Side-Channel Leakage Analysis of Inner Product Masking

The Inner Product Masking(IPM)scheme has been shown to provide higher theoretical security guarantees than the BooleanMasking(BM).This scheme aims to increase the algebraic complexity of the coding to achieve a higher level of security.Some previous work unfolds when certain(adversarial and implementation)conditions are met,and we seek to complement these investigations by understanding what happens when these conditions deviate from their expected behaviour.In this paper,we investigate the security characteristics of IPM under different conditions.In adversarial condition,the security properties of first-order IPMs obtained through parametric characterization are preserved in the face of univariate and bivariate attacks.In implementation condition,we construct two new polynomial leakage functions to observe the nonlinear leakage of the IPM and connect the security order amplification to the nonlinear function.We observe that the security of IPMis affected by the degree and the linear component in the leakage function.In addition,the comparison experiments from the coefficients,signal-to-noise ratio(SNR)and the public parameter show that the security properties of the IPM are highly implementation-dependent.

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.

ON APPROXIMATELY(p,q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES

We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.

Intuitionistic Menger inner product spaces and applications to integral equations

In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.

Self-dual Codes with Symplectic Inner Product

In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.

Some Results on Reverses of Cauchy-Schwarz Inequality in Inner Product Spaces

Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz’s inequality is provided. The results obtained in the paper complement and improve some recent work about this topic.

Fixed Point Theorems in Fuzzy Inner Product Spaces

In this paper,we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.

Inner Product Laplacian Embedding Based on Semidefinite Programming

This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.

On Linearly Topological Structure and Orthogonality of Menger Probabilistic Inner Product Spaces

In this paper the linearly topological structure of Menger Probabilistic inner product space is discussed. In virtue of these, some more general convergence theorems, Pythagorean theorem, and the orthogonal projective theorem are established.

Rolling With Simplified Stream Function Velocity and Strain Rate Vector Inner Product

The dual-stream function velocity field is reduced in order to analyze two-dimensional plate broadside roll- ing in roughing. The strain rate vector inner product and integral mean value theorem, as well as coqine vector inner product are used respectively in plastic deformation power, friction losses and shear power. A theoretical solution of roll torque and separating force for the rolling is obtained and the calculated results by the solution are compared with those measured in broadside rolling on-line. It shows that both the force and torque calculated are higher than those of measured, but the maximum relative error between them is no more than 11%.

CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ：B（H） →B（K） satisfies φ（AB^＋ ＋ B^＋A） = φ（A）φ（B）^＋ ＋ φ（B）^＋φ（A） for every pair A, B ∈ B（H） if and only if either φ（A） = cUAU^＋ for all A or φ（A） = cUA^＋U^＋ for all A; φ satisfies φ（AB^＋A） = φ;（A）φ;（B）^＋φ;（A） for every pair A, B ∈ B（H） if and only if either φ（A） = UAV for all A or φ（A） = UA^＋V for all A, where At denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U^tU = c^-1I and V^＋V = cI for some nonzero real number c.

A critical case of Rallis inner product formula

Letπbe a genuine cuspidal representation of the metaplectic group of rank n.We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n+1.We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central value of the Langlands L-function ofπtwisted by a character.The bulk of this paper focuses on proving a case of regularised Siegel-Weil formula,on which the Rallis inner product formula is based and whose proof is missing in the literature.

Efficient functional encryption for inner product with simulation-based security

Functional encryption(FE)is a novel paradigm for encryption scheme which allows tremendous flexibility in accessing encrypted information.In FE,a user can learn specific function of encrypted messages by restricted functional key and reveal nothing else about the messages.Inner product encryption(IPE)is a special type of functional encryption where the decryption algorithm,given a ciphertext related to a vector x and a secret key related to a vector y,computes the inner product x·y.In this paper,we construct an efficient private-key functional encryption(FE)for inner product with simulation-based security,which is much stronger than indistinguishability-based security,under the External Decisional Linear assumption in the standard model.Compared with the existing schemes,our construction is faster in encryption and decryption,and the master secret key,secret keys and ciphertexts are shorter.

Inner product encryption from ring learning with errors

The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks.Unfortunately,the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large,which makes the algorithm inefficient.Therefore,we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al.[Asiacrypt 2011],and its security relies on the difficulty assumption of ring learning with errors.Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.

Inner product encryption from ring learning with errors

The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks.Unfortunately,the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large,which makes the algorithm inefficient.Therefore,we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al.[Asiacrypt 2011],and its security relies on the difficulty assumption of ring learning with errors.Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.

Efficient functional encryption for inner product with simulation-based security

Functional encryption(FE)is a novel paradigm for encryption scheme which allows tremendous flexibility in accessing encrypted information.In FE,a user can learn specific function of encrypted messages by restricted functional key and reveal nothing else about the messages.Inner product encryption(IPE)is a special type of functional encryption where the decryption algorithm,given a ciphertext related to a vector x and a secret key related to a vector y,computes the inner product x·y.In this paper,we construct an efficient private-key functional encryption(FE)for inner product with simulation-based security,which is much stronger than indistinguishability-based security,under the External Decisional Linear assumption in the standard model.Compared with the existing schemes,our construction is faster in encryption and decryption,and the master secret key,secret keys and ciphertexts are shorter.

Solution for slab forging with bulge between two parallel platens by strain rate vector inner-product integration and series expansion

A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second, a summation process of term by term integrated results and a formula of the bulging were introduced, and an analytical solution of stress effective factor was obtained. It is proved that the expression of power by the above linear integration is the same as that of traditional immediate integration. Also, the solution was simplified by series expansion and compared by slab forging test with the others. It turns out that the calculated result of total forging pressure is basically in agreement with measured value in the actual press test.

An Inner Product Encryption Scheme Based on Dual Systems

The inner product encryption scheme can achieve fine-grained access control on ciphertext. For the problem that the existing inner product encryption scheme has poor security and low decryption efficiency, this paper proposes an inner product encryption scheme with adaptive security based on the dual system encryption method. The scheme is based on bilinear mapping on prime order groups. In the secret key generation algorithm of the scheme, we propose a sharing technique of random vectors and generate a secret key for each component of the attribute vector. And an encryption algorithm with a constant size ciphertext is designed. Under the k-Lin assumption, the method of the experimental sequence is used to prove that the scheme is adaptively secure. The decryption algorithm of the scheme requires only six bilinear pairs. Compared with the existing schemes, the decryption efficiency has been greatly improved.

Inner-product of strain rate vector through direction cosine in coordinates for disk forging

A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined by the ratio of coordinate increments.Furthermore,inner-product of the vector for plastic power was term integrated by term and summed.Thereafter,through a formula for determination of bulge an analytical solution of stress effective factor was obtained.Finally,through compression tests,the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine.It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%.However,when the reduction gets up to 25.34% and 33.12%,the corresponding errors between the calculated and measured results also get up to 6% and 13.5%,respectively.