RSA Private Key Format Without Chinese Remainder Theorem

kevin.sh

12/20/23, 6:21 PM

I've been implementing RSA as a learning exercise and am at a point now where I'd like to try serializing my key to a file using some standard format. I've implemented it without using the Chinese Remainder Theorem, so my private key is composed only of my modulus $n=pq$ and my modular inverse exponent $d$. I've seen that PKCS1 & PKCS8 expect the use of the Chinese Remainder theorem. I know that I could simply derive these values, but is there any standard format where I can encode only my $n$ and $d$ without deriving the values for CRT implementations?

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Crypto

poncho

12/20/23, 6:47 PM

is there any standard format where I can encode only my n and d without deriving the values for CRT implementations?

Actually, for the standard PKCS #1 private key format, the CRT parameters are optional. As you can read in the linked text, one of the options is that the private key just stores $n$ and $d$.

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dave_thompson_085

12/21/23, 12:56 AM

3.2 defines abstract representation(s) not directly serializable; A.1.2 defines ASN.1 that is serializable and requires CRT (except the 'multi-prime' part is optional). OTOH [JOSE/JWK](https://www.rfc-editor.org/rfc/rfc7518.html#section-6.3.2) makes the CRT fields 'should' -- recommended but not required. OpenPGP contains p,q but not dp,dq and pinv instead of qinv -- always. PKCS11 transfers each field separately on the API but the supported and required fields (beyond n,e,d) are up to the 'token' i.e. device or instance.

poncho

12/21/23, 1:48 PM

@dave_thompson_085: I remember a version of the PKCS #1 private key format with only the n, e, d fields (just omitting the others). However, all the references I now check have the CRT parameters mandatory...

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EN: RSA Private Key Format Without Chinese Remainder Theorem

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