Breaking public key cryptosystem based on systems of nonlinear equations over finite field

1991 ◽  
Vol 27 (13) ◽  
pp. 1121
Author(s):  
R.F. Sewell
Keyword(s):  
Finite Field ◽  
Nonlinear Equations ◽  
Public Key ◽  
Systems Of Nonlinear Equations ◽  
Public Key Cryptosystem

A public-key cryptosystem based on the difficulty of solving a system of nonlinear equations

1988 ◽  
Vol 19 (2) ◽  
pp. 10-18 ◽  
Author(s):  
Shigeo Tsujii ◽  
Toshiya Itoh ◽  
Atsushi Fujioka ◽  
Kaoru Kurosawa ◽  
Tsutomu Matsumoto
Keyword(s):  
Nonlinear Equations ◽  
Public Key ◽  
System Of Nonlinear Equations ◽  
Public Key Cryptosystem

Public-key cryptosystem based on the difficulty of solving a system of nonlinear equations

1987 ◽  
Vol 23 (11) ◽  
pp. 558-560 ◽  
Author(s):  
S. Tsujii ◽  
T. Itoh ◽  
A. Fujioka ◽  
K. Kurosawa ◽  
T. Matsumoto
Keyword(s):  
Nonlinear Equations ◽  
Public Key ◽  
System Of Nonlinear Equations ◽  
Public Key Cryptosystem

scholarly journals A Public Key Cryptosystem Using a Group of Permutation Polynomials

2020 ◽  
Vol 77 (1) ◽  
pp. 139-162
Author(s):  
Rajesh P. Singh ◽  
Bhaba K. Sarma ◽  
Anupam Saikia
Keyword(s):  
Finite Field ◽  
Public Key ◽  
Permutation Polynomials ◽  
Public Key Cryptosystem ◽  
Encryption Scheme ◽  
Public Key Cryptosystems ◽  
Polynomials Over Finite Fields ◽  
Cyclic Shifts ◽  
Trapdoor Function ◽  
Multivariate Public Key

AbstractIn this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field Fqm. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m2+3m – 4 left cyclic shifts, 5m2 +3m + 4 xor operations and 7 permutations on bits for decryption.

A New Public Key Cryptographic Scheme

2013 ◽  
Vol 303-306 ◽  
pp. 1944-1947
Author(s):  
Feng Yuan ◽  
Hai Wen Ou ◽  
Sheng Wei Xu
Keyword(s):  
Finite Field ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Prime Characteristic ◽  
New Public ◽  
Multivariate Public Key ◽  
Cryptographic Scheme

The multivariate public key cryptosystem is a new and fast public key cryptosystem. This paper presents a multivariate public key cryptographic scheme over a finite field with odd prime characteristic. The idea of embedding and layering is manifested in its construction. The security of the scheme is analyzed in detail. The result indicates that the proposed scheme can resist all known attacks effectively.

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