# Post-Quantum Cryptography

By [Untitled](https://paragraph.com/@0x2ceb41136b608cefdc7e524775b2adc6ce8ddf96) · 2023-07-27

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Post-quantum cryptography (PQC) is about devising cryptographic algorithms that are secure in the quantum era with security against both classical/conventional and quantum computers. There are several candidate approaches for building the post-quantum cryptographic schemes, as described below in [**Section 3.1**](https://www.mdpi.com/2410-387X/5/4/38#sec3dot1-cryptography-05-00038) \[[**18**](https://www.mdpi.com/2410-387X/5/4/38#B18-cryptography-05-00038),[**19**](https://www.mdpi.com/2410-387X/5/4/38#B19-cryptography-05-00038),[**20**](https://www.mdpi.com/2410-387X/5/4/38#B20-cryptography-05-00038)\].

#### _3.1. Post-Quantum Cryptography Candidates_

This subsection delineates the candidates of the PQC schemes. These are hash-based cryptography, code-based cryptography, multivariate cryptography, lattice-based cryptography, and isogeny-based cryptography schemes.

#### 3.1.1. Hash-Based Cryptography

Hash-based cryptography focuses on designing digital signature schemes based on the security of cryptographic hash functions, e.g., SHA-3. These schemes are based on the security of hash functions (as a one-way function, collision-resistant property, and hardness of second pre-image attacks), and require fewer security assumptions than the number-theoretic signature schemes (e.g. RSA, DSA). Ralph Merkle in 1989 introduced Merkle Signature Scheme (MSS) \[[**21**](https://www.mdpi.com/2410-387X/5/4/38#B21-cryptography-05-00038)\], which is based on one-time signatures (e.g., the Lamport signature scheme) and uses a binary hash tree (Merkle tree). The MSS is resistant to quantum computer algorithms. More details can be found in this survey on hash-based schemes Butin (2017) \[[**22**](https://www.mdpi.com/2410-387X/5/4/38#B22-cryptography-05-00038)\]. Sphincs+ hash-based signature \[[**23**](https://www.mdpi.com/2410-387X/5/4/38#B23-cryptography-05-00038)\] is chosen as an alternate solution in the outcome of the third round of the NIST standardization process \[[**24**](https://www.mdpi.com/2410-387X/5/4/38#B24-cryptography-05-00038)\].

#### 3.1.2. Code-Based Cryptography

Code-based cryptography \[[**25**](https://www.mdpi.com/2410-387X/5/4/38#B25-cryptography-05-00038),[**26**](https://www.mdpi.com/2410-387X/5/4/38#B26-cryptography-05-00038)\] has its security relying on the hardness of problems from coding theory, for example, syndrome decoding (SD) and learning parity with noise (LPN). These cryptosystems are based on error-correcting codes to construct a one-way function. The security is based on the hardness of decoding a message which contains random errors and recovering the code structure. A classic McEliece code-based encryption scheme \[[**5**](https://www.mdpi.com/2410-387X/5/4/38#B5-cryptography-05-00038)\] is chosen as a finalist scheme in the outcome of the third round of the NIST standardization process \[[**24**](https://www.mdpi.com/2410-387X/5/4/38#B24-cryptography-05-00038)\].

#### 3.1.3. Multivariate Cryptography

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*Originally published on [Untitled](https://paragraph.com/@0x2ceb41136b608cefdc7e524775b2adc6ce8ddf96/post-quantum-cryptography)*