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Lecture notes in computer science

Chosen Ciphertext Attacks Secure Inner-Product Functional Encryption from Learning with Errors Assumption

Kelly Yun, Rui Xue

Published Jan 1, 2021• 1 citation
Publisher
DOI
10.1007/978-3-030-71852-7_9

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Abstract The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks. Unfortunately, the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large, which makes the algorithm inefficient. Therefore, we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al. [Asiacrypt 2011], and its security relies on the difficulty assumption of ring learning with errors. Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.
Inner-product functional encryption (IPFE) is an exciting paradigm for non-interactively computing on encrypted data where a master secret key can be used to derive decryption keys associated with certain inner-product functions in such a way that the decryption operation reveals an inner-product result, and nothing else. Over the decades, all efforts regarding existing IPFE schemes have been dedicated to extending them to multi-input/multi-client scenarios, understanding the security concepts that can be achieved, and identifying a multitude of practical use cases. However, in the event of key compromise, a common issue in real-world applications, the existing IPFE schemes are unable to guarantee the confidentiality of past encryptions. This paper introduces a novel variant of IPFE that supports key updates, called updatable IPFE, potentially opening up a new avenue of research to address the common key exposure problem. In this setting, any sender can initiate the transition to the next period by computing a new public key and a special update. The special update can be processed by the system administrator and the receiver to compute the next-period master secret key and the next-period decryption key, respectively. If done honestly, future (regular) ciphertexts generated with the new public key can be decrypted with the new decryption key, but ciphertexts from the past cannot be decrypted with the new decryption key. To formally illustrate this, we formalize the notion of the indistinguishability-based security under chosen randomness chosen plaintext attacks (IND-CR-CPA). We further propose the first efficient construction of updatable IPFE in the standard model, based on Learning with Errors (LWE) assumption with polynomial modulus-to-noise rate. Finally, we conduct a comprehensive performance evaluation of our updatable IPFE, and the experimental results demonstrate its computational efficiency, making it a viable solution for real-world applications.
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