Study On The Security Of DSA Digital Signature Scheme And Electronical Voting Protocols

Since the 20th Century, with the fast development of Information technology, Internet has played the more and more important role in every aspect of our life and has influenced us tremendously. At the same time, more and more attention has been paid to the importance of Information Security. In this paper, we mainly discuss two wildly used applications of cryptographic technology-digital signature and electronical voting and their security.(1) In digital signatures, hash functions, the substitution of random oracle, are generally used for generating "message digests" or "message fingerprints." However, the hash functions can not satisfy the properties of the ROM completely, which make digital signatures unsafe. Liskov proposed to model a weak hash function by a random oracle together with another oracle allowing to break some properties of the hash function, e.g. a preimage oracle. In this paper, we give a variation signature scheme of DSA which is proven secure in a Preimage-trackable Random Oracle (PT-ROM) applied Liskov's idea. Compared with the original scheme, our scheme is still secure even using a weak hash function which makes DSA signature scheme unsafe.(2) Nowadays, the security of most electronic voting protocols based on VSS is considered under the assumption that only t malicious corruptions in all n parties (t<n/2). However, this kind of protocol do not guarantee the "fully security" if there is no honest majority. Therefore, we give a new electronic voting protocol based on VSS which can achieve the "the best of both world"-achieve "fully security" against t<n/2 malicious corruptions and "security with abort" against s>t malicious corruptions at the same time.