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New answers tagged hardness-assumptions

0

Here's the isomorphism: $ax^2 + bx + c$ (with $z$) maps to $ax^2 + (b + z - z')x + c$ (with $z'$) The only nonobvious thing about this transform is that it preserves $f$, that is, that $f(A, B)$ (with $z$) is the element that maps to $f'(A', B')$ (with $z'$, and $f', A', B'$ are the mapped versions of $f, A, B$) However, this is not hard to show; we ...

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I am struggling to understand what is meant by "standard cryptographic assumption". ‘Standard assumption’ broadly means an assumption that has withstood the scrutiny of many smart cryptanalysts for a long time. Examples: We think that, for uniform random 1024-bit primes $p$ and $q$, solving $y = x^3 \bmod pq$ for uniform random $x$ is hard given $pq$ and \$...

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There is no formal definition of standard assumption, but we usually say that an assumption is standard if it has already been used in several cryptographic schemes and if it is well-accepted in the crypto community. It usually also implies that several researchers tried to solve the problem and were not able to find efficient ways of doing so, therefore, ...

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