Generating asymmetric keys in a telecommunications system

Method for generating a key pair in a telecommunications system (UMTS) comprising a user terminal (MS / USIM) and at least one network node (HLR / AuC, SGSN) serving the user terminal (MS / USIM), wherein a key pair comprises a public key and a private key, said method comprising: generating (3-2, 4-2) a first initial value in a user terminal (MS / USIM) and a second value initial in at least one network node (HLR / AuC, SGSN), so that the initial first and second values ​​are identical; and generating (3-3, 4-3) from said first initial value, a first pair of keys on the user terminal (MS / USIM), and from the second initial value, a second key pair in at least said network node (HLR / AuC, SGSN), such that the first and second key pairs are identical; characterized in that the first and second pairs are asymmetric key pairs, wherein the method comprises generating said first and second initial values ​​using at least one ciphering key CK and an integrity key IK of a third generation network; and / or generate said first and second initial values ​​using a cryptographic key Kc from a second generation network.