How can a CSR be generated by OpenSSL without the public key

Question

Ok, so the general steps to make a Certificate Signing Request are (as I understand it) as follows:

• Generate a key pair
• Put my identifying information and the public key (or its hash) into a document
• Sign that document (CSR) with the generated private key
• Send the CSR to a CA who will verify that it's me and return a signed certificate with trust chain (possibly)

Since the actual signed certificate is to associate a trust relationship between my public key and my credentials, a certificate cannot be signed without access to the public key or at least a hash of the public key.

Here's the confusion for me: I see that there is a command I can execute in OpenSSL:

openssl req -out CSR.csr -key privateKey.key -new

This supposedly creates a new CSR using only the private key. I cannot see how this can work.

Is the public key or its hash secretly hidden inside the private key file?

Answer 1

A private key isn't just a big number, it is actually a data structure with several numbers in it.

Here's what a public key looks like (RSA):

<RSAKeyValue>
    <Modulus>yIf6e2K99p7hyCPlpjR0TDpH6Cpxy/zxctg/G8xHVGxtM00z6p9svf9YoT+TraHM8i6ZFtod9emkNSq8jAcWfWQ1q0xzuSmJNo74ZHFardNzH/oGExVpfiO1qCgeAnI3ILn5jTyV7g82j2wPImdAiL/wA7TfhE93POrKdrP1QpM=
    </Modulus>
    <Exponent>AQAB</Exponent>
</RSAKeyValue>

And private:

<RSAKeyValue>
    <Modulus>yIf6e2K99p7hyCPlpjR0TDpH6Cpxy/zxctg/G8xHVGxtM00z6p9svf9YoT+TraHM8i6ZFtod9emkNSq8jAcWfWQ1q0xzuSmJNo74ZHFardNzH/oGExVpfiO1qCgeAnI3ILn5jTyV7g82j2wPImdAiL/wA7TfhE93POrKdrP1QpM=
    </Modulus>
    <Exponent>AQAB</Exponent>
    <P>8KXqVAlsMtguk+xtLysbpcKYtNRIvLcORUc7SXtnMi6rtWnQ807IRfpXXDqK8BVDSCZCaNp5/lKFE4YSPqEKlQ==
    </P>
     <Q>1VLnPE9qWMXAIkYg7Y5w+jSNWAixuMBeKKIxx43VuwdrtRK7pRXaSYci/DZNe72XN8DHL6sbqpk93hnqx4h2hw==
    </Q>
    <DP>VIJ/qylv9N8UZGBH66Og3vJavE48iQFkIpIkUObkU6wuItRZS8ij7mc+3KW2ex+MdD7zXW00IEsMbtHLgHD/jQ==
    </DP>
    <DQ>S4Qtl4wFeaeHfJqWzYG/PNOdtaxePajbrEa+mIX9Q1g9KLyY8LfrrlvIZsBSbZuQDIyR9q37/UiCPj2ufzQvwQ==
    </DQ>
    <InverseQ>nrkYAY+YWALD4M39LfwdCWrtjVGYMUwMiebd3qQtirRfSBSvqPhhz1huKV7pZZHbrW+h3mxfZVZ/4WpaJ67GEA==
    </InverseQ>
    <D>kUSQXBnn62Slw0rd7k1Jgn8l4DX/Qfr3Hm8xKH4PnkT9xpBC79CWAf2cwxM/dCUmRrsjA772vVKINkvDUt0/mEXFZyYxg8FK1D1g9CdSoq6dPSxk/QXBYrsEPDo4Pe5gFdKTh4dqfnsBP0d6/7U4e2bAGg+3xn63w6CQ+JzCYmE=
    </D>
</RSAKeyValue>

As you can see, the private key includes everything that is in the public key.