IS6523 Chap.3 Encryption, Keys and Digital Signatures
Encryption, Keys and Digital Signatures
Cryptology splits, and the second half is the one that matters
Encryption is introduced as converting an original message into a form unauthorised individuals cannot understand. The wider science divides into cryptography, the encoding and decoding of messages, and cryptanalysis, the deciphering of a ciphertext without knowing the algorithm or key.
Holding on to that second half changes how the rest of the material reads, because every design choice here is a claim about how expensive cryptanalysis would be and none of them is a claim that it is impossible.
Three primitives, two key arrangements, one hybrid
Three functions do the work: substitution replaces one value with another using one alphabet or several, transposition rearranges values within a block at bit or byte level, and the exclusive-or function compares a bit stream against a key stream and is reversible, so applying the key stream to the ciphertext recovers the plaintext.
Symmetric encryption uses one key for both directions and is efficient but has to move that key out of band. Asymmetric encryption uses two related keys, either able to encrypt, with only the other able to decrypt, and is computationally inefficient while needing four keys for a single two-party conversation.
The arrangement actually in widespread use is a hybrid, in which the asymmetric pair carries only a randomly generated symmetric session key.
What a hash proves, and what a signature adds
A hash function produces a digest confirming that content has not changed.
Its algorithm is public, no key is required, the digest cannot reveal the message, and the probability of two messages colliding is treated as non-existent. That is an integrity claim and nothing more.
Running the asymmetric process backwards over the digest, encrypting it with a private key so that any holder of the public key can open it, is what adds origin and makes denial impossible, which the course names as the foundation of digital signatures and as crucial for electronic commerce.
What this chapter covers
- 01
Cryptography and cryptanalysis as the two halves of one science
- 02
Substitution, transposition and the reversible exclusive-or
- 03
Symmetric ciphers and the out of band key transfer problem
- 04
Asymmetric pairs, and the four operations they support
- 05
The hybrid envelope and why it exists
- 06
Key size rather than secrecy of method
- 07
Hashes, digests and digital signatures
- 08
Public key infrastructure, certificates and certificate authorities
- 09
Key management as the management of people
Assemble confidentiality, integrity and non-repudiation in one exchange
- 3State what is hashed and what the digest is encrypted with.
- 2State how the document and signature are then protected in transit.
- 2State the order in which the buyer reverses it.
Key terms
- Cryptanalysis
- Recovering an original message from a ciphertext when neither the algorithm nor the key is known. It is what every design choice in this topic is priced against.
- Transposition Cipher
- A cipher that rearranges the values within a block rather than replacing them, working at bit or byte level. It is also called a permutation cipher.
- Session Key
- A randomly generated symmetric key used for one exchange, itself encrypted under the recipient's public key. It is what allows the slow cipher to protect only a short input.
- Message Digest
- A fixed summary computed from a message by a hash function, changing if any character of the message changes. It represents the message efficiently and cannot be used to recover it.
- Digital Certificate
- An electronic document travelling with a file, certifying both that the file came from the organisation it names and that its content is unaltered.
- Certificate Authority
- The agency that runs the issuing of certificates and stands as the electronic notary for their origin and their integrity.
- Public Key Infrastructure
- All of the hardware, the software and the cryptosystems that public key encryption needs in order to run, covering enrolment, issuing, verification and revocation.
Encryption, Keys and Digital Signatures FAQ
Does a longer key make an algorithm harder to break, or does secrecy of the algorithm?
The key. The course states that the security of encrypted data does not depend on keeping the encrypting algorithm secret but on keeping some or all of the key secret, and that strength is measured by key size. Each additional bit doubles the space an exhaustive search must cover, which is the arithmetic behind the historical move to longer standards and behind the flat statement that there is no security in obscurity.
If a document arrives with a valid signature, is it confidential?
No, and separating the two is one of the most reliable marks available in this topic. A signature establishes integrity and origin, because the digest matches and only the private key holder could have produced a block the public key opens. It says nothing about who else read the document in transit. Confidentiality requires a separate encryption of the content under the recipient's key.
Why not encrypt everything with public key cryptography and abandon shared keys?
Two reasons the course gives directly. Asymmetric encryption is theoretically sound but computationally inefficient relative to a symmetric cipher, so applying it to bulk data spends the expensive operation on the largest possible input. And it requires four keys for a single conversation between two parties, with the count growing geometrically as parties are added, so the management problem is scaled rather than solved.
What does the course say about keeping keys safe?
That it is a people problem rather than a technology problem.
However sophisticated a cryptosystem is, if the key is discovered the message can be determined, so the rules it supplies are managerial: do not lose keys, know who you are communicating with, grant access only on business need, remember that a technique may be illegal in some jurisdictions, accept that every cryptosystem has weaknesses, and base use on written policy with sound procedures behind it.
Exam move
Draw the four key pair operations as a two by two before anything else, with the key used on one axis and the claim proved on the other, and check that you can say for each cell what it does not prove. Then write out the hybrid envelope in both directions without looking, because the reversal order is where it usually goes wrong.
Finish by stating the one thing a hash establishes, in a single sentence with no mention of identity in it.
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