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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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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1$\begingroup$ 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 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. $\endgroup$ Dec 21, 2022 at 0:56
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$\begingroup$ @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... $\endgroup$– ponchoDec 21, 2022 at 13:48