When encrypting, can RSACryptoServiceProvider (or any other RSA encryptor available from .NET) use SHA256 instead of SHA1?
SHA1 appears to be hard coded with no way
RSACryptoServiceProvider does work with SHA2-based signatures, but you have to invest some effort into it.
When you use a certificate to get your RSACryptoServiceProvider it really matters what's the underlying CryptoAPI provider. By default, when you create a certificate with 'makecert', it's "RSA-FULL" which only supports SHA1 hashes for signature. You need the new "RSA-AES" one that supports SHA2.
So, you can create your certificate with an additional option: -sp "Microsoft Enhanced RSA and AES Cryptographic Provider" (or an equivalent -sy 24) and then your code would look like (in .NET 4.0):
var rsa = signerCertificate.PrivateKey as RSACryptoServiceProvider;
//
byte[] signature = rsa.SignData(data, CryptoConfig.CreateFromName("SHA256"));
If you are unable to change the way your certificate is issued, there is a semi-ligitimate workaround that is based on the fact that by default RSACryptoServiceProvider is created with support for SHA2. So, the following code would also work, but it is a bit uglier: (what this code does is it creates a new RSACryptoServiceProvider and imports the keys from the one we got from the certificate)
var rsa = signerCertificate.PrivateKey as RSACryptoServiceProvider;
// Create a new RSACryptoServiceProvider
RSACryptoServiceProvider rsaClear = new RSACryptoServiceProvider();
// Export RSA parameters from 'rsa' and import them into 'rsaClear'
rsaClear.ImportParameters(rsa.ExportParameters(true));
byte[] signature = rsaClear.SignData(data, CryptoConfig.CreateFromName("SHA256"));