Computational hardness assumption
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In cryptography, a major goal is to create cryptographic primitives with provable security. In some cases cryptographic protocols are found to have information theoretic security, the one time pad is a common example. In many cases, information theoretic security cannot be achieved, and in such cases cryptographers fall back to computational security. Roughly speaking this means that these systems are secure assuming that any adversaries are computationally limited, as all adversaries are in practice. Since the P vs NP problem is still unresolved, it is unknown whether "difficult" problems actually exist, but cryptographic research must go on, so in practice certain problems are assumed to be difficult.
[edit] Common cryptographic hardness assumptions
There are many common cryptographic hardness assumptions, while the difficulty of solving any of the underlying problems is unknown, some assumptions are stronger than others. Note: that if any assumption is weaker than another that means solving the underlying problem is easier. When devising cryptographic protocols, one hopes to be able to prove security using the weakest possible assumptions.
This is a list of some of the most common cryptographic hardness assumptions, and some cryptographic protocols that use them.
- Integer factorization
- RSA problem (stronger than factorization)
- Quadratic residuosity problem (stronger than factorization)
- Composite residuosity problem (stronger than factorization)
- Higher residuosity problem (stronger than factorization)
- Phi-hiding assumption (stronger than factorization)
- Cachin-Micali-Stadler PIR
- Discrete log problem (DLP)
- Decisional Diffie-Hellman assumption (stronger than DLP)
- Computational Diffie-Hellman assumption (stronger than DLP)
