301 lines
8.5 KiB
Plaintext
301 lines
8.5 KiB
Plaintext
/*
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Copyright 2018 0KIMS association.
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This file is part of circom (Zero Knowledge Circuit Compiler).
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circom is a free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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circom is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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License for more details.
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You should have received a copy of the GNU General Public License
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along with circom. If not, see <https://www.gnu.org/licenses/>.
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*/
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include "mux3.circom";
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include "montgomery.circom";
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include "babyjub.circom";
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/*
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Window of 3 elements, it calculates
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out = base + base*in[0] + 2*base*in[1] + 4*base*in[2]
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out4 = 4*base
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The result should be compensated.
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*/
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/*
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The scalar is s = a0 + a1*2^3 + a2*2^6 + ...... + a81*2^243
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First We calculate Q = B + 2^3*B + 2^6*B + ......... + 2^246*B
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Then we calculate S1 = 2*2^246*B + (1 + a0)*B + (2^3 + a1)*B + .....+ (2^243 + a81)*B
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And Finaly we compute the result: RES = SQ - Q
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As you can see the input of the adders cannot be equal nor zero, except for the last
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substraction that it's done in montgomery.
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A good way to see it is that the accumulator input of the adder >= 2^247*B and the other input
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is the output of the windows that it's going to be <= 2^246*B
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*/
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/* base must not be the neutral element nor points of small order */
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template WindowMulFix() {
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signal input in[3];
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signal input base[2];
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signal output out[2];
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signal output out8[2]; // Returns 8*Base (To be linked)
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component mux = MultiMux3(2);
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mux.s[0] <== in[0];
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mux.s[1] <== in[1];
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mux.s[2] <== in[2];
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component dbl2 = MontgomeryDouble();
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component adr3 = MontgomeryAdd();
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component adr4 = MontgomeryAdd();
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component adr5 = MontgomeryAdd();
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component adr6 = MontgomeryAdd();
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component adr7 = MontgomeryAdd();
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component adr8 = MontgomeryAdd();
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// in[0] -> 1*BASE
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mux.c[0][0] <== base[0];
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mux.c[1][0] <== base[1];
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// in[1] -> 2*BASE
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dbl2.in[0] <== base[0];
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dbl2.in[1] <== base[1];
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mux.c[0][1] <== dbl2.out[0];
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mux.c[1][1] <== dbl2.out[1];
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// in[2] -> 3*BASE
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adr3.in1[0] <== base[0];
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adr3.in1[1] <== base[1];
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adr3.in2[0] <== dbl2.out[0];
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adr3.in2[1] <== dbl2.out[1];
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mux.c[0][2] <== adr3.out[0];
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mux.c[1][2] <== adr3.out[1];
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// in[3] -> 4*BASE
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adr4.in1[0] <== base[0];
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adr4.in1[1] <== base[1];
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adr4.in2[0] <== adr3.out[0];
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adr4.in2[1] <== adr3.out[1];
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mux.c[0][3] <== adr4.out[0];
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mux.c[1][3] <== adr4.out[1];
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// in[4] -> 5*BASE
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adr5.in1[0] <== base[0];
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adr5.in1[1] <== base[1];
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adr5.in2[0] <== adr4.out[0];
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adr5.in2[1] <== adr4.out[1];
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mux.c[0][4] <== adr5.out[0];
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mux.c[1][4] <== adr5.out[1];
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// in[5] -> 6*BASE
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adr6.in1[0] <== base[0];
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adr6.in1[1] <== base[1];
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adr6.in2[0] <== adr5.out[0];
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adr6.in2[1] <== adr5.out[1];
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mux.c[0][5] <== adr6.out[0];
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mux.c[1][5] <== adr6.out[1];
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// in[6] -> 7*BASE
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adr7.in1[0] <== base[0];
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adr7.in1[1] <== base[1];
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adr7.in2[0] <== adr6.out[0];
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adr7.in2[1] <== adr6.out[1];
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mux.c[0][6] <== adr7.out[0];
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mux.c[1][6] <== adr7.out[1];
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// in[7] -> 8*BASE
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adr8.in1[0] <== base[0];
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adr8.in1[1] <== base[1];
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adr8.in2[0] <== adr7.out[0];
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adr8.in2[1] <== adr7.out[1];
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mux.c[0][7] <== adr8.out[0];
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mux.c[1][7] <== adr8.out[1];
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out8[0] <== adr8.out[0];
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out8[1] <== adr8.out[1];
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out[0] <== mux.out[0];
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out[1] <== mux.out[1];
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}
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/*
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This component does a multiplication of a escalar times a fix base
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nWindows must not exceed 82
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Signals:
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e: The scalar in bits
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base: the base point in edwards format
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out: The result
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dbl: Point in Montgomery to be linked to the next segment.
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*/
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template SegmentMulFix(nWindows) {
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signal input e[nWindows*3];
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signal input base[2];
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signal output out[2];
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signal output dbl[2];
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var i;
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var j;
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// Convert the base to montgomery
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component e2m = Edwards2Montgomery();
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e2m.in[0] <== base[0];
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e2m.in[1] <== base[1];
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component windows[nWindows];
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component adders[nWindows];
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component cadders[nWindows];
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// In the last step we add an extra doubler so that numbers do not match.
