Showing papers on "Remainder published in 2002"

A DPA Attack against the Modular Reduction within a CRT Implementation of RSA

Abstract: Published DPA attack scenarios against the RSA implementation exploit the possibility of predicting intermediate data during a straight-forward square-multiply exponentiation algorithm. An implementation of RSA using CRT (Chinese Remainder Theorem) prevents the pre-calculation of intermediate results during the exponentiation algorithm by an attacker. In this paper, we present a DPA attack that uses byte-wise hypotheses on the remainder after the modular reduction with one of the primes. Instead of using random input data this attack uses k series of input data with an equidistant step distance of 1, 256, (256)2,.., (256)k. The basic assumption of this DPA attack named MRED ("Modular Reduction on Equidistant Data") is that the distance of the input data equals the distance of the intermediate data after the modular reduction at least for a subgroup of single measurements. A function Fk that is composed of the k DPA results is used for the approximation of a multiple of the prime. Finally the gcd gives the prime. The number of DPA calculations increases linear to the number of bytes of the prime to be attacked. MRED is demonstrated using simulated measurement data. The practical efficiency is assessed. If the applicability of this attack is limited due to padding formats in RSA signature applications, the least significant bytes of the remainder after the modular reduction step can still be revealed. Multiplicative message blinding can protect the reduction modulo a secret prime against MRED.

Dct compression using golomb-rice coding

Abstract: An apparatus and method (600) for encoding quantized frequency represented data, the data comprising zero and non-zero represented data is claimed. For zero represented data, a zero run length is determined. A Golomb parameter is determined as a function of the zero run length. A quotient is encoded as a function of the zero run length and the Golomb parameter. A remainder is encoded as a function of the zero run length, the Golomb parameter and the quotient. The coded quotient and the coded remainder are concatenated. For non-zero represented data, the nonzero data is encoded as a function of the non-zero data value and the sign of the non-zero data value.

Mapping addresses to memory banks based on at least one mathematical relationship

Abstract: One embodiment of the invention is a memory controller that maps a received address to a memory location in a plurality of memory banks, the memory controller comprising: circuitry for calculating a remainder from a division of the received address by a divisor, wherein the divisor is based on the number of the plurality of banks; circuitry for determining a particular bank of the plurality of banks based on the remainder and at least one bit of the received address; and circuitry for determining the memory location in the particular bank using at least a portion of the received address

Method and system for using modulo arithmetic to distribute processing over multiple processors

Abstract: A method, system, apparatus, and computer program product are presented for load balancing amongst a set of processors within a distributed data processing system. To accomplish the load balancing, a modulo arithmetic operation is used to divide a set of data elements from a data source substantially equally among the processors. Each of the processors performs the modulo arithmetic operation substantially independently. At a particular processor, a data element is retrieved from a data source, and the processor calculates a representational integer value for the data element. The processor then calculates a remainder value by dividing the representational integer value by the number of processors in the distributed data processing system. If the remainder value is equal to a predetermined value associated with the processor, then the data element is processed further by the processor.

Separable cyclic redundancy check

Abstract: A method and apparatus for performing a cyclic redundancy check (CRC) process is provided. The CRC is capable of being performed on data received out of order without having to store and assemble the data. One exemplary method for computing a CRC for a transmitted data stream is initiated by performing a CRC process on a first segment of the data stream (214) to generate a first CRC remainder. Next, the first CRC remainder for the first segment is projected (216). Then, the CRC process on a second segment of the data stream (218) is performed to generate a second CRC remainder. Next, the second CRC remainder for the second segment is projected (220). Then, the projected remainders are combined to calculate a complete CRC remainder (222) for the data stream in an order independent fashion.

Generalized Hardy operators and normalizing measures

Abstract: to be bounded from Lo[0 o) to Lq(s) are given Here a(s) and b(s) are similarly ordered functions and k(s,y) satisfies a modified GHO condition Nearly block diagonal decompositions of positive operators are introduced as is the concept of a normalizing measure An application is made to estimates for the remainder in a Taylor approximation

Rigorous image-series expansions of quasi-static Green's functions for regions with planar stratification

Abstract: A novel image-series expansion scheme for quasi-static Green's function in n+1 layered media is obtained by expanding the frequency-dependent Hertz potential in finite expansions and remainder terms. The expansions utilize a unique recursive representation for Green's function, which is a generic characteristic of the stratification, and are explicitly constructed for n/spl les/3. While results for 0/spl les/n/spl les/2 are given for reference only, the expansion scheme for a double-slab configuration, n=3, is quite general and outlines the procedure for n>3, without any increase in the complexity. The expansion-remainder terms can be made negligibly small for sufficiently large summation indices in the quasi-static limit, leading to rigorous image-series expansion. The image-series convergence is accelerated by including a collective image term, representing a closed-form asymptotic evaluation of the series-remainder integral. Thus, the proposed computational procedure can be used as a simple tool for producing analytical data for testing numerical subroutines applied to direct problems such as electrical simulation of muscles in the biomedical field and inverse problems, such as electromagnetic imaging.

