Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

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

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

Hidden Pair of Bijection Signature Scheme

A new signature system of multivariate public key cryptosys- tem is proposed. The new system, Hidden Pair of Bijection (HPB), is the advanced version of the Complementary STS system. This system real- ized both high security and quick signing. Experiments showed that the cryptanalysis of HPB by Gröbner bases has no less complexity than the random polynomial systems. It is secure against other way of cryptanalysis effective for Complementary STS. On the other hand, since it is based on bijections, signatures exist for any message, unlike other cryptosystems based on non-bijections such as HFE or Unbalanced Oil and Vinegar

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

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

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

Analysis of Intermediate Field Systems

We study a new generic trapdoor for public key multivariate cryptosystems, called IFS for Intermediate Field Systems, which can be seen as dual to HFE. This new trapdoor relies on the possibility to invert a system of quadratic multivariate equations with few (logarithmic with respect to the security parameter) unknowns on an intermediate field thanks to Groebner bases algorithms. We provide a comprehensive study of the security of this trapdoor and show that it is equivalent to the security provided by HFE. Therefore, while insecure in its basic form, this trapdoor may reveal quite attractive when used with, e.g., the minus modifier

On historical Multivariate Cryptosystems and their restorations as instruments of Post-Quantum Cryptography

The paper presents a short survey of the History of Multivariate Cryptography together with the usage of old broken multivariate digital signatures in the new protocol based cryptosystems constructed in terms of Noncommutative Cryptography. The general schemes of New cryptosystems is a combinations of Eulerian maps and quadratic maps with their trapdoor accelerators, which are pieces of information such than the knowledge of them allow to compute the reimages in a polynomial time. These schemes are illustrated by historical examples of Imai – Matsumoto multivariate digital signatures schemes and Unbalanced Oil and Vinegar Cryptosystems