All The Claims

1. A method of determining a public key having an optionally reduced length and a number p for a cryptosystem resident in a device that includes a memory, using a GF(p) or GF (p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising the steps of:
selecting a number q and the number p such that p2\u2212p+1 is an integer multiple of the number q;
selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
representing the powers of the conjugates of g using their trace over the field GF(p2): and
providing p, q, and B for computation of the public key as a function of p, q, and B.
2. A method of generating a private key, and computing a public key as a function of p, q, and B generated by a method of determining a public key having an optionally reduced length and a number p for a cryptosystem resident in a device that includes a memory, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising:
selecting the number q and the number p such that p2\u2212p+1 is an Integer multiple of the number q;
selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
representing the powers of the conjugates of g using their trace over the field GF(p2);
selecting a private key; and
computing a public key as a function of g and the private key.
3. A method of encrypting a message using the public key generated by the method of claim 2.
4. A method of decrypting a message using the public and private key generated by the method of claim 2.
5. A method of signing a message using the public and private key generated by the method of claim 2.
6. A method of verifying a signature using the public key generated by the method of claim 2.
7. A method of Diffie-Hellman key exchange and related schemes using the p, q, and B as generated by the method of claim 1.
8. A method of key exchange using the public and private key generated by the method of claim 2.
9. A system for determining a public key having an optionally reduced length and a number p, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising:
a processor for selecting a number q and the number p such that p2\u2212p+1 is an integer multiple of the number q;
said processor selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
a memory for storing the number g;
said processor representing the powers of the conjugates of g using their trace over the field GF(p2); and
said processor providing for the computation of the public key as a function of p, q, and B.
10. A system for generating a private key, and computing a public key as a function of p, q, and B generated by the method of determining a public key having an optionally reduced length and a number p, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising:
a processor for selecting a number q and a number p such that p2\u2212p+1 is an integer multiple of the number q;
said processor selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
said processor representing the powers of the conjugates of g using their trace over the field GF(p2);
said processor selecting a private key;
a memory coupled to said processor for storing the private key;
said processor computing a public key as a function of g and the private key; and
a network interface for distributing said public key over a network.
11. A system for encrypting a message using the public key generated by the system of claim 10.
12. A system for decrypting a message using the public and private key generated by the system of claim 10.
13. A system for signing a message using the public and private key generated by the system of claim 10.
14. A system for verifying a signature using the public key generated by the system of claim 10.
15. A system for Diffie-Hellman key exchange and related schemes using the p, q, and B as generated by the system of claim 9.
16. A system for key exchange using the public and private key generated by the system of claim 10.
17. A computer program article of manufacture, comprising:
a computer readable medium for determining a public key having an optionally reduced length and a number p, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising;
a computer program means in said computer readable medium, for selecting a number q and a number p such that p2\u2212p+1 is an integer multiple of the number q;
a computer program means in said computer readable medium, for selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p; and
a computer program means in said computer readable medium, for representing the powers of the conjugates of g using their trace over the field GF(p2).
18. A computer program article of manufacture, comprising:
a computer readable medium for generating a private key, and computing a public key as a function of p, q, and B generated by the method of determining a public key having an optionally reduced length and a number p, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising:
a computer program means in said computer readable medium, for selecting a number q and a number p such that p2\u2212p+1 is and integer multiple of the number q;
a computer program means in said computer readable medium, for selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
a computer program means in said computer readable medium, for representing the powers of the conjugates of g using their trace over the field GF(p2);
a computer program means in said computer readable medium, for selecting a private key;
a computer program means in said computer readable medium, for computing a public key as a function of g and the private key; and
a computer program means in said computer readable medium, for distributing said public key over a network.
19. The article of manufacture of claim 18, which further comprises:
a computer program means in said computer readable medium, for encrypting a message using the public key.
20. The article of manufacture of claim 18, which further comprises:
a computer program means in said computer readable medium, for decrypting a message using the public and private key.
21. The article of manufacture of claim 18, which further comprises:
a computer program means in said computer readable medium, for signing a message using the public and private key.
22. The article of manufacture of claim 18, which further comprises:
a computer program means in said computer readable medium, for verifying a signature using the public key.
23. The article of manufacture of claim 17, which further comprises:
a computer program means in said computer readable medium, for performing Diffie-Hellman key exchange and related schemes using p, q, and B.
