The Myth of Superiority of American Encryption Products

Encryption software and hardware use sophisticated mathematical algorithms to encipher a message so that only the intended recipient may read it. Fearing that criminals and terrorists will use encryption to evade authorities, the United States now restricts the export of encryption products with key lengths of more than 56 bits. The controls are futile, because strong encryption products are readily available overseas. Foreign-made encryption products are as good as, or better than, U.S.-made products. U.S. cryptographers have no monopoly on the mathematical knowledge and methods used to create strong encryption. Powerful encryption symmetric-key technologies developed in other countries include IDEA and GOST. Researchers in New Zealand have developed very strong public-key encryption systems. As patents on strong algorithms of U.S. origin expire, researchers in other countries will gain additional opportunities to develop strong encryption technology based on those algorithms

On the Optimality of Quantum Encryption Schemes

It is well known that n bits of entropy are necessary and sufficient to perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be approximate, the amount of entropy needed doesn't asymptotically change. However, this is not the case when we are encrypting quantum bits. For the perfect encryption of n quantum bits, 2n bits of entropy are necessary and sufficient (quantum one-time pad), but for approximate encryption one asymptotically needs only n bits of entropy. In this paper, we provide the optimal trade-off between the approximation measure epsilon and the amount of classical entropy used in the encryption of single quantum bits. Then, we consider n-qubit encryption schemes which are a composition of independent single-qubit ones and provide the optimal schemes both in the 2- and the operator-norm. Moreover, we provide a counterexample to show that the encryption scheme of Ambainis-Smith based on small-bias sets does not work in the operator-norm.Comment: 15 page

Block encryption of quantum messages

In modern cryptography, block encryption is a fundamental cryptographic primitive. However, it is impossible for block encryption to achieve the same security as one-time pad. Quantum mechanics has changed the modern cryptography, and lots of researches have shown that quantum cryptography can outperform the limitation of traditional cryptography. This article proposes a new constructive mode for private quantum encryption, named $\mathcal{EHE}$, which is a very simple method to construct quantum encryption from classical primitive. Based on $\mathcal{EHE}$ mode, we construct a quantum block encryption (QBE) scheme from pseudorandom functions. If the pseudorandom functions are standard secure, our scheme is indistinguishable encryption under chosen plaintext attack. If the pseudorandom functions are permutation on the key space, our scheme can achieve perfect security. In our scheme, the key can be reused and the randomness cannot, so a $2n$-bit key can be used in an exponential number of encryptions, where the randomness will be refreshed in each time of encryption. Thus $2n$-bit key can perfectly encrypt $O(n2^n)$ qubits, and the perfect secrecy would not be broken if the $2n$-bit key is reused for only exponential times. Comparing with quantum one-time pad (QOTP), our scheme can be the same secure as QOTP, and the secret key can be reused (no matter whether the eavesdropping exists or not). Thus, the limitation of perfectly secure encryption (Shannon's theory) is broken in the quantum setting. Moreover, our scheme can be viewed as a positive answer to the open problem in quantum cryptography "how to unconditionally reuse or recycle the whole key of private-key quantum encryption". In order to physically implement the QBE scheme, we only need to implement two kinds of single-qubit gates (Pauli $X$ gate and Hadamard gate), so it is within reach of current quantum technology.Comment: 13 pages, 1 figure. Prior version appears in eprint.iacr.org(iacr/2017/1247). This version adds some analysis about multiple-message encryption, and modifies lots of contents. There are no changes about the fundamental result