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[book] Fix SHA256 interpolation polynomial 

Closes #434
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ying tong 2021-12-23 22:07:09 +08:00 committed by GitHub
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book/src/design/gadgets/sha256/table16.md
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@ -669,7 +669,7 @@ with interpolation polynomials:
- $l_0(a) = \frac{(a - 7)(a - 6)(a - 5)(a - 4)(a - 3)(a - 2)(a - 1)}{(-7)(-6)(-5)(-4)(-3)(-2)(-1)}$ ($\mathtt{spread}(000) = 000000$)
- $l_1(a) = \frac{(a - 7)(a - 6)(a - 5)(a - 4)(a - 3)(a - 2)(a)}{(-6)(-5)(-4)(-3)(-2)(-1)(1)}$ ($\mathtt{spread}(001) = 000001$)
- $l_2(a) = \frac{(a - 7)(a - 6)(a - 5)(a - 4)(a - 3)(a - 1)(a)}{(-5)(-4)(-3)(-2)(-1)(1)(2)}$ ($\mathtt{spread}(010) = 000100$)
- $l_3(a) = \frac{(a - 7)(a - 6)(a - 5)(a - 3)(a - 2)(a - 1)(a)}{(-4)(-3)(-2)(-1)(1)(2)(3)}$ ($\mathtt{spread}(011) = 000101$)
- $l_3(a) = \frac{(a - 7)(a - 6)(a - 5)(a - 4)(a - 2)(a - 1)(a)}{(-4)(-3)(-2)(-1)(1)(2)(3)}$ ($\mathtt{spread}(011) = 000101$)
- $l_4(a) = \frac{(a - 7)(a - 6)(a - 5)(a - 3)(a - 2)(a - 1)(a)}{(-3)(-2)(-1)(1)(2)(3)(4)}$ ($\mathtt{spread}(100) = 010000$)
- $l_5(a) = \frac{(a - 7)(a - 6)(a - 4)(a - 3)(a - 2)(a - 1)(a)}{(-2)(-1)(1)(2)(3)(4)(5)}$ ($\mathtt{spread}(101) = 010001$)
- $l_6(a) = \frac{(a - 7)(a - 5)(a - 4)(a - 3)(a - 2)(a - 1)(a)}{(-1)(1)(2)(3)(4)(5)(6)}$ ($\mathtt{spread}(110) = 010100$)