Conventional access control systems are typically based on a single time instant authentication. However, for high-security environments, continuous user verification is needed in order to robustly prevent fraudulent or unauthorized access. The electrocardiogram (ECG) is an emerging biometric modality with the following characteristics: (i) it does not require liveliness verification, (ii) there is strong evidence that it contains sufficient discriminative information to allow the identification of individuals from a large population, (iii) it allows continuous user verification. Recently, a string matching approach for ECG-based biometrics, using the Ziv-Merhav (ZM) cross parsing, was proposed. Building on previous work, and exploiting tools from data compression, this paper goes one step further, proposing a method for ECG-based continuous authentication. An adaptive way of using the ZM cross parsing is introduced. The use of the Lloyd-Max quantization is also introduced to improve the results with the string matching approach for ECG-based biometrics. Results on one-lead ECG real data are presented, acquired during a concentration task, from 19 healthy individuals.