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This work aims to identify the algebraic problems which enable many attacks on RFID protocols. Toward this goal, three emerging types of attacks on RFID protocols, concerning authentication, untraceability, and secrecy are discussed. The paper demonstrates the types of attacks by exhibiting previously unpublished vulnerabilities in several protocols and referring to various other flawed protocols. The common theme in these attacks is the fact that the algebraic properties of operators employed by the protocols are abused. While the methodology is applicable to any operator with algebraic properties, the protocols considered in this paper make use of xor, modular addition, and elliptic curve point addition.
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