24. The article of manufacture of claim 18, which further comprises:
a computer program means in said computer readable medium, for key exchange using the public and private key.
25. A business method of determining a public key having an optionally reduced length and a number p for a cryptosystem resident in a device that includes a memory, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising the steps of:
selecting a number q and the number p such that p2\u2212p+1 is an integer multiple of the number q;
selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
representing the powers of the conjugates of g using their trace over the field GF(p2); and
providing p, q, and B for computation of the public key as a function of p, q, and B.
26. A business method of generating a private key, and computing a public key as a function of p, q, and B generated by a method of determining a public key having an optionally reduced length and a number p for a cryptosystem resident in a device that includes a memory, using GF(p) or GF(p2) arithmetic to achieve GF(p6) security, without explicitly constructing GF(p6), comprising:
selecting the number q and the number p such that p2\u2212p+1 is an integer multiple of the number q;
selecting a number g of order q, where g and its conjugates can be represented by B, where Fg(X)=X3\u2212BX2+BpX\u22121 and the roots are g, gp\u22121, g\u2212p;
representing the powers of the conjugates of g using their trace over the field GF(p2);
selecting a private key; and
computing a public key as a function of g and the private key.
27. A method of encrypting a message using the public key generated by the business method of claim 26.
28. A method of decrypting a message using the public and private key generated by the business method of claim 26.
29. A method of signing a message using the public and private key generated by the business method claim 26.
30. A method of verifying a signature using the public key generated by the business method of claim 26.
31. A method of Diffie-Hellman key exchange and related schemes using the p, q, and B as generated by the business method of claim 25.
32. A method of key exchange using the public and private key generated by the business method of claim 26.

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 forming a plurality of core-shell particles or a plurality of core-shell fibers, comprising the steps of:
applying an electric voltage to a cylindrical electrode;
drawing the cylindrical electrode through a first fluid, thereby forming a coated cylindrical electrode;
drawing the coated cylindrical electrode through a second fluid, wherein the first fluid is more viscous than the second fluid, thereby forming a bilayer-coated cylindrical electrode; and
positioning the bilayer-coated cylindrical electrode at a distance from a grounded collection surface;
wherein the plurality of core-shell particles or the plurality of core-shell fibers is deposited on the grounded collection surface.
2. The method of claim 1, wherein the density of the first fluid is greater than the density of the second fluid.
3. The method of claim 1, wherein the dielectric constant of the first fluid is greater than the dielectric constant of the second fluid.
4. The method of claim 1, wherein the electrical conductivity of the first fluid is greater than the electrical conductivity of the second fluid.
5. (canceled)
6. The method of claim 1, wherein the cylindrical electrode comprises copper or stainless steel.
7. (canceled)
8. The method of claim 1, wherein a plurality of cylindrical electrodes are arranged in parallel on a rotating spindle.
9. The method of claim 1, wherein the cylindrical electrode is wound helically around a rotating spindle.
10. The method of claim 1, wherein a plurality of cylindrical electrodes are configured as rings encircling the axis of a rotating spindle.
11. The method of claim 1, wherein the first fluid or the second fluid comprises a non-volatile component.
12. The method of claim 11, wherein the non-volatile component is a polymer, a small molecule, an active pharmaceutical agent, or a biological molecule.
13-15. (canceled)
16. The method of claim 1, wherein the first fluid comprises water, polyethylene oxide, or polyvinylpyrrolidone.
17-21. (canceled)
22. The method of claim 1, wherein the first fluid further comprises an active agent.
23. The method of claim 1, wherein the density of the first fluid is about 1.0 gmL to about 1.4 gmL.
24. The method of claim 1, wherein the conductivity of the first fluid is about 0.5 \u03bcScm to about 125 \u03bcScm.
25. The method of claim 1, wherein the viscosity of the first fluid is about 50 to about 800 mPa\xb7s.
26-28. (canceled)
29. The method of claim 1, wherein the density of the second fluid is about 0.8 gmL to about 1 gmL.
30. The method of claim 1, wherein the conductivity of the second fluid is about 0 to about 0.01 \u03bcScm.
31. The method of claim 1, wherein the viscosity of the second fluid is about 2 mPa\xb7s to about 300 mPa\xb7s.
32. The method of claim 1, wherein the second fluid comprises polystyrene, ethyl cellulose, n-propanol, n-butanol, mesitylene, amylbenzene, hexylbenzene, or a combination thereof.
