# Evaluating the Efficiency of Physical and Cryptographic Security Solutions for Quantum Immune IoT
## 3 Quantum Immune Security Solutions
### Quantum Immune Cryptography
\begin{table}
\begin{tabular}{p{56.9 pt} p{341.4 pt}} \hline \hline
**Approach** & **Description** \\ \hline \multirow{4}{*}{**Lattice-based**} & The strength of the lattice cryptography is based on difficulty of some lattice problems, e.g., the problems of finding the closest or shortest vector in the agreed lattice. \\  & Algorithms include NTRU/NTRUEncrypt for encryption, Bimodal Lattice Signature Scheme (BLISS) for signatures, and Learning with Errors (LWE) algorithms for key exchange. The approaches have been considered energy efficient [31]. \\ \hline \multirow{4}{*}{**Multivariate**} & Multivariate cryptography is based on the hardness of solving multivariate quadratic equations over a finite field. The problem has been proved to be non-deterministic polynomial-time (NP)-hard. The proposed algorithms include Tame Transformation Signatures (TTS), Rainbow, and Hidden Fields Equations (HFE). The multivariate approaches have been considered energy efficient [31]. \\ \hline \multirow{2}{*}{**Supersingular elliptic curve** **isogeny**} & Supersingular elliptic curve isogeny cryptography provides a variant of the Diffie–Hellman algorithm that uses supersingular elliptic curves. The approach can achieve compact key sizes [32] and is therefore suitable for devices with memory/bandwidth limitations (but with sufficient battery/processing capabilities). \\ \hline \multirow{4}{*}{**Code-based**} & Code-based schemes, such as [PERSON]’s [33], encrypt messages into codewords with added errors in such a way that only the private key holder can recover the original message without errors. The schemes require transmission of large keying material. \\ \hline \multirow{4}{*}{**Symmetric**} & To compensate for the threat of accelerated brute-force by [PERSON]’s algorithm, the key sizes used in existing symmetric algorithms must be doubled. As a consequence, symmetric algorithms will become more expensive in the way of memory requirements, processing costs, and speed, as well as energy consumption. For example, some estimates [34] indicate that the doubling of the Advanced Encryption Standard (AES) key size from 128 to 256 bits increases costs by 20%. \\ \hline \multirow{4}{*}{**Hash-based**} & To address the threat of [PERSON]’s algorithm, the output sizes of hash functions must be enlarged. Increasing the outputs from 254 to 512 bits has a negligible impact on the energy consumption of the CPUs [35]. There will, however, be some extra costs from increased transmissions. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Categories of quantum immune cryptography. been integrated into the Google Chrome browser [40]. Recent variations of the protocol include HILA5 [41] that optimizes error-correction functions. It is based on NewHope, but is slightly more versatile as it can also be used for encryption as well as key exchange. It has almost the same performance characteristics as NewHope. * Frodo [6] is based on the LWE problem that uses generic lattices. Frodo avoids the ring structure (of ideal lattices) that may contain some vulnerabilities. Instead, it uses generic lattices with some efficiency side effects. More specifically, the latency of TLS handshake increases 1.3\(\times\) in Frodo [39] when compared with classical Elliptic Curve Diffie-Hellman or 1.5\(\times\) when compared with NewHope. [39] Frodo utilizes different optimization techniques: communication bandwidth optimization, dynamic generation of public parameters, and carefully chosen error distribution. The hardness of lattice-based security is actively studied by the research community. All the attack vectors and vulnerabilities may not be known as the field is still relatively young. Efficient algorithms and implementations are still needed to demonstrate the secrecy and feasibility of lattice-based security approaches.