Password-based authenticated key agreement using smart cards has been widely and
intensively researched. Inspired by the semi-group property of Chebyshev maps and key
agreement protocols based on chaotic maps, we proposed a novel chaotic maps-based
password-authenticated key agreement protocol with smart cards. In our protocol, we
avoid modular exponential computing or scalar multiplication on elliptic curve used in traditional
authenticated key agreement protocols using smart cards. Our analysis shows that
our protocol has comprehensive characteristics and can withstand attacks, including the
insider attack, replay attack, and others, satisfying essential security requirements. Performance
analysis shows that our protocol can refrain from consuming modular exponential
computing and scalar multiplication on an elliptic curve. The computational cost of our
protocol compared with related protocols is acceptable.