ECC2 : Errata

1. Page 11, Algorithm 1.5:
   In OUTPUT replace

   A shared secret $G$

   with

   A shared secret $Q$

   Also in line 1 of the algorithm replace $\log_2(#K)$ with $\log_2(q)$.

2. Page 26, line -5:
   Replace

   t^{-1} H(m)

   by

   t H(m)

3. Page 112, displayed formula at the bottom:
   The formulae for $\alpha_{i+1}$ and $\beta_{i+1}$ is wrong and should read:
   

   \begin{equation*}
   \begin{split}
   \alpha_{i+1} & =  -30 x_Q2 - 5 x_Q - 9 A_{i+1}  , \\
   \beta_{i+1}  & =  -70 x_Q3 - 20 x_Q2 - (42 A_{i+1} + 1) x_2 - 2A_{i+1} - 27 B_{i+1} .\\
   \end{split}
   \end{equation*}
   

   Furthermore, one first has to translate the $x$-axis to get rid of the quadratic term and then apply (VI.4) which then gives

   \[ c_i2 = \frac{(48 A_i - 1)(864 \beta_{i+1} - 72 \alpha_{i+1} + 1)}
   {(864B_i - 72A_i + 1)(48 \alpha_{i+1} - 1)}\cdotp \]
   

4. Page 189, line -11:
   $L$ should be replaced by $L^*$ so that the conclusion reads

   "we have $L^* \subseteq $(\F_{q^k}^*)^r$."

5. Page 190, line 8:
   Change $P \in E( {\mathbb F}_q )$ to $P \in E( {\mathbb F}_{q^k} )$.

6. Page 190, line 20:
   Change `function over ${\mathbb F}_q$' to `function over ${\mathbb F}_{q^k}$'.