Editing Semantic security (section)

==== Testing and Auditing Randomness ====
To verify randomness quality, cryptographic implementations should undergo:

* [[National Institute of Standards and Technology|NIST]] SP 800-90B randomness tests<ref name="NIST90B" />
* [[Diehard tests]]<ref name="NIST22">{{cite web |date=2010-04-01 |title=A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications |url=https://csrc.nist.gov/publications/detail/sp/800-22/rev-1a/final |access-date= |publisher=National Institute of Standards and Technology (NIST)}}</ref>
* [[FIPS 140-2]] compliance checks<ref name="FIPS140">{{cite web |date=2002-05-25 |title=Security Requirements for Cryptographic Modules |url=https://csrc.nist.gov/publications/detail/fips/140/2/final |access-date= |publisher=National Institute of Standards and Technology (NIST)}}</ref>

Semantically secure encryption algorithms include [[Goldwasser-Micali cryptosystem|Goldwasser-Micali]], [[ElGamal encryption|ElGamal]] and [[Paillier]].  These schemes are considered [[provable security|provably secure]], as their semantic security can be reduced to solving some hard mathematical problem (e.g., [[Decisional Diffie-Hellman assumption|Decisional Diffie-Hellman]] or the [[Quadratic Residuosity Problem]]).  Other, semantically insecure algorithms such as [[RSA (algorithm)|RSA]], can be made semantically secure (under stronger assumptions) through the use of random encryption padding schemes such as [[Optimal Asymmetric Encryption Padding]] (OAEP).