Paper 2007/160 Original: eprint.iacr.org/2007/160 ↗

Analysis of Collusion-Attack Free ID-Based Non-Interactive Key Sharing

Abstract

Recently, Tanaka proposed an identity based non-interactive key sharing scheme and its corresponding identity based encryption scheme based on the intractability of integer factorization and discrete logarithm. The proposed identity based non-interactive key sharing scheme is similar to the well-known Maurer-Yacobi public key distribution scheme but the computational complexity for private key generation can be significantly reduced. It is also claimed that the proposed identity based non-interactive key sharing scheme is "collusion-attack free", i.e., secure against collusion attacks. In this paper, we analyze the security of the "collusion-attack free" identity based non-interactive key sharing scheme. First, we show that, without colluding with other users, a single user can recover some of the secret information of the private key generator. Then we show that a small group of users can collude to recover all of the secret information held by the private key generator. Thus, the "collusion-attack free" identity based non-interactive key sharing scheme can be completely compromised by collusion attacks.