Nosso BackBean onde aguardaremos o request

CaptchaBean.java

import dint.util.ManageBean;
import java.awt.Color;
import java.awt.Font;
import java.awt.GradientPaint;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.image.BufferedImage;
import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.Serializable;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Iterator;
import java.util.List;
import java.util.Random;
import javax.faces.bean.ManagedBean;
import javax.faces.bean.RequestScoped;
import javax.imageio.ImageIO;
import org.primefaces.model.DefaultStreamedContent;
import org.primefaces.model.StreamedContent;
 
/**
 * @author calixto
 * Referências: http://zetcode.com/tutorials/jeetutorials/captcha/
 *              http://www.kianworknotes.com/2016/01/simple-captcha-by-primefaces.html
 *              http://blog.marcoreis.net/como-usar-graphicimage-no-primefaces/
 */
@ManagedBean
//Atenção no escopo deste Bean é um Request!!!
@RequestScoped
public class CaptchaBean extends ManageBean implements Serializable {
 
    public StreamedContent getCaptcha() {
        StreamedContent dText = null;
        try {
            //tamanho da imagem gerada
            int width = 150;
            int height = 50;
            List arrayList = new ArrayList();
            //caracteres possível no captcha
            String capcode = "abcdefghijklmnopqurstuvwxyzABCDEFGHIJKLMONOPQURSTUVWXYZ0123456789!@#$%&*";
            for (int i = 1; i < capcode.length() - 1; i++) {
                arrayList.add(capcode.charAt(i));
            }
            //embaralhando cadeia de caracteres
            Collections.shuffle(arrayList);
            Iterator itr = arrayList.iterator();
            String s = "";
            String s2 = "";
            Object obj;
            while (itr.hasNext()) {
                obj = itr.next();
                s = obj.toString();
                s2 = s2 + s;
            }
            String s1 = s2.substring(0, 6);
            char[] s3 = s1.toCharArray();
            //iniciando a manipulação de imagens
            BufferedImage bufferedImage = new BufferedImage(width, height, BufferedImage.TYPE_INT_RGB);
            Graphics2D g2d = bufferedImage.createGraphics();
            //definindo a fonte a ser utilizada na imagem
            Font font = new Font("Georgia", Font.BOLD, 18);
            g2d.setFont(font);
            RenderingHints rh = new RenderingHints(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
            rh.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
            g2d.setRenderingHints(rh);
            //setando o gradiente do fundo da imagem do captcha
            GradientPaint gp = new GradientPaint(0, 0, Color.red, 0, height / 2, Color.black, true);
            g2d.setPaint(gp);
            g2d.fillRect(0, 0, width, height);
            g2d.setColor(new Color(255, 153, 0));
            Random r = new Random();
            int index = Math.abs(r.nextInt()) % 5;
            String captcha = String.copyValueOf(s3);
            //passo o captcha para a sessão, aqui fica a cargo do escopo da sua aplicação
            super.setObjetcSession("captcha", captcha);
            int x = 0;
            int y = 0;
            for (int i = 0; i < s3.length; i++) {
                x += 10 + (Math.abs(r.nextInt()) % 15);
                y = 20 + Math.abs(r.nextInt()) % 20;
                //desenhando a variável s3
                g2d.drawChars(s3, i, 1, x, y);
            }
            g2d.dispose();
            //gerando o stream da imagem
            ByteArrayOutputStream os = new ByteArrayOutputStream();
            ImageIO.write(bufferedImage, "png", os);
            os.flush();
            os.close();
            dText = new DefaultStreamedContent(new ByteArrayInputStream(os.toByteArray()), "image/png");            
        } catch (Exception e) {
            e.printStackTrace();
        }
        //StreamedContent sera recebido pelo componente <p:graphicImage>
        return dText;
    }
}