Encryption operating apparatus and method having side-channel attack resistance

Abstract: Ciphertext X and a constant C having relationships C>p and C>q with respect to secret keys p and q are input, and correction values C ←dp and C ←dq (dp=d mod (p−1), dq=d mod (q−1)) are obtained. Then, the ciphertext X is multiplied by the constant C. A remainder operation using the secret key p or q as a remainder value is conducted with respect to the multiplication result. A modular exponentiation operation based on a Chinese remainder theorem is conducted with respect to the remainder operation result, and a correction operation using a correction value C ←dp or C ←dq is conducted. Thereafter, plaintext Y before being encrypted is calculated.

Asymptotic analysis of the GI/M/1/n loss system as n increases to infinity

Abstract: This paper provides the asymptotic analysis of the loss probability in the GI/M/1/n queueing system as n increases to infinity. The approach of this paper is alternative to that of the recent papers of Choi and Kim (2000) and Choi et al. (2000) and based on application of modern Tauberian theorems with remainder. This enables us to simplify the proofs of the results on asymptotic behavior of the loss probability of the abovementioned paper of Choi and Kim (2000) as well as to obtain some new results.

Modular exponentiation calculation apparatus and modular exponentiation calculation method

Abstract: A modular exponentiation calculation apparatus obtains a first RNS representation of a value Cpdp×B mod p based on an RNS representation of a remainder value Cp=C mod p and a remainder value dp=d mod (p−1), obtains a second RNS representation of a value Cqdq×B mod q based on an RNS representation of a remainder value Cq=C mod q and a remainder value dq=d mod (p−1), obtains a third RNS representation of an integer m′ congruent with Cd mod (p×q) based on both the first and second RNS representations, and obtains m=Cd mod (p×q) based on a value of the integer m′ obtained by converting the third RNS representation into a binary representation.

Dynamical analysis of ! -Euclidean algorithms

Abstract: We study a class of Euclidean algorithms related to divisions where the remainder is constrained to belong to[! " 1,! ], for some! #[ 0,1]. Thepaper is devoted to the averagecase analysis of these algorithms, in terms of number of steps or bit-complexity. This is a new instance of the so-called “dynamical analysis” method, where dynamical systems are made a deep use of. Here, the dynamical systems of interest have an infinite number of branches and they are not Markovian, so that the general framework of dynamical analysis is more complex to adapt to this case than previously.  2002 Elsevier Science (USA). All rights reserved.

Some integral inequalities involving taylor's remainder. ii

Abstract: In this paper, using Gruss' and Chebyshev's inequalities we prove several inequal- ities involving Taylor's remainder.

A perturbed trapezoid inequality in terms of the fourth derivative

Abstract: Some error estimates in terms of the p-norms of the fourth derivative for the remainder in a perturbed trapezoid formula are given. Applications for the expectation of a random variable and the Hermite-Hadamard divergence in Information Theory are also pointed out.

Two problems associated with convex finite type domains

Abstract: We use scaling properties of convex surfaces of finite line type to derive new estimates for two problems arising in harmonic analysis. For Riesz means associated to such surfaces we obtain sharp $L^p$ estimates for $p>4$, generalizing the Carleson-Sjolin theorem. Moreover we obtain estimates for the remainder term in the lattice point problem associated to convex bodies; these estimates are sharp in some instances involving sufficiently flat boundaries.

Key generation performance improvement

Abstract: A method, apparatus, and article of manufacture provide the ability to rapidly generate a large prime number to be utilized in a cryptographic key of a cryptographic system. A candidate prime number is determined and a mod remainder table is initialized for the candidate prime number using conventional mod operations. If all mod remainder entries in the table are non-zero, the candidate number is tested for primality. If the candidate prime number tests positive for primality, the candidate number is utilized in a cryptographic key of a cryptographic system. If any of the table entries is zero, the candidate number and each mod remainder entry are decremented/incremented. If any mod remainder entry is less than zero or greater than the corresponding prime number, the corresponding prime number is added/subtracted to/from the mod remainder. The process then repeats until a satisfactory number is obtained.

Kernel-Splitting Technique for Enclosing the Solution of Fredholm Equations of the First Kind

Abstract: We derive a numerical method for solving linear Fredholm integral equations of the first kind. Based on series expansion techniques, the kernel of the corresponding integral equation is splitted into a finite rank degenerate part and an infinite dimensional, normwise small remainder. By enclosing the remainder term, the original problem, is transformed into a degenerate set-valued problem. For this problem, we derive a numerical method that provides a rigorous control of approximation and roundoff errors. We show that this approach provides a regularization scheme.

