Abstract. -Vulnerabilities related to weak passwords are a pressing global economic and security issue. We report a novel, simple, and effective approach to address the weak password problem. Building upon chaotic dynamics, criticality at phase transitions, CAPTCHA recognition, and computational round-off errors we design an algorithm that strengthens security of passwords. The core idea of our simple method is to split a long and secure password into two components. The first component is memorized by the user. The second component is transformed into a CAPTCHA image and then protected using evolution of a two-dimensional dynamical system close to a phase transition, in such a way that standard brute-force attacks become ineffective. We expect our approach to have wide applications for authentication and encryption technologies.Introduction. -Computer and information security has been subject to intensive research for over 50 years. This included investigation of cryptographic methods, as well as generic security of computing devices, operating systems and networks. However, it is only relatively recently that the importance of the human factor has been given proper attention. Passwords are the common method for authentication and encryption used to secure digital life. Humans have limited capacity to remember passwords and tend to select passwords that are too simple and predictable. Security breaches related to weak passwords are widespread events. Consumers and enterprises around the world are looking for ways to address the weak password problem [1,2]. In this paper we propose a simple method to address the problem by combining chaotic dynamics, phase transitions, and pattern recognition advantages of the human brain. We do not design a new encryption scheme. Instead we use standard encryption tschemes, and add a littel overhead on top in order to substantially enhance security. A major building block of the proposed algorithm is the dynamic behavior of complex extended non-linear systems, in particular, Hamiltonian lattices close to a phase transition [3,4]. These systems display non-ergodicity, deterministic chaos [5], and