# ECC2 : Errata

 Advances in Elliptic Curve Cryptography (Edited with I.F. Blake and G. Seroussi). London Mathematical Society Lecture Note Series. Cambridge University Press, 2004. ISBN: 0 521 60415 X (PB).

We use LaTeX terminology when this makes things clearer

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}\$'.

Thanks to Shahab Mirzadeh, Paul Morrissey, Andreas Peter and Edlyn Teske.
Nigel Smart