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Drawback of code-based public-key cryptosystems is that their public-key size is large. It takes some hundreds KB to some MB for typical parameters. While several attempts have been conducted to reduce it, most of them have failed except one, which is Quasi-Dyadic (QD) public-key (for large extention degrees). Public-key Cryptosystems (PKCs) can be divided into the categories shown in Fig. 1 and 2, respectively. Almost all of the currently deployed ones are based only on a small class of hard problems, namely Integer Factoring Problem (IFP) or Discrete Logarithm Problem (DLP). They are referred to as number theoretic problems. The number theoretic problem based PKCs have the following disadvantages that should be solved in short term and long term, respectively.
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