The algorithm(s) needed to encrypt and decrypt a message
https://en.wikipedia.org/wiki/Cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption-a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.

Public keys
https://en.wikipedia.org/wiki/Public-key_cryptography
Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys: public keys, which may be disseminated widely, and private keys, which are known only to the owner. The generation of such keys depends on cryptographic algorithms based on mathematical problems to produce one-way functions. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security.
In such a system, any person can encrypt a message using the receiver's public key, but that encrypted message can only be decrypted with the receiver's private key.
Alice and Bob have two keys of their own - just to be clear, that's four keys total. Each party has their own public key, which they share with the world, and their own private key which they well, which they keep private, of course but, more than that, which they keep as a closely guarded secret. The magic of public key cryptography is that a message encrypted with the public key can only be decrypted with the private key. Alice will encrypt her message with Bob's public key, and even though Eve knows she used Bob's public key, and even though Eve knows Bob's public key herself, she is unable to decrypt the message. Only Bob, using his secret key, can decrypt the message assuming he's kept it secret, of course.
Alice and Bob do not need to plan anything ahead of time to communicate securely: they generate their public-private key pairs independently, and happily broadcast their public keys to the world at large. Alice can rest assured that only Bob can decrypt the message she sends because she has encrypted it with his public key.

PAP
https://en.wikipedia.org/wiki/Password_Authentication_Protocol
Password Authentication Protocol (PAP) is a password-based authentication protocol used by Point to Point Protocol (PPP) to validate users. Almost all network operating system remote servers support PAP. PAP is specified in RFC 1334.
PAP is considered a weak authentication scheme (weak schemes are simple and have lighter computational overhead but are much more vulnerable to attack; while weak schemes may have limited application in some constrained environments, they are avoided in general). Among PAP's deficiencies is the fact that it transmits unencrypted passwords (i.e. in plain-text) over the network. PAP is therefore used only as a last resort when the remote server does not support a stronger scheme such as CHAP or EAP.
Incorrect answers:
SPAP - Shiva Password Authentication Protocol, PAP with encryption for the usernames/passwords that are transmitted.
CHAP - calculates a hash, shares the hash with the client system, the hash is periodically validated to ensure nothing has changed.
Kerberos - computer-network authentication protocol that works on the basis of tickets to allow nodes communicating over a non-secure network to prove their identity to one another in a secure manner. Its designers aimed it primarily at a client-server model and it provides mutual authentication-both the user and the server verify each other's identity. Kerberos protocol messages are protected against eavesdropping and replay attacks.
Kerberos builds on symmetric key cryptography and requires a trusted third party, and optionally may use public-key cryptography during certain phases of authentication.

Brute force
https://en.wikipedia.org/wiki/Brute-force_attack
A brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct one is found. Alternatively, the attacker can attempt to guess the key which is typically created from the password using a key derivation function. This is known as an exhaustive key search.
A brute-force attack is a cryptanalytic attack that can, in theory, be used to attempt to decrypt any encrypted data (except for data encrypted in an information-theoretically secure manner). Such an attack might be used when it is not possible to take advantage of other weaknesses in an encryption system (if any exist) that would make the task easier.
Incorrect answers:
Rainbow tables - is a precomputed table for caching the output of cryptographic hash functions, usually for cracking password hashes. Tables are usually used in recovering a key derivation function (or credit card numbers, etc.) up to a certain length consisting of a limited set of characters.
Dictionary attack - is a form of brute force attack technique for defeating a cipher or authentication mechanism by trying to determine its decryption key or passphrase by trying thousands or millions of likely possibilities, such as words in a dictionary or previously used passwords, often from lists obtained from past security breaches.
Shoulder surfing - is a type of social engineering technique used to obtain information such as personal identification numbers (PINs), passwords and other confidential data by looking over the victim's shoulder, either from keystrokes on a device or sensitive information being spoken and heard, also known as eavesdropping.

Finding any method that is more efficient than brute force
https://en.wikipedia.org/wiki/Cryptanalysis
Bruce Schneier notes that even computationally impractical attacks can be considered breaks: "Breaking a cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force."