11 research outputs found
TOT, a Fast Multivariate Public Key Cryptosystem with Basic Secure Trapdoor
In this paper, we design a novel one-way trapdoor function, and then propose a new multivariate public key cryptosystem called , which can be used for encryption, signature and authentication. Through analysis, we declare that is secure, because it can resist current known algebraic attacks if its parameters are properly chosen. Some practical implementations for are also given, and whose security level is at least . The comparison shows that is more secure than , and (when and , is still secure), and it can reach almost the same speed of computing the secret map by and (even though was broken, its high speed has been affirmed)
Enhanced STS using Check Equation --Extended Version of the Signature scheme proposed in the PQCrypt2010--
We propose solutions to the problems which has been left in the Enhanced STS, which was proposed in the PQCrypto 2010.
Enhanced STS signature scheme is dened as the public key with the Complementary STS structure, in which two STS public keys are symmetrically joined together. Or, the complementary STS is the public key where simply two STS public keys are joined together, without the protection with Check Equation.
We discuss the following issues left in the Enhanced STS, which was prosented in the PQCrypt2010:
(i) We implied that there may exist a way to cryptanalyze the Complementary STS structure. Although it has been proposed that the system be protected by Check Equations [35][37], in order to cope with an unknown attack, we did not show the concrete procedure. We show the actual procedure to cryptanalyze it and forge a signature.
(ii) We assumed that the Check Equation should be changed every time a document is signed. This practice is not always allowed. We improved this matter. The Check Equation which was proposed in the PQCrypto 2010 dened the valid life as a function of the number of times the documents are signed, because the secret key of Check Equation is analyzed by collecting valid signatures.
Now we propose a new method of integrating the Check Equation into the secret key and eliminate the risk of the hidden information drawn from the existing signature
Proposal of a Signature Scheme based on STS Trapdoor
A New digital signature scheme based on Stepwise Triangular Scheme (STS) is proposed. The proposed trapdoor has resolved the vulnerability of STS and secure against both Gröbner Bases and Rank Attacks. In addition, as a basic trapdoor, it
is more efficient than the existing systems. With the efficient implementation, the Multivariate Public Key Cryptosystems (MPKC) signature public key has the signature
longer than the message by less than 25 %, for example
PUBLIC KEY CRYPTOGRAPHY USING PERMUTATION P-POLYNOMIALS OVER FINITE FIELDS
In this paper we propose an efficient multivariate
public key cryptosystem based on permutation p-polynomials over
finite fields. We first characterize a class of permutation
p-polynomials over finite fields and then construct a
trapdoor function using this class of permutation p-polynomials.
The complexity of encryption in our public key cryptosystem is
multiplication which is equivalent to other
multivariate public key cryptosystems. However the decryption is
much faster than other multivariate public key cryptosystems. In
decryption we need left cyclic shifts and
xor operations
MI-T-HFE, a New Multivariate Signature Scheme
In this paper, we propose a new multivariate signature scheme named MI-T-HFE as a competitor of QUARTZ. The core map of MI-T-HFE is of an HFEv type but more importantly has a specially designed trapdoor. This special trapdoor makes MI-T-HFE have several attractive advantages over QUARTZ. First of all, the core map and the public map of MI-T-HFE are both surjective. This surjectivity property is important for signature schemes because any message should always have valid signatures; otherwise it may be troublesome to exclude those messages without valid signatures. However this property is missing for a few major signature schemes, including QUARTZ. A practical parameter set is proposed for MI-T-HFE with the same length of message and same level of security as QUARTZ, but it has smaller public key size, and is more efficient than (the underlying HFEv- of) QUARTZ with the only cost that its signature length is twice that of QUARTZ
Nonlinear Piece In Hand Perturbation Vector Method for Enhancing Security of Multivariate Public Key Cryptosystems
Abstract. The piece in hand (PH) is a general scheme which is applicable to any reasonable type of multivariate public key cryptosystems for the purpose of enhancing their security. In this paper, we propose a new class PH method called NLPHPV (NonLinear Piece in Hand Perturbation Vector) method. Although our NLPHPV uses
similar perturbation vectors as is used for the previously known internal perturbation method, this new method can avoid redundant repetitions in decryption process. With properly chosen parameter sizes, NLPHPV achieves an observable gain in security from the original multivariate public key cryptosystem. We demonstrate these by both theoretical analyses and computer simulations against major known attacks and provides the concrete sizes of security parameters, with which we even expect the grater security against potential quantum attacks
Two-Face: New Public Key Multivariate Schemes
We present here new multivariate schemes that can be seen as HFE generalization having a property called `Two-Face\u27.
Particularly, we present five such families of algorithms named `Dob\u27, `Simple Pat\u27, `General Pat\u27, `Mac\u27, and `Super Two-Face\u27. These families have connections between them, some of them are refinements or generalizations of others. Notably, some of these schemes can be used for public key encryption, and some for public key signature. We introduce also new multivariate quadratic permutations that may have interest beyond cryptography
Security Enhancement of Various MPKCs by 2-layer Nonlinear Piece In Hand Method
Following the last proposal of the nonlinear Piece in Hand method, which has 3-layer structure, 2-layer nonlinear Piece in Hand method is proposed. Both of them aim at enhancing the security of existing and future multivariate public key cryptosystems. The new nonlinear Piece in Hand is compared with the 3-layer method and PMI+, which was proposed by Ding, et al
Linearity Measures for MQ Cryptography
We propose a new general framework for the security of multivariate quadratic (\mathcal{MQ}) schemes with respect to attacks that exploit the existence of linear subspaces. We adopt linearity measures that have been used traditionally to estimate the security of symmetric cryptographic primitives, namely the nonlinearity measure for vectorial functions introduced by Nyberg at Eurocrypt \u2792, and the --linearity measure introduced recently by Boura and Canteaut at FSE\u2713. We redefine some properties of \mathcal{MQ} cryptosystems in terms of these known symmetric cryptography notions, and show that our new framework is a compact generalization of several known attacks in \mathcal{MQ} cryptography against single field schemes. We use the framework to explain various pitfalls regarding the successfulness of these attacks. Finally, we argue that linearity can be used as a solid measure for the susceptibility of \mathcal{MQ} schemes to these attacks, and also as a necessary tool for prudent design practice in \mathcal{MQ} cryptography
Proposal of PPS Multivariate Public Key Cryptosystems
In this paper we propose a new MPKC, called PPS, based on (i) the 2-layer nonlinear piece in hand method, (ii) PMI, and (iii) STS. The PPS is a specific MPKC obtained by applying the 2-layer nonlinear piece in hand method to STS, in the manner that the rank and randomness of the lower rank steps in the original secret polynomial
vector of STS are enhanced by adding a perturbation polynomial vector and moreover PMI is used in the auxiliary part. The PPS overcomes the drawbacks of the three schemes by the advantage of the three schemes themself. Thus, PPS can be thought to be immune simultaneously from the algebraic attacks, such as the Groebner bases
attacks, from the rank attacks, and from the differential attacks