an asymmetric (e.g. public-key) cryptosystem, based on modular exponentiation with big exponents and modulus. RSA can be used both for signature and encryption.

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How do other, non-RSA algorithms, compare to the PKCS #1 standard?

Arguably the PKCS suite of standards have a profit-oriented bias as they are promoted by RSA and promote their algorithms over others in the form of RFCs and other means. I'm considering the ...
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When is an asymmetric scheme considered broken?

Does the following quote imply that valid encrypted data can be created and decrypted by someone other than the owner of a private key: An asymmetric encryption scheme is considered to be broken ...
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Is it possible to create an asymmetric cryptosystem where the private keys are not easily verifiable as such?

Plaintext that consists of an RSA key is easily recognizable as such, because it satisfies certain mathematical properties, in particular (See the answer for Why can an encrypted private key be brute ...