Abstract: A fast computation method for squaring operations in Montgomery multiplication, and an arithmetic circuit for realizing the computation method are provided. A modular squaring unit compares variable i with variable j. If i and j are equal, the modular squaring unit computes T=T+ai×ai×2jk. If i and j are not equal, the modular squaring unit computes temporary variable tmp=ai×aj×2jk, shifts temporary variable tmp by one bit to the left, and computes T=T+tmp.

Abstract: An exponent preprocessing unit preprocesses an n-bit exponent k and exponentiates a base A by the preprocessed exponent k. A bit string storing unit stores a bit string including a sign bit and the exponent k. A reading unit reads a bit pattern composed of the sign bit and a bit sequence made up of a predetermined number of bits. A bit pattern generating unit generates a new bit pattern from the read bit pattern. An operation pattern specifying unit specifies an operation pattern based on the read bit pattern. An operating unit performs an operation according to the specified operation pattern and writes the new bit pattern over the previous bit pattern. The reading unit reads a next bit sequence starting from a different bit in the bit string storing unit. A repeat controlling unit repeats these procedures n+1 times.

Abstract: In a cryptography system, plaintext storage unit 101 stores a plaintext. Encryption unit 102 encrypts the plaintext to generate a ciphertext. First verification data generating unit 104 generates first verification data, and second verification data generating unit 106 generates second verification data. Decryption unit 114 decrypts the ciphertext to generate a decrypted plaintext. First verification unit 116 performs verification using the decrypted plaintext and the first verification data. Second verification unit 117 performs verification using the first verification data, the ciphertext, and the second verification data. Display unit 112 displays the results of the verifications.

Abstract: A message receiving apparatus for receiving messages from a message transmitting apparatus generates first data for producing a display which urges a user of the message transmitting apparatus to input a message, and generates second data within the first data for specifying a conversion type for secret communication of the message. The message receiving apparatus sends the first data including the second data to the message transmitting apparatus and subsequently receives the message from the message transmitting apparatus. The message transmitting apparatus for transmitting messages to the message receiving apparatus receives the first data for producing the display and the accompanying second data for specifying the conversion type and produces the display according to the first data.

Abstract: An information security device receives an input of prime q, and generates prime N that is larger than prime q. In the information security device, a partial information setting unit generates number u such that 2×u×q+1≠0 mod Li (i=1, 2, . . . , n). A random number generating unit generates random number R′. A judgement target generating unit generates R=u+L1×L2×. . . ×Ln×R′ and N=2×R×q+1, using number u and random number R′. A primality judging unit judges the primality of number N, using numbers N and R generated by the judgement target generating unit.

Abstract: In an exponentiation device, a relatively large table is generated outside of a coprocessor so as to enable high-speed exponentiation to be performed using the small window method. The selection of data from the table and transfer of data to the coprocessor are conducted in parallel with a multiple-length arithmetic operation performed in the coprocessor. So as to avoid bottlenecks occurring in the data transfer between a CPU and the coprocessor, two data banks are provided in the coprocessor for storing the data to be used in the arithmetic operation. By providing two banks in the coprocessor, it is possible to use one for transferring data while data stored in the other is being used in the arithmetic operation. When the operation using the stored data has been completed, the banks are switched, and the arithmetic operation is then repeated using the newly transferred data while at the same time conducting data transfer in readiness for the following operation.

Abstract: The modular multiplication apparatus includes a residue calculating unit, a multiplier division unit, a partial product calculation unit, an accumulation unit, a correction unit, and a control unit. The residue calculating unit recurrently calculates intermediate values in sequence. The residue calculating unit obtains the multiplicand as the intermediate value first time, and at the second time and after, calculates residues or congruent values of the modulo P multiplication of the intermediate values being preceding intermediate values left-shifted s bits. The multiplier division unit divides the multiplier into a plurality of s-bit partial multipliers in order from lower bits. The partial product calculation unit calculates partial products of intermediate values and partial multipliers in sequence. The accumulation unit and the correction unit accumulate the partial products while correcting them under the control of the control unit. The residue calculating unit includes a table unit.

Abstract: A fixed-point multiple calculation apparatus, for use in an encryption method and a signature method that use elliptic curves, finds multiples of a fixed point and an arbitrary point at high speed. The fixed-point multiple calculation apparatus generates a pre-computation tables for multiples of digits at one-word intervals and for multiples of digits at half-word intervals. Using the tables, multiples of points on an elliptic curve are calculated using a doubling process, but with a reduced number of additions. This reduces the overall amount of required calculation.