33-45. (canceled)
46. The method of claim 1, wherein the ratio of conductivity of the first fluid to conductivity of the second fluid is about 50:1 to about 100,000:1.
47. The method of claim 1, wherein the first fluid and the second fluid are substantially immiscible.
48-55. (canceled)
56. A core-shell particle or a core-shell fiber made by a method of claim 1.
57-59. (canceled)
60. A non-woven material comprising a plurality of core-shell fibers made by a method of claim 1.

1. A woodworking machine for shaping a molding, comprising:
a frame;
a shuttle mounted on the frame;
a spaced apart pair of robotic grippers mounted on the shuttle, the grippers being adapted for gripping and releasing an elongated blank strip of molding;
a hollow, cylindrical cartridge having opposing end caps, the end caps having openings defined therein dimensioned and configured for supporting the blank strip of molding when the molding is inserted through the cartridge, the cartridge being rotatably mounted on the frame;
a table mounted on the frame, the table being movable both vertically and laterally relative to the cartridge;
a cutter assembly having a plurality of cutters, the cutter assembly being mounted on the table, the table and cutter assembly being movable so that the cutters are positioned to cut through the cartridge and the blank strip of molding when the molding is inserted through the cartridge; and
an electronic control system having means for cyclically actuating the robotic grippers to grip the blank strip of molding, move the shuttle and robotic grippers to advance the molding through the cartridge in indexed increments, actuate the cutter assembly to rotate the cutters, move the table and cutter assembly so that the cutters engage the cartridge and the blank strip of molding within the cartridge to form simultaneous, spaced apart cuts in the blank strip, retract the table and cutter assembly from the cartridge, and repeat the cycle.
2. The woodworking machine as recited in claim 1, further comprising a user interface in electrical communication with said electronic control system.
3. The woodworking machine as recited in claim 1, further comprising a spindle motor for driving the plurality of cutters, the spindle motor being in electrical communication with said electronic control system.
4. The woodworking machine as recited in claim 1, further comprising a pneumatic drive system mounted to said shuttle for driving said spaced apart pair of robotic grippers, the pneumatic drive system being in electrical communication with said electronic control system.
5. The woodworking machine as recited in claim 1, wherein the openings formed through the end caps of the hollow, cylindrical cartridge define an entry opening and an exit opening, the walls of the end cap defining the entry opening being beveled.
6. The woodworking machine as recited in claim 1, further comprising an air bag disposed within said hollow, cylindrical cartridge for releasably securing the blank strip of molding therein.
7. The woodworking machine as recited in claim 6, further comprising means for selectively inflating and deflating the air bag, the means being in electrical communication with said electronic control system.
8. The woodworking machine as recited in claim 7, wherein the means for selectively inflating and deflating the air bag comprises an air compressor and a vacuum pump.
9. The woodworking machine as recited in claim 8, wherein an inlet port is formed through a housing of said hollow, cylindrical cartridge, the inlet port being in fluid communication with the air bag, the air compressor and the vacuum pump.
10. The woodworking machine as recited in claim 1, further comprising a cartridge holder bracket mounted on said frame for releasably and rotatably supporting said cartridge.
11. The woodworking machine as recited in claim 1, wherein spacing between adjacent ones of the plurality of cutters is user-selectable and adjustable.
12. The woodworking machine as recited in claim 1, wherein said cartridge is formed from plastic.
13. The woodworking machine as recited in claim 1, further comprising a pair of spaced apart secondary grippers mounted on said shuttle, said spaced apart pair of robotic grippers and the pair of spaced apart secondary grippers being positioned adjacent opposite ends of said hollow, cylindrical cartridge, the pair of spaced apart secondary grippers being adapted for removing the molding from the hollow, cylindrical cartridge.
14. The woodworking machine as recited in claim 1, further comprising a pneumatic arm mounted to said frame, the pneumatic arm driving rotation of said cartridge.
15. The woodworking machine as recited in claim 14, further comprising means for selectively driving the pneumatic arm, the means being in electrical communication with said electronic control system.
16. The woodworking machine as recited in claim 15, further comprising a pneumatic connector bracket attached to said cartridge and a proximal end of the pneumatic arm, the pneumatic connector bracket joining said cartridge to the proximal end of the pneumatic arm.
17. The woodworking machine as recited in claim 1, further comprising means for selectively driving movement of said table, the driving means being in electrical communication with said electronic control system.
