149 views

How can I prove that this encryption scheme from a random oracle is secure?

I am reading this example: A random oracle is an ideal object. What makes a random oracle convenient for proofs is the part about knowing nothing on the output for a given input if you do not ...
2
votes
1answer
148 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 $H$, $e$, ...
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votes
2answers
209 views

What are alternatives to the random oracle model for modelling hash functions? [closed]

I was looking for more realistic alternatives to the ROM for describing hash functions in theoretical proofs. I came across the common reference string model (where hash functions can be modeled as ...
2
votes
1answer
303 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 ...
7
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1answer
136 views

Why does it matter for a signature scheme to be without random oracles?

There is a profusion of articles proposing signature schemes without random oracles (see for yourself). What does that mean, and why does it matter?
4
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1answer
138 views

Does security under ROM imply exactly what?

I'm not sure I understand really the implications of proofs of security in the random oracle model. Does a proof of security in ROM translate to a reduction of security of the crypto-system to the ...
11
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2answers
902 views

Random oracle model proofs and programmability

Proving the security of a scheme with the random oracle model (ROM) involves two steps: first you prove that the scheme is secure in an idealized world where a random oracle exists, and then you ...
29
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1answer
4k views

What is the “Random Oracle Model” and why is it controversial?

What is the "Random Oracle Model"? Is it an "assumption" akin to the hardness of factoring and discrete log? Or something else? And why do some researchers have a strong distrust of this model?