Diffie–Hellman key exchange cryptographic explanation.

dh.sh

#!/usr/local/bin/bash

# d=256
d=512
g="$(((RANDOM % d) + 1))"
p="$(((RANDOM % d) + 1))"

echo ''
echo 'public:'
echo "g = $g"
echo "p = $p"

# d=8
a="$(((RANDOM % d) + 1))"
b="$(((RANDOM % d) + 1))"

for ((;;)); do
 if test "$b" != "$a"; then break; fi
 b="$(((RANDOM % d) + 1))"
done

echo ''
echo 'private:'
echo "a = $a"
echo "b = $b"

export BC_LINE_LENGTH=2048

gA="$(bc -e "$g^$a")"
gB="$(bc -e "$g^$b")"

echo ''
echo -e "g^a($g^$a):\n$gA"
echo -e "g^b($g^$b):\n$gB"

A="$(bc -e "$gA%$p")"
B="$(bc -e "$gB%$p")"

echo ''
echo 'public:'
echo "A = $A"
echo "B = $B"

Ba="$(bc -e "$B^$a")"
Ab="$(bc -e "$A^$b")"

echo ''
echo -e "B^a:\n$Ba"
echo -e "A^b:\n$Ab"

aK="$(bc -e "$Ba%$p")"
bK="$(bc -e "$Ab%$p")"

echo ''
echo 'private:'
echo "aK = $aK"
echo "bK = $bK"

echo ''
if test "$aK" == "$bK"; then
 echo 'ok'; exit 0; fi

echo 'Not implemented!'; exit 1 # todo