ON THE POLYNOMIAL MULTIPLICATION ALGORITHMS FOR POST-QUANTUM CRYPTOGRAPHY

Fidan Nuriyeva

Makale detayları

ON THE POLYNOMIAL MULTIPLICATION ALGORITHMS FOR POST-QUANTUM CRYPTOGRAPHY

Yazarlar:

Fidan Nuriyeva

Yayıncı:

Karabuk University

Ana Başlıklar:

Cryptography

Dergi:

Current Trends in Computing Vol.2 Issue 2, pp.96-107

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001338882

pISSN:

2980-3152

Anahtar kelimeler:

Özet:

 Lattice-based systems work on polynomial rings. In post-quantum cryptography, polynomial rings of large degree are used to increase security. Among the operations performed on polynomial rings, the most time-consuming operation is multiplication. Therefore, various multiplication algorithms have been proposed to optimize the efficiency of newly developed systems. These algorithms generally aim to reduce the number of multiplications. Thus, the efficiency and cost of the systems are optimized. In this study, Toom-Cook, Karatsuba, NTT, TMVP algorithms are analyzed. Information about the number of reductions in multiplication numbers, their time complexity and the benefits they provide in systems are given. Bruun algorithm, which can be an alternative to the frequently used multiplication algorithms, is described in the method section. Among the polynomial multiplication algorithms, the NTT algorithm is considered to be the most efficient, so we have investigated its potential to increase efficiency. However, it is obvious that within certain criteria, TMVP and Bruun algorithm will provide an effective multiplication reduction in the system.

 Lattice-based systems work on polynomial rings. In post-quantum cryptography, polynomial rings of large degree are used to increase security. Among the operations performed on polynomial rings, the most time-consuming operation is multiplication. Therefore, various multiplication algorithms have been proposed to optimize the efficiency of newly developed systems. These algorithms generally aim to reduce the number of multiplications. Thus, the efficiency and cost of the systems are optimized. In this study, Toom-Cook, Karatsuba, NTT, TMVP algorithms are analyzed. Information about the number of reductions in multiplication numbers, their time complexity and the benefits they provide in systems are given. Bruun algorithm, which can be an alternative to the frequently used multiplication algorithms, is described in the method section. Among the polynomial multiplication algorithms, the NTT algorithm is considered to be the most efficient, so we have investigated its potential to increase efficiency. However, it is obvious that within certain criteria, TMVP and Bruun algorithm will provide an effective multiplication reduction in the system.

 Lattice-based systems work on polynomial rings. In post-quantum cryptography, polynomial rings of large degree are used to increase security. Among the operations performed on polynomial rings, the most time-consuming operation is multiplication. Therefore, various multiplication algorithms have been proposed to optimize the efficiency of newly developed systems. These algorithms generally aim to reduce the number of multiplications. Thus, the efficiency and cost of the systems are optimized. In this study, Toom-Cook, Karatsuba, NTT, TMVP algorithms are analyzed. Information about the number of reductions in multiplication numbers, their time complexity and the benefits they provide in systems are given. Bruun algorithm, which can be an alternative to the frequently used multiplication algorithms, is described in the method section. Among the polynomial multiplication algorithms, the NTT algorithm is considered to be the most efficient, so we have investigated its potential to increase efficiency. However, it is obvious that within certain criteria, TMVP and Bruun algorithm will provide an effective multiplication reduction in the system.

 Lattice-based systems work on polynomial rings. In post-quantum cryptography, polynomial rings of large degree are used to increase security. Among the operations performed on polynomial rings, the most time-consuming operation is multiplication. Therefore, various multiplication algorithms have been proposed to optimize the efficiency of newly developed systems. These algorithms generally aim to reduce the number of multiplications. Thus, the efficiency and cost of the systems are optimized. In this study, Toom-Cook, Karatsuba, NTT, TMVP algorithms are analyzed. Information about the number of reductions in multiplication numbers, their time complexity and the benefits they provide in systems are given. Bruun algorithm, which can be an alternative to the frequently used multiplication algorithms, is described in the method section. Among the polynomial multiplication algorithms, the NTT algorithm is considered to be the most efficient, so we have investigated its potential to increase efficiency. However, it is obvious that within certain criteria, TMVP and Bruun algorithm will provide an effective multiplication reduction in the system.

Makale detayları

ON THE POLYNOMIAL MULTIPLICATION ALGORITHMS FOR POST-QUANTUM CRYPTOGRAPHY

Yazarlar:

Fidan Nuriyeva

Yayıncı:

Karabuk University

Ana Başlıklar:

Cryptography

Dergi:

Current Trends in Computing Vol.2 Issue 2, pp.96-107

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001338882

pISSN:

2980-3152

Lattice-based cryptography

Polynomial multiplication algorithms

Number theoretic transform

Bruun algorithm

Sayı

Makale detayları

ON THE POLYNOMIAL MULTIPLICATION ALGORITHMS FOR POST-QUANTUM CRYPTOGRAPHY

Yazarlar: Fidan Nuriyeva

Yayıncı: Karabuk University

Ana Başlıklar: Cryptography

Dergi: Current Trends in Computing Vol.2 Issue 2, pp.96-107

Belge Tipi: Makale

Yayın Tarihi: 1/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001338882

pISSN: 2980-3152

Lattice-based cryptography

Polynomial multiplication algorithms

Number theoretic transform

Bruun algorithm

Sayı

Yazarlar:

Fidan Nuriyeva

Yayıncı:

Karabuk University

Ana Başlıklar:

Cryptography

Dergi:

Current Trends in Computing Vol.2 Issue 2, pp.96-107

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001338882

pISSN:

2980-3152