One of the possible issues that the order of included scripts is important, this works:

  <script type="text/javascript" src="jsbn.js"></script>
  <script type="text/javascript" src="jsbn2.js"></script>
  <script type="text/javascript" src="sjcl.js"></script>
  <script type="text/javascript" src="moment.js"></script>
  <script type="text/javascript" src="aws-cognito-sdk.min.js"></script>
  <script type="text/javascript" src="amazon-cognito-identity.min.js"></script>

But this gives read property 'hex' of undefined:

  <script type="text/javascript" src="jsbn.js"></script>
  <script type="text/javascript" src="jsbn2.js"></script>
  <script type="text/javascript" src="moment.js"></script>
  <script type="text/javascript" src="aws-cognito-sdk.min.js"></script>
  <script type="text/javascript" src="amazon-cognito-identity.min.js"></script>
  <script type="text/javascript" src="sjcl.js"></script>   <!--- wrong, to late

Also not forget to use SJCL with code byte options. Here is very basic demo with all lib js files included:

cognito_login_demo.zip

AWS Cognito pool

You need to enter Cognito pool parameters on demo form

You can found Cognito User Pool Id on Pool details page. You also need to add App on Apps page, and when you add an app ensure not to generate secret (this is not supported by javascript SDK):

21c9c526.png

When App created copy Cognito Client ID form Apps page

#aws