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component dblLast = MontgomeryDouble();
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for (i=0; i<nWindows; i++) {
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windows[i] = WindowMulFix();
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cadders[i] = MontgomeryAdd();
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if (i==0) {
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windows[i].base[0] <== e2m.out[0];
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windows[i].base[1] <== e2m.out[1];
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cadders[i].in1[0] <== e2m.out[0];
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cadders[i].in1[1] <== e2m.out[1];
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} else {
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windows[i].base[0] <== windows[i-1].out8[0];
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windows[i].base[1] <== windows[i-1].out8[1];
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cadders[i].in1[0] <== cadders[i-1].out[0];
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cadders[i].in1[1] <== cadders[i-1].out[1];
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}
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if (i<nWindows-1) {
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cadders[i].in2[0] <== windows[i].out8[0];
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cadders[i].in2[1] <== windows[i].out8[1];
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} else {
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dblLast.in[0] <== windows[i].out8[0];
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dblLast.in[1] <== windows[i].out8[1];
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cadders[i].in2[0] <== dblLast.out[0];
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cadders[i].in2[1] <== dblLast.out[1];
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}
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for (j=0; j<3; j++) {
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windows[i].in[j] <== e[3*i+j];
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}
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}
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for (i=0; i<nWindows; i++) {
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adders[i] = MontgomeryAdd();
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if (i==0) {
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adders[i].in1[0] <== dblLast.out[0];
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adders[i].in1[1] <== dblLast.out[1];
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} else {
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adders[i].in1[0] <== adders[i-1].out[0];
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adders[i].in1[1] <== adders[i-1].out[1];
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}
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adders[i].in2[0] <== windows[i].out[0];
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adders[i].in2[1] <== windows[i].out[1];
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}
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component m2e = Montgomery2Edwards();
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component cm2e = Montgomery2Edwards();
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m2e.in[0] <== adders[nWindows-1].out[0];
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m2e.in[1] <== adders[nWindows-1].out[1];
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cm2e.in[0] <== cadders[nWindows-1].out[0];
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cm2e.in[1] <== cadders[nWindows-1].out[1];
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component cAdd = BabyAdd();
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cAdd.x1 <== m2e.out[0];
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cAdd.y1 <== m2e.out[1];
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cAdd.x2 <== -cm2e.out[0];
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cAdd.y2 <== cm2e.out[1];
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cAdd.xout ==> out[0];
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cAdd.yout ==> out[1];
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windows[nWindows-1].out8[0] ==> dbl[0];
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windows[nWindows-1].out8[1] ==> dbl[1];
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}
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/*
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This component multiplies a escalar times a fixed point BASE (twisted edwards format)
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Signals
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e: The escalar in binary format
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out: The output point in twisted edwards
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*/
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template EscalarMulFix(n, BASE) {
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signal input e[n]; // Input in binary format
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signal output out[2]; // Point (Twisted format)
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var nsegments = (n-1)\246 +1; // 249 probably would work. But I'm not sure and for security I keep 246
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var nlastsegment = n - (nsegments-1)*246;
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component segments[nsegments];
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component m2e[nsegments-1];
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component adders[nsegments-1];
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var s;
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var i;
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var nseg;
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var nWindows;
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for (s=0; s<nsegments; s++) {
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nseg = (s < nsegments-1) ? 246 : nlastsegment;
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nWindows = ((nseg - 1)\3)+1;
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segments[s] = SegmentMulFix(nWindows);
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for (i=0; i<nseg; i++) {
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segments[s].e[i] <== e[s*246+i];
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}
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for (i = nseg; i<nWindows*3; i++) {
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segments[s].e[i] <== 0;
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}
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if (s==0) {
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segments[s].base[0] <== BASE[0];
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segments[s].base[1] <== BASE[1];
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} else {
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m2e[s-1] = Montgomery2Edwards();
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adders[s-1] = BabyAdd();
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segments[s-1].dbl[0] ==> m2e[s-1].in[0];
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segments[s-1].dbl[1] ==> m2e[s-1].in[1];
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m2e[s-1].out[0] ==> segments[s].base[0];
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m2e[s-1].out[1] ==> segments[s].base[1];
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if (s==1) {
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segments[s-1].out[0] ==> adders[s-1].x1;
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segments[s-1].out[1] ==> adders[s-1].y1;
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} else {
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adders[s-2].xout ==> adders[s-1].x1;
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adders[s-2].yout ==> adders[s-1].y1;
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}
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segments[s].out[0] ==> adders[s-1].x2;
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segments[s].out[1] ==> adders[s-1].y2;
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}
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}
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if (nsegments == 1) {
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segments[0].out[0] ==> out[0];
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segments[0].out[1] ==> out[1];
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} else {
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adders[nsegments-2].xout ==> out[0];
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adders[nsegments-2].yout ==> out[1];
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}
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}
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