Author: claimsbot

1. An optical pickup device for irradiating a recording medium having laminated recording layers and servo layers with laser light, the optical pickup device comprising:
a first laser light source for emitting first laser light having a first wavelength;
a second laser light source for emitting second laser light having a second wavelength different from the first wavelength;
an objective lens for converting the first laser light emitted from the first laser light source, and the second laser light emitted from the second laser light source on the recording medium;
a focus position adjuster for changing a focus position of the first laser light by the objective lens in an optical axis direction,
an astigmatism element for imparting astigmatism to the first laser light and the second laser light reflected on the recording medium;
a spectral element for imparting diffraction in such a manner that at least four light fluxes of the first laser light are separated from each other, when a light flux of the first laser light and a light flux of the second laser light reflected on the recording medium are divided into four by a first straight line in parallel to a converging direction by the astigmatism element, and a second straight line perpendicular to the first straight line, and that the four light fluxes of the first laser light propagate on an outer side than the light flux of the second laser light; and
a photodetector including a first sensor group for receiving the separated four light fluxes of the first laser light to generate a reproduction signal, and a second sensor group for receiving the second laser light to generate a servo signal for use in controlling the objective lens.
2. The optical pickup device according to claim 1, wherein
the spectral element imparts diffraction in such a manner that four light fluxes of the second laser light obtained by dividing the light flux of the second laser light by the first straight line and the second straight line are separated from each other, and that the four light fluxes of the second laser light propagate on an inner side than the light fluxes of the first laser light, and
the second sensor group receives each light flux of the second laser light separated by the spectral element.
3. The optical pickup device according to claim 1, wherein
the spectral element transmits a part of the light flux of the second laser light without diffraction, and
the second sensor group receives the light flux of the second laser light transmitted through the spectral element without diffraction.
4. The optical pickup device according to claim 1, wherein
the spectral element is configured to guide each light flux after the separation to four different vertex positions of a square on a light receiving surface of the photodetector.
5. The optical pickup device according to claim 1, wherein
sensing portions constituting the first sensor group and for receiving the four light fluxes are electrically connected to each other.
6. The optical pickup device according to claim 1, further comprising
an optical system which irradiates the recording medium with the first laser light in a direction opposite to an incident direction from the objective lens.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1-34. (canceled)
35. A cylinder adapted for use in a machine that is usable for processing lengths of material, said cylinder comprising:
a non-rotatable shaft having a longitudinal shaft axis;
a casing supported for rotation on said shaft and adapted to receive a sleeve on a casing circumferential surface;
spaced bearing assemblies between an outer surface of said shaft and an inner surface of said casing;
a lubricant channel in said shaft; and
a compressed gas bore in said shaft.
36. The cylinder of claim 35 further including at least one lubricant chamber between said shaft and said casing and divided axially into lubricant chamber sections, at least one compressed gas chamber between said shaft and said casing and divided axially into compressed gas chamber sections, and compressed gas outlet openings extending from said compressed gas chamber sections to said casing circumferential surface.
37. The cylinder of claim 36 further including at least one lubricant-side sealing ring and one compressed gas-side sealing ring separating each said lubricant chamber and an adjacent compressed gas chamber.
38. The cylinder of claim 37 wherein each said sealing ring has a sealing edge and an annular sealing body extending radially between said shaft and casing inner surface, each said sealing edge facing its respective one of said lubricant chamber and said compressed gas chamber.
39. The cylinder of claim 36 wherein said at least one compressed gas chamber is supplied with a gas under pressure through said compressed gas bore.
40. The cylinder of claim 35 further including a shaft axial end with a compressed gas bore inlet at said shaft axial end.
41. The cylinder of claim 39 further including at least one radially extending compressed gas supply bore extending between said compressed gas bore and said compressed gas chamber.
42. The cylinder of claim 35 further including at least one lubricant chamber between said shaft and said casing and divided into lubricant chamber sections by one of said spaced bearing assemblies, said at least one lubricant channel extending between said lubricant chamber sections divided by said bearing assembly.
43. The cylinder of claim 42 wherein said at least one lubricant channel extends through said shaft at an angle with respect to said shaft longitudinal axis.
44. The cylinder of claim 43 further wherein said at least one lubricant channel intersects said compressed gas bore and is seated in an airtight manner with respect to said compressed gas bore.
45. The cylinder of claim 44 wherein said at least one lubricant channel is a tube in a through bore located in said shaft.
46. The cylinder of claim 36 further including at least a first oil deflector in each said lubricant chamber.
47. The cylinder of claim 46 wherein said at least first oil deflector is located adjacent an inner surface of said casing and adjacent said one of said bearings located in said lubricant chamber.
48. The cylinder of claim 47 wherein said at least first oil deflector is angled whereby oil removed from said inner surface of said casing, during rotation of said casing, is accelerated axially by said at least first oil deflector in a direction of said bearing.
49. The cylinder of claim 46 further including a second oil deflector in each said lubricant chamber.
50. The cylinder of claim 49 further including a lubricant-side sealing ring defining a portion of said lubricant chamber and wherein said second oil deflector is arranged near an inner surface of said casing and adjacent said lubricant-side sealing ring.
51. The cylinder of claim 50 wherein a first end of said lubricant channel ends in said lubricant chamber adjacent said first oil deflector and a second end of said lubricant channel ends in said lubricant chamber adjacent said second oil deflector.
52. The cylinder of claim 50 wherein said second oil deflector is between said bearing and said lubricant-side sealing ring.
53. The cylinder of claim 36 wherein said at least one lubricant chamber is located axially adjacent an end of said cylinder and said at least one compressed gas chamber is located axially centrally in said cylinder.
54. The cylinder of claim 36 wherein said bearings are roller bearings in said lubricant chamber.
55. The cylinder of claim 37 wherein said lubricant-side sealing ring is made of a first material and said compressed gas-side sealing ring is made of a second material which is different from said first material.
56. The cylinder of claim 37 wherein each said lubricant-side sealing ring is located adjacent one of said spaced bearing assemblies.
57. The cylinder of claim 37 further including a spacer ring between said lubricant-side sealing ring and said compressed gas-side sealing ring and usable to allow lubricant flow to said compressed gas-side sealing ring.
58. The cylinder of claim 36 further including an oil fill bore in said shaft and extending from an oil fill opening to said at least one lubricant chamber.
59. The cylinder of claim 58 wherein said oil fill bore extends through said shaft at an angle with respect to said longitudinal shaft axis.
60. The cylinder of claim 58 wherein said oil fill bore acts as a lubricant chamber vent opening.
61. The cylinder of claim 58 further including an oil level gauge insertable in said oil fill bore.
62. The cylinder of claim 35 wherein said cylinder is an impression cylinder of a printing machine.
63. The cylinder of claim 35 wherein said cylinder is a printing cylinder.
64. The cylinder of claim 35 wherein a sleeve positionable on said casing is a printing forme.
65. The cylinder of claim 35 wherein said cylinder is arranged in a printing press.
66. The cylinder of claim 35 wherein said cylinder is arranged in a gravure printing press.

