Quantum Circuit Implementation and Resource Analysis of LBlock and LiCi

Due to Grover's algorithm, any exhaustive search attack of block ciphers can achieve a quadratic speed-up. To implement Grover,s exhaustive search and accurately estimate the required resources, one needs to implement the target ciphers as quantum circuits. Recently, there has been increasing interest in quantum circuits implementing lightweight ciphers. In this paper we present the quantum implementations and resource estimates of the lightweight ciphers LBlock and LiCi. We optimize the quantum circuit implementations in the number of gates, required qubits and the circuit depth, and simulate the quantum circuits on ProjectQ. Furthermore, based on the quantum implementations, we analyze the resources required for exhaustive key search attacks of LBlock and LiCi with Grover's algorithm. Finally, we compare the resources for implementing LBlock and LiCi with those of other lightweight ciphers.Comment: 29 pages,21 figure

Quantum Simulation Logic, Oracles, and the Quantum Advantage

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure

Quantum linearization attacks

Recent works have shown that quantum period-finding can be used to break many popular constructions (some block ciphers such as Even-Mansour, multiple MACs and AEs...) in the superposition query model. So far, all the constructions broken exhibited a strong algebraic structure, which enables to craft a periodic function of a single input block. Recoverin

Quantum forgery attacks on COPA,AES-COPA and marble authenticated encryption algorithms

The classic forgery attacks on COPA, AES-COPA and Marble authenticated encryption algorithms need to query about 2^(n/2) times, and their success probability is not high. To solve this problem, the corresponding quantum forgery attacks on COPA, AES-COPA and Marble authenticated encryption algorithms are presented. In the quantum forgery attacks on COPA and AES-COPA, we use Simon's algorithm to find the period of the tag generation function in COPA and AES-COPA by querying in superposition, and then generate a forged tag for a new message. In the quantum forgery attack on Marble, Simon's algorithm is used to recover the secret parameter L, and the forged tag can be computed with L. Compared with classic forgery attacks on COPA, AES-COPA and Marble, our attack can reduce the number of queries from O(2^(n/2)) to O(n) and improve success probability close to 100%.Comment: 21 pages, 11 figure

Homomorphic Encryption of the k=2 Bernstein-Vazirani Algorithm

The nonrecursive Bernstein-Vazirani algorithm was the first quantum algorithm to show a superpolynomial improvement over the corresponding best classical algorithm. Here we define a class of circuits that solve a particular case of this problem for second-level recursion. This class of circuits simplifies the number of gates $T$ required to construct the oracle by making it grow linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE) which is an important cryptographic technology useful for delegated quantum computation. It allows a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client's data. Liang developed QHE schemes with perfect security, $\mathcal{F}$-homomorphism, no interaction between server and client, and quasi-compactness bounded by $O(M)$ where M is the number of gates $T$ in the circuit. Precisely these schemes are suitable for circuits with a polynomial number of gates $T/T^{\dagger}$. Following these schemes, the simplified circuits we have constructed can be evaluated homomorphically in an efficient way.Comment: Revtex file, color figure

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler