In FIPS-202 specification, the padding required for SHA3 were not clearly mentioned.
I beg to differ. From the FIPS 202. section B2.:
For most applications, the message is byte-aligned, i.e., $len(M)
= 8m$ for a nonnegative integer $m$.
In this case, the total number of bytes, denoted by $q$,
that are appended to the message is determined as follows by
$m$ and the rate $r$:
$$q = \frac{r}{8} – (m \bmod{\frac{r}{8}})$$
The value of $q$ determines the hexadecimal form of these bytes
in this case according to the conversion functions specified in Sec. B.1. The padded messages that result are summarized in
Table 6:
+-------------------------+--------------------------------+
| | |
| Number of padding bytes | Padded message |
| | |
+----------------------------------------------------------+
| | |
| q = 1 | M || 0x86 |
| | |
| q = 2 | M || 0x0680 |
| | |
| q > 2 | M || 0x06 || 0x00... || 0x80 |
| | |
+-------------------------+--------------------------------+
the notation 0x00...
indicates the string that consists of $q – 2 $ “zero” bytes.
If you look at your test vector, for $\operatorname{SHA3-224}$. $224$ means $224$ bits of security. So we have $c = 224 \times 2 = 448$ and $r = 1600 - c = 1152$.
Because message is empty, $len(M) = 0$, therefore $m = 0$. Hence $$q = \frac{1152}{8} - 0 \bmod \frac{1152}{8} = 144$$
Therefore we are in the third case: ($q > 2$).
The padding will be : 0x06 || 144 - 2 zeros || 0x80
.
Therefore we find back the data to be absorbed
:
06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 80
06
followed by 284 0
(or 142 00
) then followed by 80
. The followings 00
are provided to show that the capacity won't change during the absorption.