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Public Key Cryptography

Any cryptographic system that uses the public key and private key pair is said to be public key cryptography or asymmetric cryptography.

The best-known uses for public key cryptography are:

authentication (Profing that holder of private key sent a message)
encryption (Only the holder of the private key can decrypt a message encrypted with a public key.

Asymmetric encryption is slower than symmetric encryption.

RSA is one of the dominant public key cryptosystems.

Apparently, a public/private key pair can be generated with ssh-keygen.

Public Key Cryptographic Standards (PKCS)

The PKCS are a set of standards which are published by RSA Security LLC.

PKCS #1	RSA Cryptography Standard	RFC 8017
PKCS #3	Diffie–Hellman Key Agreement Standard
PKCS #5	Password-based Encryption Standard	RFC 8018, PBKDF2
PKCS #6	Extended-Certificate Syntax Standard
PKCS #7	Cryptographic Message Syntax Standard	RFC 2315
PKCS #8	Private-Key Information Syntax Standard	Storing private key information, see RFC 5958 and Public key cryptography
PKCS #9	Selected Attribute Types	RFC 2985
PKCS #10	Certification Request Standard	RFC 2986
PKCS #11	Cryptographic Token Interface
PKCS #12	Personal Information Exchange Syntax Standard	RFC 7292
PKCS #15	Cryptographic Token Information Format Standard

Some standards (which are not listed in the table above) are withdrawn or were not published.

A is Alice's public key, and a is her private key. Thus,

{msg}^A is an encrypted cyphertext,

{msg}^a is a signed message.

Alice sends Bob a signed and encrypted message {{msg}^a}^B.

Using his private key, Bob gets {msg}^a.

Using Charlies public key, Bob encrypts this to {{msg}^a}^C and sends it to Charlie.

Using his private key, Charlie decrypts it to {msg}^a and then uses Alice's public key to (naively) verify that Alice sent {msg}.

Thus, Charlie is under the wrong impression that Alice sent {msg} to Charlie rather than to Bob.