Quantum Secure Lightweight Cryptography with Quantum Permutation Pad

Abstract

Quantum logic gates represent certain quantum operations to perform quantum computations. Of those quantum gates, there is a category of classical behavior gates called quantum permutation gates. As a quantum algorithm, quantum permutation pad or QPP consists of multiple quantum permutation gates to be implemented both in a quantum computing system as a quantum circuit operating on n-qubits' states for transformations and in a classical computing system represented by a pad of n-bit permutation matrices. Since first time proposed in 2020, QPP has been recently applied to create a quantum safe lightweight block cipher by replacing SubBytes and AddRoundKey with QPP in AES called AES-QPP. In AES-QPP, QPP consists of 16 selected 8-bit permutation matrices based on the shared classical key materials. For quantum safe, the key length can be any size from 256 bits to 4 KB. That means, this QPP holds up to 4 KB of Shannon information entropy. Its code size is less than 2 KB with 4 KB of RAM memory. In this paper, we propose to apply QPP for a streaming cipher and carry out its encryption performance and the randomness analysis of this streaming cipher. The proposed QPP streaming cipher demonstrates not only good randomness in its ciphertexts but also huge performance improvement: 13x faster than AES-256, with an overall runtime space (6.8 KB).

Benchmark Performance of Digital QKD Platform Using Quantum Permutation Pad

“…The star symbols in Table III indicate these cases. QE Expansion in Table III shows less failure cases, that is because QPP itself has the whitening capability on the input data [27,28].…”

“…QPP can be also used for entropy expansion [27] and pseudoquantum random number generation or pQRNG [28]. This can allow us to expand the true QE multiple times such as 10x as shown in Fig.…”

“…With this round reduction, they achieved improvement in performance by up to 5x. Kuang, et al reported their streaming cipher implementation with QPP in 2021 [27]. [28] carried out an entropy expansion and distribution with QPP for 5G backhaul using for AES true random keys and nonces, either from a true QRNG distributed by QPP or local expansions by QPP at 5G local stations.…”

Quantum encryption with quantum permutation pad in IBMQ systems

“…Kuang et al reported their QPP implementations as a lightweight quantum safe block cipher [23] and streaming cipher [24], entropy transformation and expansion [25], pseudo quantum random number generation [27]. Kuang and Barbeau recently proposed a universal quantum safe cryptography with QPP [26] for potential quantum encrypted communications between two quantum computers and one quantum one classical computers over the existing internet or future quantum internet.…”

“…It is well-known that permutation transformations are bijective over computational basis, so the QPP encryption holds the property of Shannon perfect secrecy. The QPP encryption scheme has been applied to different cases recently in classical computing [23][24][25]. For an n-qubit computational basis, there exist a total of 2 n !…”