Group key exchanges with failures

A computer program element comprising program code means for performing a method for generating a session key (sk) on demand in a network among n participating network devices (A, B, C, D) with up to t faulty devices when the computer program element is run on a computer, wherein t<n/2, the method comprising each participating network device (D):

• choosing a private and public key (di, ei) according to a public key encryption scheme, and broadcasting the public key (ei) to each other participating network device (A, B, C);
• choosing a local contribution value (yj) from a multiplicative group (Gq) of size q;
• in each case of receiving a public key (ej) from one of the other participating network devices (A, B, C), encrypting the local contribution value (yj) under the received public key (ej) to an encrypted contribution value (yij) and sending in reply to the one of the other participating network devices (A, B, C) the encrypted contribution value (yij);
• receiving at least n−t−1 encrypted contribution values (yji) and deriving decrypted contribution values (yj) by applying the private key (di);
• deriving a blinded session key (bski) from the decrypted contribution values (yj) and the local contribution value (yi);
• agreeing on one of the blinded session keys (bskj) by using an agreement protocol;
• and
• deriving the session key (sk) from the agreed-on blinded session key (bskj) by applying one of the decrypted contribution values (yj) and the contribution value (yi).

A computer program product stored on a computer usable medium, comprising computer readable program means for causing a computer to perform a method for generating a session key (sk) on demand in a network among n participating network devices (A, B, C, D) with up to t faulty devices, wherein t<n/2, the method comprising each participating network device (D):

• choosing a private and public key (di, ei) according to a public key encryption scheme, and broadcasting the public key (ei) to each other participating network device (A, B, C);
• choosing a local contribution value (yi) from a multiplicative group (Gq) of size q;
• in each case of receiving a public key (ej) from one of the other participating network devices (A, B, C), encrypting the local contribution value (yj) under the received public key (ej) to an encrypted contribution value (yij) and sending in reply to the one of the other participating network devices (A, B, C) the encrypted contribution value (yij);
• receiving at least n−t−1 encrypted contribution values (yji) and deriving decrypted contribution values (yj) by applying the private key (di);
• deriving a blinded session key (bski) from the decrypted contribution values (yj) and the local contribution value (yj);
• agreeing on one of the blinded session keys (bskj) by using an agreement protocol;
• and
• deriving the session key (sk) from the agreed-on blinded session key (bskj) by applying one of the decrypted contribution values (yj) and the contribution value (yi).

A computer device, comprising:

• a computer program product stored on a computer usable medium, comprising computer readable program means for causing a computer to perform a method for generating a session key (sk) on demand in a network among n participating network devices (A, B, C, D) with up to t faulty devices, wherein t<n/2, the method comprising each participating network device (D):
• choosing a private and public key (di, ei) according to a public key encryption scheme, and broadcasting the public key (ei) to each other participating network device (A, B, C);
• choosing a local contribution value (yi) from a multiplicative group (Gq) of size q;
• in each case of receiving a public key (ej) from one of the other participating network devices (A, B, C), encrypting the local contribution value (yi) under the received public key (ej) to an encrypted contribution value (yij) and sending in reply to the one of the other participating network devices (A, B, C) the encrypted contribution value (yij);
• receiving at least n−t−1 encrypted contribution values (yji) and deriving decrypted contribution values (yj) by applying the private key (di);
• deriving a blinded session key (bski) from the decrypted contribution values (yj) and the local contribution value (yj);
• agreeing on one of the blinded session keys (bskj) by using an agreement protocol;
• and
• deriving the session key (sk) from the agreed-on blinded session key (bskj) by applying one of the decrypted contribution values (yj) and the contribution value (yi);
• wherein the network device (A, B, C, D) comprises a processor for executing the computer program product when the computer program product is run on the computer device.