18. The woodworking machine as recited in claim 17, wherein the means for selectively driving movement of said table comprises a hydraulic drive system.
19. The woodworking machine as recited in claim 1, wherein said cutter assembly further comprises:
a spindle, the plurality of cutters being mounted on the spindle;
a headstock assembly; and
a tailstock assembly, the spindle having opposite ends mounted to the headstock and tailstock assemblies, respectively, the plurality of cutters being positioned therebetween.
20. The woodworking machine as recited in claim 1, further comprising a hydraulic cushion mounted to said frame for stabilizing and aligning said spaced apart pair of robotic grippers.

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

What is claimed is:

1. A thin film transistor comprising an insulation film and a semiconductor film on an upper side of a substrate, wherein the insulation film is an insulation film containing SiO, the thin film transistor includes minute pores in the insulation film, and the dielectric constant of the insulation film is about 3.4 or less.
2. A thin film transistor as in claim 1 wherein the thin film transistor contains pores in the insulation film mainly having a diameter of between 0.05 nm and 4 nm.
3. A thin film transistor as in claim 2 wherein the thin film transistor contains pores in the insulation film mainly having a diameter of between 0.05 nm and 1 nm.
4. A thin film transistor according to claim 1 wherein the insulation film is an insulation film formed by heating a coating film having a hydrogen silsesquioxane compound or a methyl silsesquioxane compound as its principal component.
5. A thin film transistor according to claim 2 wherein the insulation film is an insulation film formed by heating a coating film having a hydrogen silsesquioxane compound or a methyl silsesquioxane compound as its principal component.
6. A thin film transistor according to claim 1 wherein the transistor includes a polycrystalline silicon film formed by heat treatment of an amorphous silicon film.
7. A thin film transistor according to claim 2 wherein the transistor includes a polycrystalline silicon film formed by heat treatment of an amorphous silicon film.
8. A thin film transistor comprising an underlying insulation film, a gate insulation film, a semiconductor insulation film, an interlayer insulation film and a passivation film on the upper side of a substrate, wherein:
at least one of the insulation films is an insulation film containing SiO and contains pores mainly having a diameter of between 0.05 nm and 1 nm; and
the dielectric constant of the insulation film is 3.4 or less.
9. A thin film transistor according to claim 8 wherein the insulation film is an insulation film formed by heating a coating film having a hydrogen silsesquioxane compound or a methyl silsesquioxane compound as its principal component.
10. A liquid crystal display comprising a thin film transistor, wherein:
an insulation film forming a portion of the thin film transistor comprises an insulation film containing SiO;
the thin film transistor has minute pores in the insulation film; and
the dielectric constant of the insulation film is 3.4 or less.
11. A liquid crystal display according to claim 10 wherein the insulation film comprises at least one layer chosen from an underlying insulation film, a gate insulation film, a semiconductor insulation film, an interlayer insulation film and a passivation film formed on the upper side of a substrate.
12. A liquid crystal display according to claim 11 wherein the insulation film is an insulation film formed by heating a coating film having a hydrogen silsesquioxane compound or a methyl silsesquioxane compound as its principal component.
13. A liquid crystal display according to claim 12 wherein the liquid crystal display includes a semiconductor thin film comprising polycrystalline silicon formed by heat-treating an amorphous silicon film.
14. A liquid crystal display according to claim 10 wherein the thin film transistor comprises a circuit wiring formed by employing aluminum or a metal material having a resistivity smaller than the aluminum.
15. A self-emitting display comprising a thin film transistor, wherein:
an insulation film constituting the thin film transistor comprises an insulation film containing SiO,
the thin film transistor has minute pores in the insulation film, and
the dielectric constant of the insulation film is 3.4 or less.
16. A self-emitting display according to claim 15 wherein the insulation film is at least one layer among an underlying insulation film, a gate insulation film, a semiconductor insulation film an interlayer insulation film and a passivation film formed on the upper side of a substrate.
17. A self-emitting display according to claim 16 wherein the insulation film is an insulation film formed by heating a coating film having a hydrogen silsesquioxane compound or a methyl silsesquioxane compound as its principal component.
18. A self-emitting display according to claim 16 wherein the semiconductor thin film is a polycrystalline silicon film formed by heat-treating an amorphous silicon film.
19. A self-emitting display according to claim 16 wherein the thin film transistor comprises a circuit wiring formed by employing aluminum or a metal material having a resistivity smaller than the aluminum.