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@@ -105,3 +105,32 @@ sb = P(list(Ai * vector(F17, [1, 15, 8, 9])))
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sc = P(list(Ai * vector(F17, [4, 16, 14, 5])))
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# Setup phase complete
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+
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+# Prove phase
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+
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+# Round 1
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+
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+# Create vanishing polynomial which is zero for every root of unity.
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+# That is Z(w_1) = Z(w_2) = ... = 0
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+Z = x^4 - 1
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+assert Z(1) == 0
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+assert Z(4) == 0
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+assert Z(16) == 0
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+assert Z(13) == 0
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+
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+# 9 random blinding values. We will use:
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+# 7, 4, 11, 12, 16, 2
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+
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+# Blind our witness polynomials
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+# The blinding factors will disappear at the evaluation points.
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+a = (7*x + 4) * Z + fa
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+b = (11*x + 12) * Z + fb
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+c = (16*x + 2) * Z + fc
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+
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+# During the SRS phase we created a random s point and its powers
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+s = 2
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+# So now we evaluate a, b, c with these powers of G
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+a_s = ZZ(a(s)) * G
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+b_s = ZZ(b(s)) * G
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+c_s = ZZ(c(s)) * G
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+
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narodnik