# What are these fields in ASN.1 encoding of RSA

Nice resource for ASN.1 structured RSA keys https://etherhack.co.uk/asymmetric/docs/rsa_key_breakdown.html in private key section shows following RSA private key related fields:

• modulus
• public exp
• private expo
• prime 1
• prime 2
• exponent 1
• exponent 2
• coefficient

I understand the majority of these fields as per https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Key_generation.

But what are the bolded exponent 1, exponent 2 and coefficient? I cannot find their use in RSA in the linked wiki article.

• Although RSA Labs seems to have disappeared with the acquisition of EMC by Dell, the PKCS1 standard remains available as several RFCs; 8017 sec 3.2 shows the generation process and A.1.2 shows the ASN.1 (used by OpenSSL and many others except 'multiprime' is very rare). – dave_thompson_085 Nov 16 '17 at 22:14

The are the $d_P$, $d_Q$ and of course $q_{inv}$ - in that order - in the Wikipedia article. As you can see in the formulas relating to the Chinese Remainder Theorem the primes are also used but $d$, the private exponent, isn't.