1. An apparatus comprising:
a virtually imaged phased array (VIPA) generator receiving an input light at a respective wavelength and having a double-hump shaped far field distribution, and producing a corresponding collimated output light traveling from the VIPA generator in a direction determined by the wavelength of the input light; and
a reflecting surface reflecting the output light back to the VIPA generator.
2. An apparatus as in claim 1, further comprising:
a lens or mirror focusing the output light traveling from the VIPA generator onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by said lens or mirror back to the VIPA generator.
3. An apparatus as in claim 1, further comprising:
means for causing the input light received by the VIPA generator to have a double-hump shaped far field distribution.
4. An apparatus as in claim 1, further comprising:
at least one phase mask causing the input light received by the VIPA generator to have a double-hump shaped far field distribution.
5. An apparatus as in claim 1, further comprising:
a fiber providing the input light to the VIPA generator; and
at least one phase mask on the fiber to cause the input light received by the VIPA generator to have a double-hump shaped far field distribution.
6. An apparatus as in claim 1, further comprising:
at least one phase mask on a surface of the VIPA generator to cause the input light received by the VIPA generator to have a double-hump shaped far field distribution.
7. An apparatus comprising:
a virtually imaged phased array (VIPA) generator receiving an input light at a respective wavelength and having a double-hump shaped far field distribution, and producing a corresponding collimate output light traveling from the VIPA generator in a direction determined by the wavelength of the input light, the output light thereby being spatially distinguishable from an output light produced for an input light at a different wavelength;
a reflecting surface; and
a lens or mirror focusing the output light traveling from the VIPA generator onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by said lens or mirror back to the VIPA generator.
8. An apparatus as in claim 7, further comprising:
means for causing the input light received by the VIPA generator to have a double-hump shaped far field distribution.
9. An apparatus as in claim 7, further comprising:
at least one phase mask causing the input light received by the VIPA generator to have a double-hump shaped far field distribution.
10. An apparatus as in claim 7, further comprising:
a fiber providing the input light to the VIPA generator; and
at least one phase mask on the fiber to cause the input light received by the VIPA generator to have a double-hump shaped far field distribution.
11. An apparatus as in claim 7, further comprising:
at least one phase mask on a surface of the VIPA generator to cause the input light received by the VIPA generator to have a double-hump shaped far field distribution.
12. An apparatus comprising:
an angular dispersive component having a passage area to receive light into, and to output light from, the angular dispersive component, the angular dispersive component receiving, through the passage area, an input light having a respective wavelength within a continuous range of wavelengths and having a double-hump shaped far field distribution, and causing multiple reflection of the input light to produce self-interference that forms a collimated output light which travels from the angular dispersive component along a direction determined by the wavelength of the input light and is thereby spatially distinguishable from an output light formed for an input light having any other wavelength within the continuous range of wavelengths; and
a reflecting surface reflecting the output light back to the angular dispersive component to undergo multiple reflection in the angular dispersive component and then be output from the passage area.
13. An apparatus as in claim 12, further comprising:
a lens or mirror focusing the output light traveling from the angular dispersive component onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by said lens or mirror back to the angular dispersive component.
14. An apparatus as in claim 12, further comprising:
means for causing the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
15. An apparatus as in claim 12, further comprising:
at least one phase mask causing the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
16. An apparatus as in claim 12, further comprising:
a fiber providing the input light to the angular dispersive component; and
at least one phase mask on the fiber to cause the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
17. An apparatus as in claim 12, further comprising:
at least one phase mask on a surface of the angular dispersive component to cause the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
18. An apparatus comprising:
an angular dispersive component having a passage area to receive light into, and to output light from, the angular dispersive component, the angular dispersive component receiving, through the passage area, a line focused input light having a double-hump shaped far field distribution and causing multiple reflection of the input light to produce self-interference that forms a collimated output light which travels from the angular dispersive component along a direction determined by the wavelength of the input light and is thereby spatially distinguishable from an output light formed for an input light having a different wavelength; and
a reflecting surface reflecting the output light back to the angular dispersive component to undergo multiple reflection in the angular dispersive component and then be output from the passage area.
19. An apparatus as in claim 18, further comprising:
a lens or mirror focusing the output light traveling from the angular dispersive component onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by the lens or mirror back to the angular dispersive component.
20. An apparatus as in claim 18, further comprising:
means for causing the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
21. An apparatus as in claim 18, further comprising:
at least one phase mask causing the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
22. An apparatus as in claim 18, further comprising:
a fiber providing the input light to the angular dispersive component; and
at least one phase mask on the fiber to cause the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
23. An apparatus as in claim 18, further comprising:
at least one phase mask on a surface of the angular dispersive component to cause the input light received by the angular dispersive component to have a double-hump shaped far field distribution.
24. An apparatus comprising:
first and second reflecting surfaces, the second reflecting surface having a reflectivity which causes a portion of light incident thereon to be transmitted therethrough, where
an input light at a respective wavelength is focused into a line and has a double-hump shaped far field distribution, and
the first and second reflecting surfaces are positioned so that the input light radiates from the line to be reflected a plurality of times between the first and second reflecting surfaces and thereby cause a plurality of lights to be transmitted through the second reflecting surface, the plurality of transmitted lights interfering with each other to produce a collimated output light which travels from the second reflecting surface along a direction determined by the wavelength of the input light, and is thereby specially distinguishable from an output light formed for an input light having a different wavelength; and

