Joint Encryption and Message-Efficient Secure Computation

Matthew Franklin, Stuart Haber

Matthew Franklin, Stuart Haber

Elette Boyle, Abhishek Jain, Sacha Servan-Schreiber +1 more

Michael O. Rabin, Yan Zong Ding

Traditional modern cryptography relies on unproven complexity assumptions that certain problems, such as integer factorization, are computationally hard, and the adversary is bounded in computing power. However, advances in algorithms and computing technology may render current cryptosystems insecure, and lead to the decryption of past secret messages. On the other hand, Shannon's pessimistic negative result essentially implies that if the adversary is all-powerful and has complete access to the communication line, then efficient practical solutions for information-theoretic security do not exist. This thesis is a study of cryptography in the bounded storage model, where provable everlasting security can be achieved efficiently without any complexity assumption. It first presents an efficient scheme for encryption and authentication that is provably secure against strong adaptive attacks, by an adversary who is computationally unbounded and only storage-bounded. A major new result is that the shared secret key employed by the sender and the receiver can be re-used to send an exponential number of messages. Our encryption scheme further enjoys the surprising property that even if the secret key is captured by the adversary after the transmission of the ciphertext, the secrecy of the message is assured. The above is joint work with Michael Rabin. Oblivious transfer is a cryptographic protocol that can serve as a basic primitive for all of cryptography. This thesis presents an implementation of oblivious transfer in the bounded storage model, which is again provably secure without complexity assumption.

Binger Zuo, Jiguo Li, Yichen Zhang +1 more

With quantum computers, the quantum resistance of cryptographic systems has gradually attracted attention. To overcome the shortcoming of existing identity-based encryption (IBE) schemes in resisting quantum attacks, we introduce an IBE scheme based on learning with errors (LWE). In addition, devices with limited computing power are becoming increasingly common in practice, making it increasingly important to improve the efficiency of online computation of encryption algorithms. The classic solution is to directly improve the efficiency of the Gaussian sampling algorithm, thereby increasing the overall efficiency of the scheme. However, our scheme combines the efficient Gaussian sampling algorithm, G-trapdoor, with online/offline method to further improve the online encryption efficiency of the encryption algorithm. Our scheme completes partial computation before knowing the message and receiver’s identity, and once the message and receiver’s identity are obtained, the online part encryption can be efficiently completed. We construct an identity-based online/offline encryption (IBOOE) scheme from LWE with G-trapdoor, improve the efficiency of online encryption while achieving quantum resistant security. We prove the scheme’s security under the standard model for chosen-plaintext attack (CPA). By comparing with relevant schemes in terms of experiments and analysis, our scheme has improved efficiency by 65% to 80% compared to the classical LWE IBE scheme (increasing with LWE security parameters), and by 60% to 70% compared to the recent IBE scheme from LWE. This greatly improves the efficiency of online computing for low-power encryption devices while ensuring security.

Thomas H. Schneider, Michael Zohner