Claims
- 1. A bit serial finite field GF(2.sup.m) multiplier for multiplying an element W in a finite field GF(2.sup.m) by a constant C such that Y=C*W, comprising:
- (a) a first serial input for receiving the bits of W, low order first;
- (b) a linear feedback shift register having m storage elements Ym-1 to Y0 where:
- each storage element stores a single bit and has an input and an output;
- a predetermined number of the storage elements have an XOR gate connected to the output of the storage element and an output of the XOR gate is connected to the input of the next storage element;
- for the storage elements that do not have an XOR gate connected to their output, the output is connected directly to the input of the next storage element;
- the output of the Y0 element is connected to a predetermined number of the XOR gates as determined by a field generator polynomial;
- the bits in the storage elements are shifted on a clock cycle such that Ym-1=Y0 or the output of a corresponding XOR gate, and Yj-1=Yj or the output of a corresponding XOR gate, for j=1 to m-1; and
- (c) a connection from the first serial input to a predetermined number of the XOR gates as determined by the constant C, wherein at each clock cycle a next bit of the element W is added into the XOR gates connected to the first serial input.
- 2. The bit serial finite field GF(2.sup.m) multiplier as recited in claim 1, wherein the output of the Y0 element is connected to an XOR gate between Yi and Yi+1 for i=0 to m-2 and to an XOR gate connected to Yi for i=m-1 only if a corresponding i-bit in a field element .alpha..sup.(2.spsp.m.sup.-2) is 1.
- 3. The bit serial finite field GF(2.sup.m) multiplier as recited in claim 1, wherein the first serial input is connected to an XOR gate between Yi and Yi+1 for i=0 to m-2 and to an XOR gate connected to Yi for i=m-1 only if a corresponding i-bit in a field element C*.alpha..sup.(m-1) is 1.
- 4. The bit serial finite field GF(2.sup.m) multiplier as recited in claim 1, wherein after m number of clock cycles the storage elements Ym-1 to Y0 store the resulting product Y=C*W.
- 5. The bit serial finite field GF(2.sup.m) multiplier as recited in claim 1, wherein the multiplier circuit generates a product Y=.alpha..sup.i *W where .alpha..sup.i =C*.alpha..sup.(m-1).
- 6. The bit serial finite field GF(2.sup.m) multiplier as recited in claim 1, wherein the resulting product is Y=C1*W+C2*X, further comprising:
- (a) a second serial input for receiving the bits of a second finite field element X, low order first; and
- (b) a connection from the second serial input to the XOR gates that are connected to the first serial input.
- 7. A k-bit serial finite field GF(2.sup.m) multiplier for multiplying an element W in a finite field GF(2.sup.m) by a constant C such that Y=C*W, comprising:
- (a) first k serial inputs for receiving the interleaved bits of W, low order first;
- (b) k linear feedback shift registers each having m/k storage elements Ym/k-1 to Y0, wherein for each shift register:
- each storage element stores a single bit and has an input and an output;
- a predetermined number of the storage elements have an XOR gate connected to the output of the storage element and an output of the XOR gate is connected to the input of the next storage element;
- for the storage elements that do not have an XOR gate connected to their output, the output is connected directly to the input of the next storage element;
- the output of the Y0 element is connected to a predetermined number of the XOR gates as determined by a field generator polynomial;
- the bits in the storage elements are shifted on a clock cycle such that Ym/k-1=Y0 or the output of a corresponding XOR gate, and Yj-1=Yj or the output of a corresponding XOR gate, for j=1 to m/k-1; and
- (c) k connections from the first k serial inputs to a predetermined number of the XOR gates as determined by the constant C, wherein at each clock cycle a next k-bits of the element W are added into the XOR gates connected to the first k serial inputs.
- 8. The k-bit serial finite field GF(2.sup.m) multiplier as recited in claim 7, wherein the output of the Y0 element for 0.ltoreq.j<k the jth shift register is connected to an XOR gate between Yi and Yi+1 for i=0 to m/k-2 and to an XOR gate connected to Yi for i=m/k-1 only if a corresponding i-bit in a field element .alpha..sup.(2.spsp.m.sup.-k+j-1) is 1.
- 9. The k-bit serial finite field GF(2.sup.m) multiplier as recited in claim 7, wherein for 0.ltoreq.j<k the jth serial input of the first k serial inputs is connected to an XOR gate between Yi and Yi+1 for i=0 to m/k-2 and to an XOR gate connected to Yi for i=m/k-1 only if a corresponding i-bit in a field element C*.alpha..sup.(m-k+j) is 1.
- 10. The k-bit serial finite field GF(2.sup.m) multiplier as recited in claim 7, wherein after a m/k number of clock cycles the storage elements Ym/k-1 to Y0 of the shift registers store the resulting product Y=C*W.
- 11. The k-bit serial finite field GF(2.sup.m) multiplier as recited in claim 7, wherein for 0.ltoreq.j<k the multiplier circuit generates products Y(j)=.alpha..sup.i (j)*W(j) where .alpha..sup.i (j)=C*.alpha..sup.(m-k+j) and W(j) is an interleaved portion of W.
- 12. The k-bit serial finite field GF(2.sup.m) multiplier as recited in claim 7, wherein the resulting product is Y=C1*W+C2*X, further comprising:
- (a) second k serial inputs for receiving the interleaved bits of a second finite field element X, low order first; and
- (b) k connections from the second k serial inputs to the XOR gates that are connected to the corresponding first k serial inputs.
Parent Case Info
The present application is a divisional of application Ser. No. 08/056,839, filed May 3, 1993, which is a continuation of application Ser. No. 07/612,430, filed Nov. 8, 1990, issued as U.S. Pat. No. 5,280,488 on Jan. 18, 1994.
US Referenced Citations (3)
Non-Patent Literature Citations (1)
Entry |
"Architectures for Exponentiation in GF(2.sup.n)," Beth et al. (No date). |
Divisions (1)
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56839 |
May 1993 |
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Continuations (1)
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612430 |
Nov 1990 |
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