Machine to Machine (M2M) applications enable a better management of resources and provide users With greater cornfort. Unfortunately, they also entail serious security and privacy concerns. ln this thesis, we focus on M2M security, and particularly on the authentication and privacy issues of M2M applications involving a SIM card. ln the first part, we design five new cryptographic primitives and formally prove that they meet the expected security requirements. More precisely, they consist of a partially blind signature scheme, a sequential aggregate Message Authentication Codes (MAC) scheme, an algebraic MAC scheme and two pre-Direct Anonymous Attestation (pre-DAA) schemes. Some of the proposed schemes aim to achieve a particular property that was not provided by previous constructions whereas others intend to improve the efficiency of state-of-the-art schemes. Our five schemes do not require the userls device to compute pairings. Thus, they are suitable for resource constrained environments such as SIM cards. ln a second part, we rely on these primitives to propose new privacy-preserving protocols. More specifically, we design an efficient private eCash system. We also propose a protocol enabling anonymous authentication and identification of embedded SIMs (eSlMs). Furthermore, we rely on our algebraic MAC scheme to build a practical Keyed-Verification Anonymous Credentials (KVAC) system. Finally, based on our sequential aggregate MAC scheme, we introduce a remote electronic voting system that is coercion-resistant and practical for real polls. The security of our protocols is formally proven in the Random Oracle Model (ROM) under classical computational assumptions.