The production of quantum computers with fast processing power and practical use will adversely affect the foundations of secure communication, especially for public-key cryptosystems (PKCs). Potential problems and solution scenarios are created early to design quantum-resistant PKCs. In this paper, the emergence of the concept of post-quantum cryptography (PQC) and early precautionary actions are explained. In addition, cryptosystem families that are known/believed to be secure in the presence of quantum computers are discussed. Based on these classes, the selected encryption/key encapsulation (KEM) and signature schemes of the NIST PQC process are expressed. Finally, some open problems for the post-quantum era are summarized.The production of quantum computers with fast processing power and practical use will adversely affect the foundations of secure communication, especially for public-key cryptosystems (PKCs). Potential problems and solution scenarios are created early to design quantum-resistant PKCs. In this paper, the emergence of the concept of post-quantum cryptography (PQC) and early precautionary actions are explained. In addition, cryptosystem families that are known/believed to be secure in the presence of quantum computers are discussed. Based on these classes, the selected encryption/key encapsulation (KEM) and signature schemes of the NIST PQC process are expressed. Finally, some open problems for the post-quantum era are summarized.

NATO science for peace and security series. D, Information and communication securityNov 9, 20224 citations

Key Compression for Isogeny-Based Cryptosystems

Reza Azarderakhsh, David Jao, Kassem Kalach +2 more

We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identi cation, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identi cation, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.

May 24, 201693 citations

Practical post-quantum cryptography

L.C.J. Rijneveld

Jan 1, 201918 citations

NTRU cryptosystem a solution to the quantum threat

Guiot Cusidó, Miquel, Guitart Morales, Xavier

Most of the current public key cryptosystems’ security is based on the integer factorization and the discrete logarithm, which are mathematical problems that are considered difficult to solve. However, the publication in 1994 of the Shor’s algorithm [1] was a major setback for the world of cryptography, since it provided a quantum algorithm capable of solving efficiently these mathematical problems. Therefore, in recent years many governments and technology companies have put a lot of effort into developing what is known as post-quantum cryptography, i.e. the science that studies cryptosystems that are resistant to quantum attacks. Along these lines, in 2016 the National Institute of Standards & Technology launched a competition with the aim of establishing and standardising the best performing post-quantum cryptosystems, being the NTRU (Nth Degree Truncated polynomial Ring Units) cryptosystem one of the candidates still on the table. The aim of this project is to study the quantum-resistant cryptosystem NTRU, both from a theoretical and practical point of view. Firstly, the mathematical results on which it is based are presented and the existing attacks against it are analyzed. Finally, a practical implementation of the cryptosystem and four of its attack is carried out, from which experimental results are extracted.Most of the current public key cryptosystems’ security is based on the integer factorization and the discrete logarithm, which are mathematical problems that are considered difficult to solve. However, the publication in 1994 of the Shor’s algorithm [1] was a major setback for the world of cryptography, since it provided a quantum algorithm capable of solving efficiently these mathematical problems. Therefore, in recent years many governments and technology companies have put a lot of effort into developing what is known as post-quantum cryptography, i.e. the science that studies cryptosystems that are resistant to quantum attacks. Along these lines, in 2016 the National Institute of Standards & Technology launched a competition with the aim of establishing and standardising the best performing post-quantum cryptosystems, being the NTRU (Nth Degree Truncated polynomial Ring Units) cryptosystem one of the candidates still on the table. The aim of this project is to study the quantum-resistant cryptosystem NTRU, both from a theoretical and practical point of view. Firstly, the mathematical results on which it is based are presented and the existing attacks against it are analyzed. Finally, a practical implementation of the cryptosystem and four of its attack is carried out, from which experimental results are extracted.

May 1, 20230 citations

A Practical Post-Quantum Public-Key Cryptosystem Based on

\textsf {spLWE}