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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.

croraf
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1 Answers1

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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.

The CRT calculations can be used to speed up RSA private key operations, which are the slowest part of the RSA cryptosystem after the prime generation. The calculations also have different side channel attacks linked to them compared to "plain" RSA.

Maarten Bodewes
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