An ASN.1-encoded SSH private key contains the following integers in order:

• The public modulus $n$ and exponent $e$;
• The private exponent $d$;
• The prime factors $p$ and $q$ of $n$;
• The “reduced” private exponents $d_p=dbmod(p-1)$ and $d_q=dbmod(q-1)$;
• The “CRT coefficient” $q_{text{inv}}=q^{-1}bmod p$.

The observation that the value of $d$ in such a key may be irrelevant is due to the following: To speed up exponentiation modulo $n$ by a factor of about $4$, the Chinese Remainder Theorem can be utilized to compute the result modulo $p$ and $q$ se