Quantum Cryptosystems with Key Evolution

Hachiro Fujita

The McEliece cryptosystem is one of the best-known (classical) public-key cryptosystems, which is based on algebraic coding theory. In this paper, we present a quantum analogue of the classical McEliece cryptosystem. Our quantum McEliece public-key cryptosystem is based on the theory of stabilizer codes and has the key generation, encryption and decryption algorithms similar to those in the classical McEliece cryptosystem. We present an explicit construction of the quantum McEliece public-key cryptosystem using Calderbank-Shor-Steane codes based on generalized Reed-Solomon codes. We examine the security of our quantum McEliece cryptosystem and compare it with alternative systems.

Tatsuaki Okamoto, Keisuke Tanaka, Shigenori Uchiyama

Jose-Antonio Septien-Hernandez, Magali Arellano-Vázquez, Marco Antonio Contreras-Cruz +1 more

The existence of quantum computers and Shor's algorithm poses an imminent threat to classical public-key cryptosystems. These cryptosystems are currently used for the exchange of keys between servers and clients over the Internet. The Internet of Things (IoT) is the next step in the evolution of the Internet, and it involves the connection of millions of low-powered and resource-constrained devices to the network. Because quantum computers are becoming more capable, the creation of a new cryptographic standard that cannot be compromised by them is indispensable. There are several current proposals of quantum-resistant or post-quantum algorithms that are being considered for future standards. Given that the IoT is increasing in popularity, and given its resource-constrained nature, it is worth adapting those new standards to IoT devices. In this work, we study some post-quantum cryptosystems that could be suitable for IoT devices, adapting them to work with current cryptography and communication software, and conduct a performance measurement on them, obtaining guidelines for selecting the best for different applications in resource-constrained hardware. Our results show that many of these algorithms can be efficiently executed in current IoT hardware, providing adequate protection from the attacks that quantum computers will eventually be capable of.

圭介 田中, Keisuke Tanaka

Takeshi Koshiba

It is well known that Shor's quantum algorithm for integer factorization can break down the RSA public-key cryptosystem, which is widely used in many cryptographic applications. Thus, public-key cryptosystems in the quantum computational setting are longed for cryptology. In order to define the security notions of public-key cryptosystems, we have to model the power of the sender, receiver, adversary and channel. While we may consider a setting where quantum computers are available only to adversaries, we generally discuss what are the right security notions for (quantum) public-key cryptosystems in the quantum computational setting. Moreover, we consider the security of quantum public-key cryptosystems known so far.