a mirror surface reflecting output the light back to the second reflecting surface to pass through the second reflecting surface and undergo multiple reflection between the first and second reflecting surfaces.
25. An apparatus as in claim 24, further comprising:
a lens or light directing mirror focusing the output light traveling from the second reflecting surface onto the mirror surface so that the mirror surface reflects the output light, the reflected light being directed by said lens or light directing mirror back to the second reflecting surface.
26. An apparatus as in claim 24, further comprising:
means for causing the input light to have a double-hump shaped far field distribution.
27. An apparatus as in claim 24, further comprising:
at least one phase mask causing the input light to have a double-hump shaped far field distribution.
28. An apparatus as in claim 24, further comprising:
a fiber providing the input light to be focused into the line; and
at least one phase mask on the fiber to cause the input light to have a double-hump shaped far field distribution.
29. An apparatus as in claim 24, further comprising:
at least one phase mask on one of the group consisting of first and second reflecting surfaces, to cause the input light to have a double-hump shaped far field distribution.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A method of operating digital logic circuitry to execute a finite field scalar multiplication of a multiplicand representative of a point in the finite field by a binary-valued scalar, comprising the steps of:
initializing one or more memory locations storing components of a sum, the sum representative of a point in the finite field; and
operating the digital logic circuitry to execute a plurality of operations comprising, for each of a plurality of bit positions in the scalar:
doubling an operand representative of one of the sum and the multiplicand;
responsive to the bit position having a \u201c1\u201d value, adding first and second operands, the first and second operands representative of the sum and the multiplicand; and
then advancing to a next bit position in the scalar;

