From 8d4f67532692e21aa0c5d0d0443ae984c192dac6 Mon Sep 17 00:00:00 2001 From: DrPeterVanNostrand Date: Thu, 7 Oct 2021 12:46:33 -0400 Subject: [PATCH] fix: Poseidon spec's sparse-factorization w vector --- content/algorithms/crypto/poseidon.md | 12 ++++-------- 1 file changed, 4 insertions(+), 8 deletions(-) diff --git a/content/algorithms/crypto/poseidon.md b/content/algorithms/crypto/poseidon.md index b222adc17..8d0b6564e 100644 --- a/content/algorithms/crypto/poseidon.md +++ b/content/algorithms/crypto/poseidon.md @@ -698,14 +698,10 @@ $\overline{\underline{\Function \textsf{sparse\_factorize}(m \typecolon \Zp^{[t 0 & m_{t - 1, 1} & \dots & m_{t - 1, t - 1} \end{bmatrix} \\~ \\ -\line{3} \wb \typecolon \Zp^{[t - 1 {\times} 1]} = \hat{m}_{\ast, 0} = \begin{bmatrix} - \hat{m}_{0, 0} \\ +\line{3} \wb \typecolon \Zp^{[t - 1 {\times} 1]} = m_{1 \dotdot, 0} = \begin{bmatrix} + m_{1, 0} \\ \vdots \\ - \hat{m}_{t - 2, 0} -\end{bmatrix} = m_{1 \dotdot, 1} = \begin{bmatrix} - m_{1, 1} \\ - \vdots \\ - m_{t - 1, 1} + m_{t - 1, 0} \end{bmatrix} \\~ \\ \line{4} \hat\wb \typecolon \Zp^{[t - 1 {\times} 1]} = \hat{m}^{\neg 1} {\times} \hso \wb = \begin{bmatrix} @@ -730,7 +726,7 @@ $\overline{\underline{\Function \textsf{sparse\_factorize}(m \typecolon \Zp^{[t **Algorithm Comments:**\ **Line 1.** $\hat{m}$ is a submatrix of $m$ which excludes $m$'s first row and first column.\ **Line 2.** $m'$ is a copy of $m$ where $m$'s first row and first column have been replaced with $[1, 0, \dots, 0]$.\ -**Line 3.** $\wb$ is a column vector which is the first column of $\hat{m}$ or the second column of $m$ excluding the first row's value.\ +**Line 3.** $\wb$ is a column vector whose values are the first column of $m$ excluding $m$'s first row. **Line 4.** $\hat\wb$ is the matrix-column vector product of $\hat{m}^{\neg 1}$ and $\wb$.\ **Line 5.** $m''$ is a sparse matrix whose first row is the first row of $m$, remaining first column is $\hat\wb$, and remaining entries are the identity matrix.