Somewhat homomorphic encryption is public key encryption supporting a limited number of additions and multiplications on encrypted data. This encryption gives a powerful tool in performing meaningful computations with protecting data confidentiality, whose property is suitable mainly in cloud computing. In this paper, we focus on the scheme proposed by Brakerski and Vaikuntanathan, and present two types of packed ciphertexts in order to improve performance and reduce size of the encrypted data. One type of our packed ciphertexts is based on the message encoding technique proposed by Lauter, Naehrig and Vaikuntanathan. While their technique empowers efficient secure computation of sums and products over the integers, our second type of packed ciphertexts enables efficient secure computation of more complex functionalities such as multiple inner products and multiple Hamming distances. We apply our packing method to construct several protocols for secure biometric authentication and secure pattern matching computations. Our implementation shows that our method gives faster performance than the state-of-the-art work in such applications. Copyright © 2015 John Wiley & Sons, Ltd.

This paper proposes a new algorithm for evaluating the number of chaining variable conditions(CVCs) in the selecting step of a distrubance vector (DV) for the analysis of SHA-1 collision attack. The algorithm is constructed by combining the following four strategies, Strict Bit Compression, DV expansion, Precise Counting Rules in Every Step and Differential Path Confirmation for Rounds 2 to 4, that can evaluate the number of CVCs morestrictly compared with the previous approach.

In 2006, Bleichenbacher presented a new forgery attack against the signature scheme RSASSA-PKCS1-v1_5. The attack allows an adversary to forge a signature on almost arbitrary messages, if an implementation is not proper. Since the example was only limited to the case when the public exponent is 3 and the bit-length of the public composite is 3072, a potential threat is not known. This paper analyzes Bleichenbacher's forgery attack and shows applicable composite sizes for given exponents. We also propose two extended attacks with numerical examples