<![CDATA[Commutative public key cryptosystems are vulnerable to quantum algorithm attacks. For this reason, experts have developed a public key cryptography system that involves matrix algebra with non-commutative multiplication operations. In addition, there is the NTRU public key cryptosystem, which is claimed to be not vulnerable to quantum algorithm attacks. The NTRU system works on a truncated polynomial ring so the resulting key length will be difficult to guess. In addition, encryption and description in NTRU are very fast compared to RSA, ElGamal and ECC because NTRU only involves polynomial multiplication. Researchers have formed a modified public key cryptosystem using a singular matrix in previous research. This study uses non-commutative algebra and a matrix that has no inverse. For this reason, in this study, researchers adopted polynomials in the NTRU public key cryptographic system so that the resulting key length is difficult to predict. The researcher changed the matrix entries in the form of integers into polynomial entries. Meanwhile, the singular matrix entry remains a ring matrix over integers. The results show that the proposed system produces polynomials whose length cannot be guessed, so a brute-force attack is tricky. Apart from that, this system is superior to NTRU because it does not use the inverse principle. If in NTRU, the resulting polynomial does not have an inverse, then another polynomial must be found and repeated until the step is successful.]]>
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