Quantum Secure Non-Malleable Codes in the Split-State Model

y Non-malleable codes introduced by Dziembowski et al. (2018) encode a classical message S in a manner such that the tampered codeword either decodes to the original message S or a message that is unrelated/independent of S. Constructing non-malleable codes for various tampering function families has received significant attention in the recent years. We consider the well studied (2-part) split-state model, in which the message S is encoded into two parts X and Y, and the adversary is allowed to arbitrarily tamper with each X and Y individually. Non-malleable codes in the split-state model have found applications in other important security notions like non-malleable commitments and non-malleable secret sharing. Thus, it is vital to understand if such non-malleable codes are secure against quantum adversaries. We consider the security of non-malleable codes in the split-state model when the adversary is allowed to make use of arbitrary entanglement to tamper the parts X and Y. We construct explicit quantum secure non-malleable codes in the split-state model. Our construction of quantum secure non-malleable codes is based on the recent construction of quantum secure 2-source non-malleable extractors by Boddu et al. (2021). 1) We extend the connection of Cheraghchi and Guruswami (2016) between 2-source nonmalleable extractors and non-malleable codes in the split-state model in the classical setting to the quantum setting, i.e. we show that explicit quantum secure 2-source non-malleable extractors in (k(1), k(2))-qpa-state framework of Boddu et al. (2021) give rise to explicit quantum secure non-malleable codes in the split-state model. 2) We construct the first quantum secure non-malleable code with efficient encoding and decoding procedures for message length m = n(ohm(1)), error epsilon = 2(-n ohm(1)) and codeword of size 2n. Prior to this work, it remained open to provide such quantum secure non-malleable code even for a single bit message in the split-state model. 3) We also study its natural extension when the tampering of the codeword is performed t -times. We construct quantum secure one-many non-malleable code with efficient encoding and decoding procedures for t = n(ohm(1)), message length m = n(ohm(1)), error epsilon = 2(-n ohm(1)) and codeword of size 2n. 4) As an application, we also construct the first quantum secure 2-out-of-2 non-malleable secret sharing scheme for message/secret length m = n ohm(1), error epsilon = 2(-n ohm(1)) and share of size n.