RSA Algorithm (private key calculation) in bash -

looking on how calculate rsa secret key in bash script 'd' when p, q & e given.

although know query has come before, seem find theoretical advice on calculation of rsa private key when p, q & e given.

i trying put calculation in bash script , explanation on calculations possible in bash (with expr or bc)

i found site advised following; (with 't' being totient of p*q, or rather totient of 'n')

d=$(echo "((2 * $t) + 1) / $e" | bc)

but seems work on specific case , did not provide correct output when trying on different cases.

any on how write bash formula calculation ?

from defition of rsa

|e*d| = 1 (mod fi(p*q))

where fi(n) euler function

so need calculate inversion of e in modulo. don't forget check if gcd(e,fi(p*q))=1 or may not find inversion of e in given modulo.

you can achieve using extended euclidean algorithm. there lot of pseudocodes on web. need more help?