Construction of A New Class of Linear Multivariate Public Key Cryptosystem, K(I)SE(1)PKC

In this paper, we present a new class of linear multivariate PKC referred to as K(I)SE(1)PKC. We shall show that K(I)SE(1)PKC, a linear multivariate PKC, can be sufficiently secure against any linear transformation attack due to the probabilistic structure. We show that the probabilistic structure can be successfully introduced by the use of the Chinese Remainder Theorem

A New Class of Multivariate Public Key Cryptosystem Constructed on the Basis of Message-Dependent Transformation

In this paper, a new class of Public-Key Cryptosystem(PKC) based on Random Simultaneous Equation of degree g(RSE(g)PKC) is presented. The proposed scheme uses a new class of trap-doors based on two classes of transformation, i.e. random transformation and message-dependent random transformation. For constructing the proposed scheme,random transformations X and Ψ are used. The transformation Ψ would yield a breakthrough to a field of multivaliate cryptosystem in a sense that the transformation is dependent on a message. Namely it is a message-dependent transformation on the basis of random coding. We show that the proposed PKC’s, can be secure against the various excellent attacks such as the attack based on the Gr¨obner bases calculation(Gröbner bases attack, GB attack), Patarin’s attack and Braeken-Wolf-Preneel attack, due to the random transformations using new trap-doors

Forgotten Secret Recovering Scheme and Fuzzy Vault Scheme Constructed Based on Systematic Error-Correcting Codes

In this paper, we revisit the Forgotten Secret Recovering Scheme for $k$ users, referred to as FSRS($k$) previously proposed by the present author. FSRS($k$) takes advantage of the fact that Reed-Solomon code used in FSRS($k$) is constructed in a form of systematic code. We show that a particular class of FSRS($k$), FSRS($1$), can be successfully applied to the various cryptoscheme including Fuzzy Vault Scheme (FVS)

Public Key Cryptosystems Constructed Based on Random Pseudo Cyclic Codes, K(IX)SE(1)PKC, Realizing Coding Rate of Exactly 1.0

In this paper, we present a new class of public-key cryptosystems, K(IX)SE(1)PKC realizing the coding rate of exactly 1.0, based on random pseudo cyclic codes. We show that K(IX)SE(1)PKC is secure against the various attacks including the attack based on the Gröbner bases calculaion (GB attack)

New Classes of Public Key Cryptosystems over F28F_2^8 Constructed Based on Reed-Solomon Codes, K(XVII)SE(1)PKC and K(XVII)ΣΠ\Sigma \PiPKC

In this paper, we present new classes of public key cryptosystem over $F_2^8$ based on Reed-Solomon codes, referred to as K(XVII)SE(1)PKC and K(XVII)$\Sigma \Pi$PKC, a subclass of K(XVII)SE(1)PKC. We show that K(XVII)SE(1)PKC over $F_2^8$ can be secure against the various attacks. We also present K(XVII)$\Sigma \Pi$PKC over $F_2^8$, a subclass of K(XVII)SE(1)PKC. We show that any assertion of successfull attack on K(XVII)SE(1)PKC including K(XVII)$\Sigma \Pi$PKC whose parameters are properly chosen is a coding theoretical contradiction. We thus conclude that K(XVII)SE(1)PKC and K(XVII)$\Sigma \Pi$PKC would be secure against the various attacks including LLL attack. The schemes presented in this paper would yield brand-new techniques in the field of code-based PKC

A New Class of Multivariate Public Key Cryptosystems Constructed Based on Random Pseudo Cyclic Codes, K(XIII)SE(2)PKC, Realizing Coding Rate of Exactly 1.0

In this paper, we present a new class of multivariate public-key cryptosystems, K(XIII)SE(2)PKC realizing the coding rate of exactly 1.0, based on random pseudo cyclic codes. The K(XIII)SE(2)PKC is constructed on the basis of K(IX)SE(1)PKC, formerly presented by the author. We show that K(XIII)SE(2)PKC is secure against the various attacks including the attack based on the Gröbner bases calculaion(GB attack) and the rank attack

Presentation of a new class of public key cryptosystems K(XIII)SE(1)PKC along with Kp(XIII)SE(1)PKC that realizes the coding rate of exactly 1.0, constructed by modifying K(XII)SE(1)PKC.

In this paper, we present a new class of public key cryptosystems by modifying K(XII)SE(1)PKC[1], referred to as K(XIII)SE(1)PKC, and a particular class of K(XIII)SE(1)PKC, Kp(XIII)SE(1)PKC. We show that K(XIII)SE(1)PKC would improve both the coding rate and the security, compared with K(XII)SE(1)PKC. We also show that Kp(XIII)SE(1)PKC realizes the coding rate of exactly 1.0. In a sharp contrast with the conventional code based PKC (CB･PKC) that uses Goppa code, in K(XII)SE(1)PKC, K(XIII)SE(1)PKC and Kp(XIII)SE(1)PKC, we do not care for the security of the primitive polynominal that generates the Reed-Solomon code

A New Class of Public Key Cryptosystems Constructed Based on Reed-Solomon Codes, K(XII)SE(1)PKC.-- Along with a presentation of K(XII)SE(1)PKC over the extension field extensively used for present day various storage and transmission systems --

In this paper, we present a new class of public key cryptosystem based on Reed-Solomon codes, a member of the code based PKC(CBPKC), referred to as K(XII)SE(1)PKC. We show that K(XII)SE(1)PKC can be secure against the various attacks. Particularly we present a member of K(XII)SE(1)PKC constructed based on the Reed-Solomon code over the extension field, which is extensively used in the present day storage systems and the various digital transmission systems. In a sharp contrast with the conventional CBPKC that uses Goppa code, in K(XII)SE(1)PKC, we do not care for the security of the primitive polynominal that generates the Reed-Solomon code. The probabilistic scheme presented in this paper would yield a brand-new technique in the field of CBPKC

A New Class of Public Key Cryptosystems Constructed Based on Error-Correcting Codes, Using K(III) Scheme

In this paper, we present a new scheme referred to as K(III) scheme which would be effective for improving a certain class of PKC\u27s. Using K(III) scheme, we propose a new method for constructing the public-key cryptosystems based on error-correcting codes. The constructed PKC is referred to as K(V)SE(1)PKC. We also present more secure version of K(V)SE(1)PKC, referred to as K*(V)SE(1)PKC, using K(I) scheme previously proposed by the present author, as well as K(III) scheme