Ad hoc网络中基于环Zn上椭圆曲线和RSA的密钥管理

探讨了ad hoc网络密钥管理问题,首次利用环Zn上椭圆曲线所构成的陷门离散对数的同态性质,结合Shamir秘密分享方案,提出了一种新的适用于ad hoc网络的密钥管理方案.在该方案中,新加入的成员向组内成员提供环Zn上的椭圆曲线加密体制,并保密相应的陷门.利用该加密体制的同态性,参与密钥分发的成员将关于新成员的子密钥加密后依次相加,新成员得到最后的和,然后解密;为防止攻击者来自于组内成员,在每次子密钥加密中都加入了混合因子.新方案具有很好的安全性,破解该方案的难度不低于破解RSA.

Key management based on elliptic curves over the ring Zn and RSA in ad hoc networks

The problem of key management in ad hoc networks was analyzed. Based on the homeostasis of trapdooring discrete logarithms on elliptic curves over the ring Zn and Shamir secret sharing scheme, a new key management scheme that adapts to ad hoc networks was proposed for the first time. In this scheme, the new user provided the elliptic curve encryption scheme to the users in the system, and kept the corresponding trapdoor secret. Making use of the homeostasis, the users who take part in the key distribution encrypted the sub-keys and added them step by step. At last, the sum was sent to the new user and was decrypted. In order to prevent the attacker from the system, the shuffling factors were added to the encryption. The new scheme has better security, and the difficulties to break the scheme are not less than to break RSA.