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Using a mathematical algorithm to generate a new password based on the previous password (OTPs are effectively a chain and must be used in a predefined order). Using a mathematical algorithm where the new password is based on a challenge (e.g., a random number chosen by the authentication server or transaction details) and/or a counter.
Key vs password. A password is a memorized series of characters including letters, digits, and other special symbols that are used to verify identity. It is often produced by a human user or a password management software to protect personal and sensitive information or generate cryptographic keys.
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight.
Common PRNG (pseudorandom number generator) — preferably cryptographically secure — in both transmitter and receiver; Transmitter sends 'next' code in sequence; Receiver compares 'next' to its calculated 'next' code. A typical implementation compares within the next 256 codes in case receiver missed some transmitted keypresses.
Bitwarden is a free/freemium open-source password management service that stores sensitive information such as website credentials in an encrypted vault. The platform offers a variety of client applications including a web interface, desktop applications, browser extensions, mobile apps, and a command-line interface.
Backtracking is a class of algorithm for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.
For example you cannot use bcrypt to derive a 512-bit key from a password. At the same time, algorithms like pbkdf2, scrypt, and argon2 are password-based key derivation functions - where the output is then used for the purpose of password hashing rather than just key derivation. Password hashing generally needs to complete < 1000 ms.
A sufficiently long, randomly chosen, key can resist any practical brute force attack, though not in principle if an attacker has sufficient computational power (see password strength and password cracking for more discussion). Unavoidably, however, pre-shared keys are held by both parties to the communication, and so can be compromised at one ...