RSA Security claims that 1024-bit keys are likely to become crackable some time between 2006 and 2010 and that 2048-bit keys are sufficient until 2030. An RSA key length of 3072 bits should be used if security is required beyond 2030.
Starting from 1st of January 2014 SSL certificates with key length 1024 are considered too weak by Chrome and Firefox browsers.
The following steps allows to make an SSL certificate with a custom key size:
1. Generate private key
openssl genrsa -out privkey.pem 2048
2. Create a Certificate Signature Request (CSR) based on this key
openssl req -new -key privkey.pem -out cert.csr
3. Submit the CSR to a Certificate Authority (CA) and get signed certificate back
4. Combine signed certificate and private key into a single container
openssl pkcs12 -export -out container.pfx -inkey privkey.pem -in pubcert.pem
See also: ECDSA vs RSA