wherein the doubling step is executed using an atomic pattern consisting of:
a first addition;
then a first multiplication followed by a second multiplication;
then a second addition;
then a third multiplication followed by a fourth multiplication;
then a third addition;
then a fifth multiplication;
then a fourth addition;
then a sixth multiplication followed by a seventh multiplication followed by an eighth multiplication;
then a fifth addition;
then a ninth multiplication;
then a sixth addition followed by a seventh addition;
then a tenth multiplication; and
then an eighth addition;

wherein the adding step is executed using an atomic pattern consisting of:
a first addition;
then a first multiplication followed by a second multiplication;
then a second addition;
then a third multiplication followed by a fourth multiplication;
then a third addition;
then a fifth multiplication;
then a fourth addition;
then a sixth multiplication followed by a seventh multiplication followed by an eighth multiplication;
then a fifth addition;
then a ninth multiplication;
then a sixth addition followed by a seventh addition;
then a tenth multiplication; and
then an eighth addition;

and wherein, following the executing step, the memory locations storing components of a sum represent the product of the multiplication.
2. The method of claim 1, wherein the second and fifth multiplications are squaring operations.
3. The method of claim 2, wherein the second and fifth through eighth additions comprises a subtracting operation.
4. The method of claim 1, wherein the second and fifth through eighth additions comprises a subtracting operation.
5. The method of claim 1, wherein the digital logic circuitry comprises a processor and a register file;
wherein the initializing step comprises:
loading projective coordinates corresponding to the multiplicand into first, second, and third register locations of the register file;

