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In the Bitcoin network, the simplified payment verification protocol (SPV) enables a lightweight device such as a mobile phone to participate in the bitcoin network without needed todownload and store the whole Bitcoin blocks. A Bitcoin SPV node initiates and verifies transactions of the Bitcoin network through the Bitcoin wallet software which is deployed on a resource constrained device such as a mobile phone.Thus, the security of the wallet is critical for the SPV nodes as it may affect the security of users cryptocurrencies. However, there are some concerns about the security flaws within the SPV nodes which could lead to significant economic losses. Most of these vulnerabilities can be resolved by employing a secure user authentication protocol. Over the years, researchers have engaged in designing a secure authentication protocol. However, most proposals have security flaws or performance issues. Recently, Park et al. proposed a two-party authenticated key exchange protocol for the mobile environment. They claimed that their protocol is not only secure against various attacks but also can be deployed efficiently. However, after a thorough security analysis, we find that the Park et al.s protocol is vulnerable to user forgery attack, smart card stolen attack and unable to provide user anonymity. To enhance security, we proposed an efficient and secure user authentication protocol for the SPV nodes in the mobile environment which can fulfill all the security requirements and has provable security. Additionally, we provide performance analysis which shows our proposed protocol is efficient for the SPV nodes in the Bitcoin network.

Weng et al. introduced the notion of conditional proxy re-encryption (C-PRE), whereby only the ciphertext satisfying one condition set by Alice can be re-encrypted by the proxy. To achieve more fine-grained delegation on the condition set, we introduce a new cryptographic primitive called fuzzy conditional proxy re-encryption (FC-PRE) in which we view conditions in C-PRE as a set of descriptive keywords. A FC-PRE scheme allows for a proxy with the re-encryption key for a conditional keyword set, W, to re-encrypt a ciphertext encrypted with a conditional keyword set, W′, if and only if W and W′ are close to each other as measured by the “set overlap” distance metric. Therefore, our system allows a certain amount of error-tolerance in the conditions. We formalize the FC-PRE security model by incorporating the advantages in previous C-PRE. Finally, we present an efficient construction of FC-PRE scheme, and prove its CCA-security under the well-studied decisional bilinear Diffie-Hellman (DBDH) assumption in the random oracle model.