diff --git a/_posts/2020-03-16-polynomials-for-crypto.md b/_posts/2020-03-16-polynomials-for-crypto.md index 490b89b6f83..5aefdc28695 100644 --- a/_posts/2020-03-16-polynomials-for-crypto.md +++ b/_posts/2020-03-16-polynomials-for-crypto.md @@ -17,14 +17,14 @@ A **polynomial** $\phi$ of **degree** $d$ is a vector of $d+1$ **coefficients**: For example, $\phi = [1, 10, 9]$ is a degree 2 polynomial. Also, $\phi' = [1, 10, 9, 0, 0, 0]$ is also a degree 2 polynomial, since the zero coefficients at the end do not count. -But $\phi'' = [1, 10, 9, 0, 0, 0, 1]$ is a degree 6 polynomial, since the last non-zero coefficient is $\phi_6 = 3$. +But $\phi'' = [1, 10, 9, 0, 0, 0, 1]$ is a degree 6 polynomial, since the last non-zero coefficient is $\phi_6 = 1$. _"A list of numbers? That makes no sense!"_ Don't panic! You are probably more familiar to polynomials expressed as function of a variable $X$: \begin{align} \phi(X) &= \phi_0 + \phi_1\cdot X + \phi_2\cdot X^2 + \cdots + \phi_d\cdot X^d\\\\\ - &= \sum_{i=0}^{d+1} \phi_i X^i + &= \sum_{i=0}^{d} \phi_i X^i \end{align} For example, $\phi = [1, 10, 9]$ and $\phi(X) = 9X^2 + 10X + 1$ are one and the same thing.