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added 8 characters in body
e-sushi
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Yes, die can be noticeably biased but i would be very surprised if the output of die from different manufacturers were to be bad enough to lead to any practical attack whatsoever of even something with requirements as stringent as that of a one-time pad (unless the dice were deliberately sabotaged).

Personally, if you are not allowed to use a computer i would do the following: get d6 dice from different manufacturers (at least 2 dice, look for die without rounded edges), build a 6x6 table (example below, but there could be many variations of this) and choose your characters from the intersection of 2 die rolls. If you want to determine if a letter is upper or lower case you could do something like a coin flip.

Keep building your key via this method until you have the desired output amount.

\|1|2|3|4|5|6|
1|a|b|c|d|e|f|
2|g|h|i|j|k|l|
3|m|n|o|p|q|r|
4|s|t|u|v|w|x|
5|y|z|0|1|2|3|
6|4|5|6|7|8|9|

Update:

I just noticed you said you needed to generate numbers only. here's a different table (but 16.67% of your rolls will be invalid):

\|1|2|3|4|5|6
1|0|1|2|3|4|5
2|6|7|8|9|0|1
3|2|3|4|5|6|7
4|8|9|0|1|2|3
5|4|5|6|7|8|9
6|R|E|R|O|L|L

A 6x6 table with 86.11% odds of only 2 dice rolls (with 2.77% odds of invalid roll) and 13.89% odds of 2 dice rolls + 1 coin flip:

\|1  |2  |3  |4  |5   |6
1|0  |1  |2  |3  |4   |5
2|6  |7  |8  |9  |0   |1
3|2  |3  |4  |5  |6   |7
4|8  |9  |0  |1  |2   |3
5|4  |5  |6  |7  |8   |9
6|0/1|2/3|4/5|6/7|8/9 |REROLL