wherein each of the addition and multiplication operations that comprise the doubling and addition steps operate on operands comprising the contents stored in the register file;
wherein the results of the doubling and adding steps are stored in the first, second, and third register locations;
and wherein the operating step is performed for each of the second most significant to least significant bit positions of the scalar.
6. The method of claim 5, wherein constant register locations store coordinates of the multiplicand as constants;
wherein the doubling step doubles the sum;
and wherein the first operand of the adding step corresponds to the sum and the second operand of the adding step corresponds to the contents of the constant register locations.
7. The method of claim 1, wherein the multiplicand represents a point in a cyclic group that is a subset of points on an elliptic curve over the finite field, the elliptic curve represented by an equation of the short Weierstrass form.
8. The method of claim 1, wherein the plurality of operations executed by the digital logic circuitry further comprises subtracting the first and second operands using an atomic pattern consisting of:
a first addition;
then a first multiplication followed by a second multiplication;
then a second addition;
then a third multiplication followed by a fourth multiplication;
then a third addition;
then a fifth multiplication;
then a fourth addition;
then a sixth multiplication followed by a seventh multiplication followed by an eighth multiplication;
then a fifth addition;
then a ninth multiplication;
then a sixth addition followed by a seventh addition;
then a tenth multiplication; and
then an eighth addition.
9. A method of communicating a digital message with a digital signature, comprising the steps of:
generating a privatepublic key pair;
selecting a random number r;
executing a finite field scalar multiplication of a generator point in the finite field by the random number r to calculate a product point R in the finite field by performing a plurality of operations comprising:
initializing one or more memory locations storing components of a sum, the sum representative of a point in the finite field; and
operating digital logic circuitry to execute a plurality of operations comprising, for each of a plurality of bit positions in the random number r:
doubling an operand representative of one of the sum and the generator point;
responsive to the bit position having a \u201c1\u201d value, adding first and second operands, the first and second operands representative of the sum and the generator point; and
then advancing to a next bit position in the random number r;
computing a signature component by combining an inverse modulo of the random number r, a coordinate component of the product point R, and the private key k; and
transmitting the digital signature in combination with a digital signature comprising the coordinate component of the product point R and the computed signature component;
wherein the doubling step is executed using an atomic pattern consisting of:
a first addition;
then a first multiplication followed by a second multiplication;
then a second addition;
then a third multiplication followed by a fourth multiplication;
then a third addition;
then a fifth multiplication;
then a fourth addition;
then a sixth multiplication followed by a seventh multiplication followed by an eighth multiplication;
then a fifth addition;
then a ninth multiplication;
then a sixth addition followed by a seventh addition;
then a tenth multiplication; and
then an eighth addition;

and wherein the adding step is executed using an atomic pattern consisting of:
a first addition;
then a first multiplication followed by a second multiplication;
then a second addition;
then a third multiplication followed by a fourth multiplication;
then a third addition;
then a fifth multiplication;
then a fourth addition;
then a sixth multiplication followed by a seventh multiplication followed by an eighth multiplication;
then a fifth addition;
then a ninth multiplication;
then a sixth addition followed by a seventh addition;
then a tenth multiplication; and
then an eighth addition.
10. The method of claim 9, wherein the second and fifth multiplications are squaring operations.
11. The method of claim 10, wherein the second and fifth through eighth additions comprises a subtracting operation.
12. The method of claim 9, wherein the second and fifth through eighth additions comprises a subtracting operation.
13. The method of claim 9, wherein the digital logic circuitry comprises a processor and a register file;
wherein the initializing step comprises:
loading projective coordinates corresponding to the generator point into first, second, and third register locations of the register file;

wherein each of the addition and multiplication operations that comprise the doubling and addition steps operate on operands comprising the contents stored in the register file;
wherein the results of the doubling and adding steps are stored in the first, second, and third register locations;
and wherein the operating step is performed for each of the second most significant to least significant bit positions of the random number r.
14. The method of claim 9, further comprising:
storing x and y coordinates of the generator point in memory locations;
wherein the doubling step doubles the sum;
and wherein the first operand of the adding step corresponds to the sum, and the second operand of the adding step corresponds to the x and y coordinates of the generator point.
15. The method of claim 9, wherein the generator point represents a point in a cyclic group that is a subset of points on an elliptic curve over the finite field, the elliptic curve represented by an equation of the short Weierstrass form.
16. The method of claim 9, wherein the plurality of operations executed by the digital logic circuitry further comprises subtracting the first and second operands using an atomic pattern consisting of:
a first addition;
then a first multiplication followed by a second multiplication;
then a second addition;
then a third multiplication followed by a fourth multiplication;
then a third addition;
then a fifth multiplication;
then a fourth addition;
then a sixth multiplication followed by a seventh multiplication followed by an eighth multiplication;
then a fifth addition;
then a ninth multiplication;
then a sixth addition followed by a seventh addition;
then a tenth multiplication; and
then an eighth addition.