Radio communications terminal

Abstract: PROBLEM TO BE SOLVED: To preferentially enable communication with a communication mode having a large remainder of communication by checking the remainder of communication in each communication mode in a radio communications terminal having plurality of communication modes including a free communication fee by a given call rate. SOLUTION: A portable telephone set 2 has the plurality of communication modes including the free communication fee by the given call rate. A first IC card 212 and a second IC card 213 store the remainder of communication of the communication modes 1, 2, respectively. A processor 203 checks the remainder of communication of the respective communication modes when a user tries calling, and selects the communication mode having a large remainder of communication for calling operation. The processor 203 calculates the communication fee based on the communication by the user to calculate the latest remainder of communication. COPYRIGHT: (C)2004,JPO

The remainder in Weyl's law for random two-dimensional

Abstract: We prove that the average order of the remainder in counting the number of points of a random lattice inside a disc of radius \( \sqrt{\lambda} \)\( {\cal O}(\lambda^{1/4+\epsilon}) \). Our proof is spectral in nature.

Approximating Csiszár f-divergence by the use of Taylor's formula with integral remainder

Abstract: Some approximations of the Csiszár f − divergence by the use of Taylor’s formula and perturbed Taylor’s formula and some applications for Kullback-Leibler distance are given. Mathematics subject classification (2000): 26D15.

Partitioned R-matrix theory

Abstract: The traditional implementation of R-matrix theory to electron scattering and photoionization requires the computationally demanding diagonalization of dense symmetric matrices of Hamiltonian elements. To make this task more efficient and to improve the convergence of the R-matrix basis, we develop an alternative R-matrix theory based on partitioning the eigenvectors and eigenvalues into a group of accurately known low-lying ones and derive an approximation to account for the remainder. We give the appropriate expressions for the R-matrix, its energy derivative, and the dipole matrix in this basis. Scattering from a diffuse hydrogen-like oxygen target with n≤8 states is used to illustrate the convergence of the method.

Remainder arithmetic calculating method and remainder arithmetic calculating device

Abstract: PROBLEM TO BE SOLVED: To realize a remainder arithmetic calculating device capable of quickly performing the remainder arithmetic operation of long bit length. SOLUTION: This remainder arithmetic calculating device for performing a remainder arithmetic operation is provided with a calculating means for generating the divided value of redundant expression in the intermediate result of the arithmetic operation. Moreover, in a redundant remainder multiplication loop, parallel arithmetic operations can be performed by a circuit in which RAM 1-7, registers 8-20, multipliers 21-23, and adders 24-26 are combined.

Method and device for modulo calculation

Abstract: In a data processing method, a remainder R that is produced during the division of an integer A by a prescribed integer B is calculated recursively. For this purpose, a data symbol word representing the integer A is decomposed into K data symbol part-words W0, W1, . . . , WK−1 of word length L, and in each recursion step a function F determined by the numbers B and L is applied to an argument that depends on the function value Fi−1 obtained in the preceding recursion step, and on a data symbol part-word WK−i.

Taylor's formula with remainder

Abstract: In this paper, we present a proof in ACL2(r) of Taylor's formula with remainder. This important theorem allows a function f with n + 1 derivatives on the interval [a, b] to be approximated with a Taylor series of n terms centered at a. Moreover, the formula allows the error in the approximation to be bounded by a term involving the (n + 1)st derivative of f on (a, b). The results in this paper were motivated in part by Jun Sawada's work with ACL2(r) verifying that the approximation used in the square root calculation of the IBM Power4 processor has the accuracy required. Sawada's proof effort used a Taylor approximation to the square root function. However, the support for such development in ACL2(r) is lacking [17]. This paper shows how such results can be proved in ACL2(r). It also shines a spotlight on some limitations of ACL2(r) that complicate the proof. Future work will address these limitations.

Method and device for embedding and extracting electronic watermark

Abstract: PROBLEM TO BE SOLVED: To provide an electronic watermark technique suitable for a picture based on a line drawing like a comic picture. SOLUTION: A block division part 41 divides a binary image into a plurality of blocks (S104). A pixel number calculation part 42 obtains the number Bi of black pixels in each block Ai (S106). An operation part 44 obtains a remainder bi of the number Bi of black pixels by a reference value p with respect to the object block Ai (S112). A change pixel number calculation part 45 decides whether watermark information di to be embedded in the object block Ai is '1' or '0' (S114). When watermark information di is '1' as the result of decision, the number ci of pixels to be changed is so obtained that the remainder bi may be (3/4)p (S116). When watermark information di is '0', the number ci is so obtained that the remainder bi may be (1/4)p (S118). A pixel change part 46 changes pixel values of pixels in the object block Ai in accordance with the number ci of pixels to be changed.

Apparatus and method for calculation of divisions and square roots

Abstract: Non-restoring radix-2 division and square rooting procedures are provided. The proposed procedures utilize a quotient/root digit set {−1, 0, +1} and a quotient/root prediction table (QRT/RPT). The i'th quotient/root digit is determined with reference to a partial remainder from (i−2)'th iterative operation and by the quotient/root prediction table. The present procedures generate the (i−1)'th correction term, which is to be applied in calculating the i'th partial remainder, simultaneously with the (i−2)'th correction term, and need not to perform an iterative operation to obtain the i'th partial remainder.