Classification and Verification of Online Handwritten Signatures with Time Causal Information Theory Quantifiers Osvaldo A. Rosso 1,2,3,* , Raydonal Ospina 4,5 , and Alejandro C. Frery 5 1 Instituto de F´ ısica, Universidade Federal de Alagoas (UFAL), Av. Lourival Melo Mota, s/n, 57072-900 Macei ´ o, AL, Brazil 2 Instituto Tecnol ´ ogico de Buenos Aires (ITBA), Av. Eduardo Madero 399, C1106ACD Ciudad Aut ´ onoma de Buenos Aires, Argentina 3 Complex Systems Group, Facultad de Ingenier´ ıa y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. ´ Alvaro del Portillo 12.455, Las Condes, Santiago, Chile. 4 Centro de Ci ˆ encias Exatas e da Natureza, Departamento de Estat´ ıstica, Universidade Federal de Pernambuco (UFPE), Cidade Universit ´ aria, 50740-540 Recife, PE, Brasil 5 Instituto de Computac ¸˜ ao, Universidade Federal de Alagoas (UFAL), Av. Lourival Melo Mota, s/n, 57072-900, Macei ´ o, AL, Brazil * oarosso@gmail.com ABSTRACT We present a new approach for online handwritten signature classification and verification based on descriptors stemming from Information Theory. The proposal uses the Shannon Entropy, the Statistical Complexity, and the Fisher Information evaluated over the Bandt and Pompe symbolization of the horizontal and vertical coordinates of signatures. These six features are easy and fast to compute, and they are the input to an One-Class Support Vector Machine classifier. The results produced surpass state-of-the-art techniques that employ higher-dimensional feature spaces which often require specialized software and hardware. We assess the consistency of our proposal with respect to the size of the training sample, and we also use it to classify the signatures into meaningful groups. Introduction The word biometrics is associated to human traits or behaviors which can be measured and used for individual recognition. In fact, the biometry recognition, as a personal authentication signal processing, can be used in applications where users need to be security identified. 1 Clearly, these kind of systems can either verify or identify. Two types of biometrics can be defined according to the personal traits considered: physical/physiological or behavioral. Physical/physiological biometrics is about catering the biological traits of users, like fingerprints, iris, face, hand, etc. Behavioral biometrics takes into account dynamic traits of users, such as, voice, handwritten and signature expressions. One of the main advantages of biometric systems is that users do not have to remember passwords or carry access keys. Another important advantage lies in the difficulty to steal, imitate or generate genuine biometric data, leading to enhanced security. 1 As mentioned, behavioral biometrics is based on measurements extracted from an activity performed by the user, in conscious or unconscious way, that are inherent to his/her own personality or learned behavior. In this aspect, behavioral biometrics has interesting pros, like user acceptance and cancelability, but it still lacks of some level of the uniqueness physiological biometrics has. Among the pure behavioral biometric traits, the handwritten signature and the way we sign is the one with widest social and legal acceptance. 2–6 Identity verification by signature analysis requires no invasive measurements and people are familiar with the use of signatures in their daily life. Also, it is the modality confronted with the highest level of attacks. A signature is a handwritten depiction of someone’s name or some other mark of identification written on documents and devices as proof of identification. The formation of signature varies from person to person, or even from the same person due to the psychophysical state of the signer and the conditions under which the signature apposition process occurs. Hilton 7 studied how signatures are produced, and found that the signature has at least three attributes: form, movement and variation; being movement the most important, because signatures are produced by moving a writing device. The study also noted that a person’s signature does evolve over time and, with the vast majority of users, once the signature style has