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computation: given: group: pkGroup = <f,g_1,g_2,g_3,g_4,h> group: G1 = <g1,h1> group: G2 = <g2,h2> group: G3 = <g3,h3> integers: x[1:l], stat, modSize compute: random integer in [0,2^(modSize+stat)): vprime C := h^vprime * for(i, 1:l, *, g_i^x_i) proof: given:group: pkGroup = <f,g_1,g_2,g_3,g_4,h> group: G1 = <g1,h1> group: G2 = <g2,h2> group: G3 = <g3,h3> element in pkGroup: C element in G1: c_1 commitment to x_1: c_1 = g1^x_1*h1^r_1 element in G2: c_2 commitment to x_2: c_2 = g2^x_2*h2^r_2 element in G3: c_3 commitment to x_3: c_3 = g3^x_3*h3^r_3 integer: l_x prove knowledge of: integers: x[1:l], r[1:l] exponent in pkGroup: vprime such that: for(i, 1:l, range: (-(2^l_x-1)) <= x_i < 2^l_x) C = h^vprime * for(i, 1:l, *, g_i^x_i) c_1 = g1^x_1*h1^r_1 c_2 = g2^x_2*h2^r_2 c_3 = g3^x_3*h3^r_3 |
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