The public_key variable appears to contains a truncated Base64 fragment of a 1024-bit RSA public key. Assuming you actually have the full value you can convert it to an rsa_public() type like this:

public_key_base64 = "MIGJAoGBAM1fmNUvezts3yglTdhXuqG7OhHxQtDFA..." # truncated
public_key = :public_key.der_decode(:RSAPublicKey, Base.decode64!(public_key_base64))

The signature also appears to be truncated. Given the full Base64 encoded signature you can verify the signature with :crypto.verify:

message = "whatever"
signature_base64 = "zFuf7bRH4RHwyktaqHQwmX5rn3LfSb4dKo..." # truncated
signature = Base.decode64!(signature_base64)
:crypto.verify(:rsa, :sha256, message, signature, public_key)

Note the use of binary strings as opposed to chartists (single quotes), as others have pointed out.

According to crypto — OTP 29.0.2 (crypto 5.9), the message needs to be a binary, not a charlist. As well as signature and it shouldn’t be encoded either. And public key needs to be in the format erlang understands.

The function signature of :crypto.verify/5 does not match with your params.

verify(Algorithm, DigestType, Msg, Signature, Key) -> Result
verify(Algorithm, DigestType, Msg, Signature, Key, Options) ->
          Result
Types
Algorithm = pk_sign_verify_algs()
DigestType =
    rsa_digest_type() | dss_digest_type() | ecdsa_digest_type()
Msg = binary() | {digest, binary()}
Signature = binary()
Key =
    rsa_public() |
    dss_public() |
    [ecdsa_public() | ecdsa_params()] |
    [eddsa_public() | eddsa_params()] |
    engine_key_ref()
Options = pk_sign_verify_opts()
Result = boolean()

First 2 parameters seem to match but your message seems not to be “cleartext” so you’d need to pass it wrapped in a tuple. Your public key also does not match the typespec.

Here is a StackOverflow example: https://stackoverflow.com/a/20509599/1397594

Also note your parameters are passing charlists and not binaries.