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Optimal Asymmetric Encryption Padding is a padding scheme for RSA, codifying how short plaintext is enciphered and deciphered. It has a security reduction to the RSA problem.
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Why not use OAEP for signatures?
There seems to be a distinct lack of implementations of RSA signatures using OAEP to pad the digest. Other than the old, funky, padding schemes, it's PSS all the way. … OAEP, on the other hand, is accompanied by long diversions about its theoretical safety presented as claim and counterclaim.
Is it, in principle, very wrong to use OAEP with RSA for signatures? …