We introduce quantitative usability and security models to guide the design
of password management schemes --- systematic strategies to help users create
and remember multiple passwords. In the same way that security proofs in
cryptography are based on complexity-theoretic assumptions (e.g., hardness of
factoring and discrete logarithm), we quantify usability by introducing
usability assumptions. In particular, password management relies on assumptions
about human memory, e.g., that a user who follows a particular rehearsal
schedule will successfully maintain the corresponding memory. These assumptions
are informed by research in cognitive science and validated through empirical
studies. Given rehearsal requirements and a user's visitation schedule for each
account, we use the total number of extra rehearsals that the user would have
to do to remember all of his passwords as a measure of the usability of the
password scheme. Our usability model leads us to a key observation: password
reuse benefits users not only by reducing the number of passwords that the user
has to memorize, but more importantly by increasing the natural rehearsal rate
for each password. We also present a security model which accounts for the
complexity of password management with multiple accounts and associated
threats, including online, offline, and plaintext password leak attacks.
Observing that current password management schemes are either insecure or
unusable, we present Shared Cues--- a new scheme in which the underlying secret
is strategically shared across accounts to ensure that most rehearsal
requirements are satisfied naturally while simultaneously providing strong
security. The construction uses the Chinese Remainder Theorem to achieve these
competing goals
