Distinguishing cryptographic properties: hiding and collision resistance

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I saw from Another question the following definitions, which clarifies somewhat:



Collision-resistance:



Given: $x$ and $h(x)$



Hard to find: $y$ that is distinct from $x$ and such that $h(y)=h(x)$.



Hiding:



Given: $h(r|x)$, where $r|x$ is the concatenation of $r$ and $x$



Secret: $x$ and a highly-unlikely-and-randomly-chosen $r$



Hard to find: $y$ such that $h(y)=h(r|x)$.



This is different from collision-resistance in that it doesn’t matter whether or not $y=r|x$.



My question:



Does this mean that any hash function $h(x)$ is non-hiding if there is no secret $r$, that is, the hash is $h(x)$, not $h(r|x)$?



Example:



Say I make a simple hash function $h(x) = g^x pmod n$, where $g$ is the generator for the group. The hash should be Collision resistant with $$p(x_1 ne x_2, h(x_1) = h(x_2)) = frac12^fracn2$$ but I would think it is hiding as well?






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  • You "collision resistance" is usually called "second preimage resistant". Collision resistance means for it to be hard to find $x neq y$ with $h(x) = h(y)$.
    – Henno Brandsma
    Sep 9 at 10:24










  • $r$ is given in the hiding property, right? What's the difference between "highly unlikely" and randomly chosen?
    – Henno Brandsma
    Sep 9 at 10:25










  • "generator for the group". What group? The invertible integers modulo $n$? If so, that's not "collision resistant" in your weird sense of the word.
    – Henno Brandsma
    Sep 9 at 10:27















up vote
0
down vote

favorite












I saw from Another question the following definitions, which clarifies somewhat:



Collision-resistance:



Given: $x$ and $h(x)$



Hard to find: $y$ that is distinct from $x$ and such that $h(y)=h(x)$.



Hiding:



Given: $h(r|x)$, where $r|x$ is the concatenation of $r$ and $x$



Secret: $x$ and a highly-unlikely-and-randomly-chosen $r$



Hard to find: $y$ such that $h(y)=h(r|x)$.



This is different from collision-resistance in that it doesn’t matter whether or not $y=r|x$.



My question:



Does this mean that any hash function $h(x)$ is non-hiding if there is no secret $r$, that is, the hash is $h(x)$, not $h(r|x)$?



Example:



Say I make a simple hash function $h(x) = g^x pmod n$, where $g$ is the generator for the group. The hash should be Collision resistant with $$p(x_1 ne x_2, h(x_1) = h(x_2)) = frac12^fracn2$$ but I would think it is hiding as well?






cryptography hash-function







share|cite|improve this question























  • You "collision resistance" is usually called "second preimage resistant". Collision resistance means for it to be hard to find $x neq y$ with $h(x) = h(y)$.
    – Henno Brandsma
    Sep 9 at 10:24










  • $r$ is given in the hiding property, right? What's the difference between "highly unlikely" and randomly chosen?
    – Henno Brandsma
    Sep 9 at 10:25










  • "generator for the group". What group? The invertible integers modulo $n$? If so, that's not "collision resistant" in your weird sense of the word.
    – Henno Brandsma
    Sep 9 at 10:27













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I saw from Another question the following definitions, which clarifies somewhat:



Collision-resistance:



Given: $x$ and $h(x)$



Hard to find: $y$ that is distinct from $x$ and such that $h(y)=h(x)$.



Hiding:



Given: $h(r|x)$, where $r|x$ is the concatenation of $r$ and $x$



Secret: $x$ and a highly-unlikely-and-randomly-chosen $r$



Hard to find: $y$ such that $h(y)=h(r|x)$.



This is different from collision-resistance in that it doesn’t matter whether or not $y=r|x$.



My question:



Does this mean that any hash function $h(x)$ is non-hiding if there is no secret $r$, that is, the hash is $h(x)$, not $h(r|x)$?



Example:



Say I make a simple hash function $h(x) = g^x pmod n$, where $g$ is the generator for the group. The hash should be Collision resistant with $$p(x_1 ne x_2, h(x_1) = h(x_2)) = frac12^fracn2$$ but I would think it is hiding as well?






cryptography hash-function







share|cite|improve this question















I saw from Another question the following definitions, which clarifies somewhat:



Collision-resistance:



Given: $x$ and $h(x)$



Hard to find: $y$ that is distinct from $x$ and such that $h(y)=h(x)$.



Hiding:



Given: $h(r|x)$, where $r|x$ is the concatenation of $r$ and $x$



Secret: $x$ and a highly-unlikely-and-randomly-chosen $r$



Hard to find: $y$ such that $h(y)=h(r|x)$.



This is different from collision-resistance in that it doesn’t matter whether or not $y=r|x$.



My question:



Does this mean that any hash function $h(x)$ is non-hiding if there is no secret $r$, that is, the hash is $h(x)$, not $h(r|x)$?



Example:



Say I make a simple hash function $h(x) = g^x pmod n$, where $g$ is the generator for the group. The hash should be Collision resistant with $$p(x_1 ne x_2, h(x_1) = h(x_2)) = frac12^fracn2$$ but I would think it is hiding as well?






cryptography hash-function




cryptography hash-function






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edited Sep 4 at 11:26









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asked Sep 4 at 11:18









owninggreendragsdude

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  • You "collision resistance" is usually called "second preimage resistant". Collision resistance means for it to be hard to find $x neq y$ with $h(x) = h(y)$.
    – Henno Brandsma
    Sep 9 at 10:24










  • $r$ is given in the hiding property, right? What's the difference between "highly unlikely" and randomly chosen?
    – Henno Brandsma
    Sep 9 at 10:25










  • "generator for the group". What group? The invertible integers modulo $n$? If so, that's not "collision resistant" in your weird sense of the word.
    – Henno Brandsma
    Sep 9 at 10:27

















  • You "collision resistance" is usually called "second preimage resistant". Collision resistance means for it to be hard to find $x neq y$ with $h(x) = h(y)$.
    – Henno Brandsma
    Sep 9 at 10:24










  • $r$ is given in the hiding property, right? What's the difference between "highly unlikely" and randomly chosen?
    – Henno Brandsma
    Sep 9 at 10:25










  • "generator for the group". What group? The invertible integers modulo $n$? If so, that's not "collision resistant" in your weird sense of the word.
    – Henno Brandsma
    Sep 9 at 10:27
















You "collision resistance" is usually called "second preimage resistant". Collision resistance means for it to be hard to find $x neq y$ with $h(x) = h(y)$.
– Henno Brandsma
Sep 9 at 10:24




You "collision resistance" is usually called "second preimage resistant". Collision resistance means for it to be hard to find $x neq y$ with $h(x) = h(y)$.
– Henno Brandsma
Sep 9 at 10:24












$r$ is given in the hiding property, right? What's the difference between "highly unlikely" and randomly chosen?
– Henno Brandsma
Sep 9 at 10:25




$r$ is given in the hiding property, right? What's the difference between "highly unlikely" and randomly chosen?
– Henno Brandsma
Sep 9 at 10:25












"generator for the group". What group? The invertible integers modulo $n$? If so, that's not "collision resistant" in your weird sense of the word.
– Henno Brandsma
Sep 9 at 10:27





"generator for the group". What group? The invertible integers modulo $n$? If so, that's not "collision resistant" in your weird sense of the word.
– Henno Brandsma
Sep 9 at 10:27
















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