Efficient Sharing of RSA Keys and Diffie-Hellman Bit Security

点击翻译按钮获取中文摘要

The research focuses on two topics in Applied Cryptography: efficient generation of shared RSA keys and the bit security of the Diffie-Hellman secret. To protect a high security private key one may wish to share it among a few sites. If a small number of sites are compromised no harm is done. An obvious question is who generates the shared key? Traditionally, a "trusted dealer" generates an RSA key pair and then splits the private key among the sites. This project studies various protocols for enabling three or more parties to efficiently generate a shared RSA key WITHOUT a trusted dealer. At the end of the computation the participants have an RSA modulus N=pq. They are all convinced that N is the product of two large distinct primes; however no proper coalition knows the factorization of N. The protocols should be appropriate for small, low bandwidth devices such as smartcards or Personal Digital Assistants (PDA's). The project's second topic is the bit security of the Diffie- Hellman secret. The Diffie-Hellman protocol enables two parties to exchange a secret. Although an adversary may not be able to compute the entire secret, she may be able to infer certain information about it. The proposed research will provide bounds on the amount of information an adversary can infer. To do so one shows that if an adversary can recover certain bits of the Diffie-Hellman secret then she can also break the entire protocol. The techniques needed for such reductions involve lattices and the LLL algorithm.