# Digital Signature/Security
## Basic Question and Answers about Security of Digital Signature

The initial questions a learner often has is:
    Q: Why is it technically/mathematically so difficult, to create a new digital signature for an altered message (see changes of e-mail above)?
    A: The digital signature is even very long for short messages and has a huge number of combinatoric options to be tested until someone is able to create a new valid signature for an altered message without having the private key of the sender, that signed the message. You need the private key to sign the altered message again and even for a minor change of one character in a short message the digital signature looks totally differnt. Depending on the length of the keys all computers of the world would need more than 100 years to test all possible digital signatures and find a new valid signature. Capabilities of quantum computers may require a reassessment of the security. Mathematically the problem is equivalent to the factorization of a number, that is a product of 2 very large prime numbers and for such a number factorization is a very difficult and extremely time consuming task. The underlying strong cryptographic architecture (the digital signature is part of) is used to secure banking transactions, which are extremely vulnerable from risk management perspective.
    Q: What is the difference between digital signature and encryption of a message in terms of security?
    A: The digital signature attaches a cryptic set of symbols to messages or to digital media. A digital media is still readible for everyone. It provides security for "unallowed" alteration of the digital documents. The binary content of the message or digital media in general is not changed (e.g. images, video, audio, databases). The encryption is used in cases, when the content itself should be protected against public access (e.g. make secured financial transaction, exchange personal medical data, plan and secure digital military application and others). Encryption is used when a public available information could have a negative impact on the community, that uses the encryption.
    Q: Can digital signature and encryption of a message be used in conjunction?
    A: Yes. This will be explain with an example.
   * (Communication) Assume Susann (Sender of Message) wants to submit a message to Ralph (Recipient of the Message).
   * (Message) The message is
   * (Encryption: Public key of the Recipient) The sender Susann uses the public key of the recipient Ralph to encrypt the message.
   * (Encrypted Message) The encrypted message may look like this
       This message can be decrypted with the private key of the recipient Ralph only.
   * (Attach a Digital Signature of Sender) Susann uses her private key to attach a digital signature to the encrypted message. That assures that the encrypted message was not altered. E.g. an attacker Antony encrypts another message "Hi Ralph, do not want to see again, Susann" and sends that encrypted message to Ralph pretending to be Susann. Even if the alternative message is now encrypted and could be decrypted by Ralph only with his private key, the message was not really send by the sender Susann. Attaching the digital signature by Susann with her private key allows Ralph be sure that the attached encrypted message is really from Susann, assuming that Susann is the only one who has access to her private key. So the conjunction of an encryted message with a digital signature may look like this.
       Changing a single character of the encrypted message will make the digital signature invalid.
   * (Ralph Receives the Message) When Ralph receives the message, then the mail software checks with the public key of Susann if the message was really from Susann. If the digital signature is valid, then Ralph trust the message to be from Susann. The attacker Antony does not have the private key of Susann to provide a valid digital signature for the alternative message.
   * (Ralph decrypts Message) The message was encrypted with the public key of Ralph and Ralph is the only one to be capable to decrypt the message, if he is the only one who has access to the private key of Ralph
       With this example you see the importance that private keys must be kept private. If other people have access to your private key, they would be able to digital sign a document on behalf of you or the may decrypt encrypted messages that are encrypted for your eyes only.
    Q: I understand that example above but how can I check the if a digital signature is valid or invalid, because someone has altered the message and how do I decrypt an e-mail that was encrypted with my private key? :
    A: That must not be done manually. If would not be operational workflow, to require a lot of actions from a user to sign, decrypt or encrypt message. E.g. with the OpenSource software Thunderbird and the plugin Enigmail Susann just needs to press a button to sign a message with your private key. If you want to encrypt the message for Ralph she needs the public key from Ralph. The public keys can be retrieved e.g. from a public key server where Ralph provided his public key or Ralph may have shared the public key directly with Susann. Ralph will see a valid digital signature in green in his mail client and the encrypted message will be decode automatically by the mail client if a specific plugin is installed.

## Learning Task

* (Create Keys) Create a Public and Private Key with GunPG - Search for Video Tutorials
* (Publish or Share your Public Key) You can share your public key on a public key server (e.g. http://keys.gnupg.net/ ) or share your public key with a friend if you want play around with encryption and digital signature.
* (Send e-Mail with digital Signature) Install OpenSource Thunderbird and in that e-Mail client install Enigmail. Send
** an e-mail with a digital signature with your friend and receive an e-mail from your friend with a digital signature.
** an encrypted message to your friend and receive an encrypted message from your friend.
** an encrypted message with a digital signature from you to your friend.
** try to forward an encrypted message for you back to your friend without encryption.
* (Use Cases) Identify use cases in which digital signature is useful. What use cases in which you would expect the e-mail to be encrypted. When would you expect to use digital signature and encryption together (e.g. medical results send to you). Elaborate your use case more in details. What are the requirements and constraints e.g. in health system and on the patient side and what is the legal framework in which encryption and digital signature can be used?
* (Risk Literacy) What are the requirements and constraints in an educational setting to become IT risk literate.
* (Digital Learning Environments) Digital learning environments can collect data about students. Intelligent Tutoring Systems (ITS) are adaptive to the prerequisites of the learner. What kind of privacy issues should be respected in Digital Learning Environments and how can digital signature and encryption can be used to assure that privacy?
* (Quantum Computers) Discuss the performance of quantum computers and the design of such kind of computers. Explain why the availability of quantum computers would require a reassessment of the security of the RSA method.

## Subtopic

* Wikipedia:RSA
* RSA as part of mathematical number theory
* Intelligent Tutoring Systems (ITS)

## Teachers Information

* this learning resource is designed around questions and answers.
* if learners sometimes want just a few basic questions to be answered, this learning resource may satisfied these needs with this rough information about digital signature and its security.
* at the same time this learning resources provides an entry point for deeper analysis of the topic, please feel free to add helpful learning resources to this page.