Abstract: A dicing machine for cutting a semiconductor wafer along cutting lines arranged in a lattice pattern. The dicing machine comprises a cutting station, at least one alignment station, a cutting means disposed in the cutting station, a detecting means disposed in the alignment station for detecting the cutting lines of the wafer, and a wafer transferring means. The wafer transferring means includes two wafer supporting means and the dicing machine is capable of positioning one of the two wafer supporting means in the alignment station and performing alignment of a semiconductor wafer supported with said one of the wafer supporting means while positioning the other of the wafer supporting means in the cutting station and cutting a semiconductor wafer supported with said the other of the supporting means by the cutting means. The cutting means includes two cutting blades and a cutting blade interval setting-up means for setting up the interval of these cutting blades.

Abstract: An article holding apparatus provided with a plate on which an article is placed. A light transmitting opening is formed in the plate. There is provided an optical system optically connected to the light transmitting opening. Reflection light from a part of the undersurface of the article placed on the plate comes into the optical system through the light transmitting opening.

Abstract: A grinding wheel that can rotate at high speed to grind flat plates is comprised of a thin conical grindstone fastened to the open end of a rotatable inverted cup, with the grinding edge projecting outwardly from and at an inclined angle with respect to the open end. The grindstone includes a cylindrical fitting part which is fastened to the inside of the cup and a conical grinding part formed by electroplating from a nickel plating solution in which super hard abrasive grains are dispersed. The grindstone can also be prepared by electrodepositing abrasive grains directly onto a flange formed at the open end of the cup.

Abstract: Grinding of flat plates is performed by using a very thin, conical grinding wheel which is attached to the open end of a revolving cup and which projects outwardly from and is inclined with respect to the cup. The peripheral cutting edge of the grinding wheel revolving at high speed is brought into contact with the work. As the grinding wheel is fed, the work is cut by the grinding wheel across its thickness and an undercut part of the work disrupts (i.e. breaks off) by itself to a desired thickness. Thick grinding is also possible if a multiplicity of the grinding wheels are placed one over another at proper intervals.

Abstract: A machining device equipped with a rotating machining tool having a blade. A blade inspecting means is provided in the machining device. The blade inspecting means comprises an emission means for emitting electromagnetic radiation and a receiving means for receiving the electromagnetic radiation emitted by the emitting means and producing a signal corresponding to the received electromagnetic radiation. The emitting means and receiving means are disposed such that the electromagnetic radiation emitted from the emitting means undergoes interference by the blade of the machining tool and the electromagnetic radiation received by the receiving means varies according to a variation in the condition of the blade.

Abstract: A grinding wheel that can rotate at high speed to grind flat plates comprised of a thin conical grindstone fastened to the open end of a rotatable inverted cup, with the grinding edge projecting outwardly from and at an inclined angle with respect to the open end. The grindstone includes a cylindrical fitting part which is fastened to the inside of the cup and a conical grinding part formed by electroplating from a nickel plating solution in which super hard abrasive grains are dispersed. The grindstone can also be prepared by electrodepositing abrasive grains directly onto a flange formed at the open end of the cup.

Abstract: Grinding of flat plates is performed by using a very thin, conical grinding wheel which is attached to the open end of a revolving cup and which projects outwardly from and is inclined with respect to the cup. The peripheral cutting edge of the grinding wheel revolving at high speed is brought into contact with the work. As the grinding wheel is fed, the work is cut by the grinding wheel across its thickness and an undercut part of the work disrupts (i.e. breaks off) by itself to a desired thickness. Thick grinding is also possible if a multiplicity of the grinding wheels are placed one over another at proper intervals.

Abstract: A grinding wheel that can rotate at high speed to grind flat plates is comprised of a thin conical grindstone fastened to the open end of a rotatable inverted cup, with the grinding edge projecting outwardly from and at an inclined angle with respect to the open end. The grindstone includes a cylindrical fitting part which is fastened to the inside of the cup and a conical grinding part formed by electroplating from a nickel plating solution in which super hard abrasive grains are dispersed. The grindstone can also be prepared by electrodepositing abrasive grains directly onto a flange formed at the open end of the cup.

Abstract: Suction apparatus for holding workpieces such as semiconductor substrates or wafers having different diameters comprises a table having an upper surface with a plurality of concentric circular air grooves having different diameters and a plurality of sleeves in radial arcuately spaced bores, respectively, for selectively switching a vacuum source to all or less than all of the grooves. In a preferred embodiment, each sleeve is rotatable about its axis and has a plurality of axially spaced holes which communicate with the vacuum source through the central axial passage in the sleeve. Correspondingly axially spaced holes in the table connect the respective grooves with the bore and are registerable with the sleeve holes through selective rotation of the sleeve to connect the vacuum source and the grooves.