[SalesForce] Generate a JWT with HS256 signature

I am trying to generate an HS256 signed JWT token via Apex. I am using this token in the Authy registration process to enable 2FA for community users.

Per the Authy documentation HS256 is the only algorithm supported for the registration flow i'm using.

I did a little digging and I found a JWT example apex class on github. I modified it to support the context object defined in the Authy api documentation. The token seems to generate just fine but when I go to validate the signature it fails validation.

Here is the code I am using and how I am invoking it:

public class Authy_JWT {
    
public String alg {get;set;}
public String iss {get;set;}
public String exp {get;set;}
public String app_id {get;set;}
public String user_id {get;set;}
public String iat {get;set;}
public Map<String,String> claims {get;set;}
public Integer validFor {get;set;}
public String cert {get;set;}
public String pkcs8 {get;set;}
public String privateKey {get;set;}


public static final String HS256 = 'HS256';
public static final String RS256 = 'RS256';
public static final String NONE = 'none';


public Authy_JWT(String alg) {
    this.alg = alg;
    this.validFor = 300;
}


public String issue() {

    String jwt = '';

    JSONGenerator header = JSON.createGenerator(false);
    header.writeStartObject();
    header.writeStringField('alg', this.alg);
    header.writeEndObject();
    String encodedHeader = base64URLencode(Blob.valueOf(header.getAsString()));
        
    JSONGenerator body = JSON.createGenerator(false);
    body.writeStartObject();
    Long rightNow = (dateTime.now().getTime()/1000)+1;
    body.writeStringField('iss', this.iss);
    body.writeNumberField('iat', rightNow);
    body.writeNumberField('exp', (rightNow + validFor));
    if (claims != null) {
        for (String claim : claims.keySet()) {
            body.writeStringField(claim, claims.get(claim));
        }
    }
    body.writeFieldName('context');
    body.writeStartObject();
    body.writeStringField('custom_user_id', user_id);
    body.writeStringField('authy_app_id', app_id);
    body.writeEndObject();
    body.writeEndObject();
    system.debug('body ' + body.getAsString());
    jwt = encodedHeader + '.' + base64URLencode(Blob.valueOf(body.getAsString()));
    
    if ( this.alg == HS256 ) {
        Blob key = EncodingUtil.base64Decode(privateKey);
        Blob signature = Crypto.generateMac('HmacSHA256',Blob.valueof(jwt),key);
        jwt += '.' + base64URLencode(signature);  
    } else if ( this.alg == RS256 ) {
        Blob signature = null;
        
        if (cert != null ) {
            signature = Crypto.signWithCertificate('rsa-sha256', Blob.valueOf(jwt), cert);
        } else {
            Blob privateKey = EncodingUtil.base64Decode(pkcs8);
            signature = Crypto.sign('rsa-sha256', Blob.valueOf(jwt), privateKey);
        }
        jwt += '.' + base64URLencode(signature);  
    } else if ( this.alg == NONE ) {
        jwt += '.';
    }
    
    return jwt;

}


public String base64URLencode(Blob input){ 
    String output = encodingUtil.base64Encode(input);
    output = output.replace('+', '-');
    output = output.replace('/', '_');
    while ( output.endsWith('=')){
        output = output.subString(0,output.length()-1);
    }
    return output;
}

And here is how I am issuing the token from this class:

authy_JWT jwt = new authy_JWT('HS256');
jwt.privateKey = 'my_private_key';
jwt.iss = 'Test';
jwt.app_id = 'my_app_id';
jwt.validfor = 999999999;
jwt.user_id = userinfo.getuserid();
string token = jwt.issue();

If I try to use this jwt token in the authy registration process I receive an error that it's not in an accepted format.

When I try to validate the token at https://jwt.io/ I see the message invalid signature but the header and payload look right. What am I missing?