Editing Prepare-and-Send Verifiable Quantum Fully Homomorphic Encryption
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==Hardware Requirements== | ==Hardware Requirements== | ||
* Classical HE scheme is required here. The communication can be performed over a classical network with only one quantum node (in case of classical input and output). | * Classical HE scheme is required here. The communication can be performed over a classical network with only one quantum node (in case of classical input and output). | ||
==Properties== | ==Properties== | ||
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* Privacy: this scheme is private if its ciphertexts are indistinguishable under chosen plaintext attack. | * Privacy: this scheme is private if its ciphertexts are indistinguishable under chosen plaintext attack. | ||
* Computational logs are generally classical in nature. | * Computational logs are generally classical in nature. | ||
* The chosen message authentication code MAC = (Tag, Ver) is existentially unforgeable under adaptive chosen message | * The chosen message authentication code MAC = (Tag, Ver) is existentially unforgeable under adaptive chosen message attacks (EUF-CMA [16]) from a quantum adversary | ||
==Notation== | ==Notation== | ||
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* <math>h</math>: Upper bound on H gate. | * <math>h</math>: Upper bound on H gate. | ||
* <math>k</math>: All keys | * <math>k</math>: All keys | ||
* <math>\pi</math>: Global permutation which are used to encrypt the states | * <math>\pi</math>: Global permutation which are used to encrypt the states. | ||
* MAC: Message authentication code, MAC = (Tag, Ver) | * MAC: Message authentication code, MAC = (Tag, Ver) | ||
* <math>pk_i, sk_i, evk_i</math>: <math>i_{th}</math> homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, respectively for given k, the security parameter. | * <math>pk_i, sk_i, evk_i</math>: <math>i_{th}</math> homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, respectively for given k, the security parameter. | ||
* <math>v</math>: | |||
* <math>\mu</math>: | |||
* <math>\tilde{\sigma}</math>: ciphertext | * <math>\tilde{\sigma}</math>: ciphertext | ||
== | ==Pseudo Code== | ||
'''Stage 1''': Key generation and encryption </br> | '''Stage 1''': Key generation and encryption </br> | ||
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** <math>\pi_i \xleftarrow[r]{r} S_{3m}</math> | ** <math>\pi_i \xleftarrow[r]{r} S_{3m}</math> | ||
** <math>(g_i, \gamma_i^{in}, \gamma_i^{mid}, \gamma_i^{out}) \xleftarrow[]{}</math> TrapTP.GadgetGen<math>(sk_{i-1})</math> | ** <math>(g_i, \gamma_i^{in}, \gamma_i^{mid}, \gamma_i^{out}) \xleftarrow[]{}</math> TrapTP.GadgetGen<math>(sk_{i-1})</math> | ||
** <math>\Gamma_i \xleftarrow[]{}</math> MAC.Sign(HE.ENC<math>_{pk_i}(g_i, \pi_i)) \otimes</math> TrapTP.ENC<math>((\pi_i, k, sk_0, ..., sk_t, pk_i), \gamma^{mid}_i \otimes</math> TrapTP.Enc<math>(sk, \gamma^{in}_i, \gamma^{out}_i | ** <math>\Gamma_i \xleftarrow[]{}</math> MAC.Sign(HE.ENC<math>_{pk_i}(g_i, \pi_i)) \otimes</math> TrapTP.ENC<math>((\pi_i, k, sk_0, ..., sk_t, pk_i), \gamma^{mid}_i \otimes</math> TrapTP.Enc<math>(sk, \gamma^{in}_i, \gamma^{out}_i</math> | ||
* <math>keys \xleftarrow[]{}</math> MAC.Sign<math>(evk_0, ..., evk_t, pk_0, ..., pk_t,</math> HE.Enc<math>_{pk_0}(\pi))</math> | * <math>keys \xleftarrow[]{}</math> MAC.Sign<math>(evk_0, ..., evk_t, pk_0, ..., pk_t,</math> HE.Enc<math>_{pk_0}(\pi))</math> | ||
* <math>\rho_{evk} \xleftarrow[]{} (keys, \mu^{P}_0, ..., \mu^{P}_p, \mu^{T}_0, ..., \mu^{T}_t, \mu^{H}_0, ..., \mu^{H}_h, \Gamma_1, ..., \Gamma_t)</math> | * <math>\rho_{evk} \xleftarrow[]{} (keys, \mu^{P}_0, ..., \mu^{P}_p, \mu^{T}_0, ..., \mu^{T}_t, \mu^{H}_0, ..., \mu^{H}_h, \Gamma_1, ..., \Gamma_t)</math> | ||
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==Further Information== | ==Further Information== | ||
<div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | <div style='text-align: right;'>''*contributed by Rhea Parekh''</div> |