IN THIS CHAPTER Code-based cryptography ................................................................................................................................................ Lattice-based cryptography ................................................................................................................................................ Hash-based cryptography ................................................................................................................................................ Multivariate cryptography ................................................................................................................................................ Supersingular elliptic-curve isogeny cryptography ................................................................................................................................................ Chapter 3 Families of Post-quantum Schemes The cryptographic community is discussing five different families of postquantum cryptography. Each of these families is based on different mathematical problems that are hard to solve both with traditional computers as well as quantum computers. They differ in efficiency, e.g., in the size of public and private keys, sizes of cipher texts and key-exchange messages, and computational cost, their maturity, and the amount of trust in their strength. Efficiency of post-quantum schemes is important because it determines how well the schemes can be used on current and future devices, in particular on devices with few resources or limited network bandwidth like embedded and handheld devices. In general post-quantum schemes require more resources compared to traditional cryptography, in particular ECC. Therefore, security against quantum-computer attacks comes at a cost. Some post-quantum schemes have been known and investigated for many years. For example code-based 43 and hash-based 44 schemes were introduced at the end of the 1970s. Therefore, code-based and hash-based cryptography is well understood and trusted. Multivariate cryptography developed over the 1980s 42 and its underlying mathematical problem is well understood as well. However, constructing an efficient public-key cryptosystem based on multivariate cryptography is challenging and only few multivariate public-key schemes are
PQC_for_Dummies
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