Study Guide
Symmetric, Asymmetric and Hybrid Encryption
One shared key or a public and private pair: how symmetric encryption (AES) and asymmetric encryption (RSA and elliptic curves) work, what each is good and bad at, and how hybrid encryption uses both to send a large file to someone you have never met.
Lesson 6.2 Cryptography & PKI
There are two families of encryption, and modern systems use both. This lesson works out what each family does, what problem each one cannot solve on its own, and how they are combined.
Stage: Think
One strongbox, two cities
Think it through
You and a friend want to pass a locked strongbox back and forth, and each of you needs a copy of its key. You live in different cities and have never met. How could you get the key to your friend safely?
- Hint 1: Who else might handle the key on its way?
Show what happens
That is hard: posting it or describing it risks someone else getting a copy. Sharing one secret key safely, before any secret has been shared, is the problem this lesson starts from.
Think it through
Show the answer
Answer: A. Lock it; only they can open it.
You could lock the box with it, and only your friend could open it. No secret had to travel at all.
Stage: Predict
Asymmetric encryption: a key pair
Think it through
Suppose there were two keys: one that can only lock and one that can only unlock. Which would you give away freely, and which would you guard?
- Hint 1: What harm could a stranger do with a key that only locks?
Show what happens
Give away the one that only locks: anyone can lock a box for you with it. Guard the one that unlocks, because it alone opens what others have locked.
Asymmetric encryption uses two mathematically related keys: a public key and a private key.
- The public key can be given to anyone. It is not a secret.
- The private key is kept secret by its owner and is never shared.
- What one key of the pair does, only the other can undo. Data encrypted with a public key can be decrypted only with the matching private key.
- Knowing the public key does not let anyone work out the private key in any practical amount of time.
The two keys together are a key pair. Asymmetric encryption is also called public-key cryptography.
Bob buys a thousand identical padlocks, keeps the only key, and leaves the padlocks, open, in a basket where anyone can take one.
Alice wants to send Bob a private letter. She takes one of Bob’s padlocks, puts the letter in a box and snaps the padlock shut. Now nobody can open the box, including Alice. Only Bob’s key opens it.
- The open padlock is Bob’s public key: anyone may have one, and it can only lock.
- Bob’s key is his private key: it never leaves him, and it is the only thing that unlocks.
Alice and Bob never had to meet or share a secret, which is exactly the problem symmetric encryption could not solve.
Where the analogy stops. A real public key is a number, not an object, so it can be copied endlessly and sent over the same network as the message. And the analogy leaves out an important danger: Alice must be sure the padlock really is Bob’s. If Mallory swaps in her own padlocks, Alice will lock the box for Mallory. Proving whose public key is whose is the job of certificates.
Check your understanding
Show the answer
Answer: C. Only Bob.
Only Bob: his key is the only thing that unlocks it, so not even Alice can open it again.
Alice sends Bob a confidential message in two ways. Follow each row from left to right and notice which key is used at each operation.
Symmetric
One shared secret key. Alice and Bob must both already hold it.
- DataPlaintext (Alice)
- OperationEncryptKey: the shared secret key
- DataCiphertext (in transit)
- OperationDecryptKey: the same shared secret key
- DataPlaintext (Bob)
Asymmetric
Bob’s key pair. Alice needs only Bob’s public key, which is not secret.
- DataPlaintext (Alice)
- OperationEncryptKey: Bob’s public key
- DataCiphertext (in transit)
- OperationDecryptKey: Bob’s private key
- DataPlaintext (Bob)
In the asymmetric row, Alice’s own keys are not used at all. Encrypting for confidentiality always uses the recipient’s public key.
Stage: Predict
RSA and prime numbers
RSA, published in 1977 and named after Rivest, Shamir and Adleman, is the best-known asymmetric algorithm. Its security rests on a simple imbalance.
Think it through
Show the answer
Answer: C. Multiplying them.
Multiplying. Going back from 3,233 to 61 and 53 takes trial and error, and with numbers hundreds of digits long it becomes infeasible.
Multiplying two numbers is easy. Take the primes 61 and 53: their product is 3,233, and a child can check that. Going the other way is harder. Given only 3,233, finding the two primes that produced it means trial and error.
With tiny numbers the search is quick. RSA uses two primes that are each hundreds of digits long. Multiplying them takes a computer a fraction of a second. Factoring the product, that is, recovering the two primes from it, is not feasible with any known method on today’s computers. The public key is derived from the product; the private key depends on knowing the two primes.
Go deeper RSA key sizes and what “2048-bit” means
An RSA key’s length is the size of that product, the modulus. Common sizes are 2048, 3072 and 4096 bits. NIST treats 2048 bits as the minimum for current use and rates it at about 112 bits of security.
RSA can be used for two different jobs: encrypting small amounts of data, and creating digital signatures. The keys are used differently in each, which Digital Signatures sets out.
A large enough quantum computer would break RSA and elliptic-curve cryptography, which is why NIST published new “post-quantum” algorithm standards in 2024. That transition is beyond this lesson.
Elliptic curve cryptography
Elliptic curve cryptography (ECC) is a family of algorithms, not one algorithm. Its members are built on the mathematics of elliptic curves instead of on factoring. Different members do different jobs: ECDH agrees a shared key between two parties, and ECDSA creates digital signatures.
What the family has in common is efficiency. ECC gives the same strength as RSA with much shorter keys, which means less computation and less data to send. That is why it is widely used on phones, smart cards and in modern web connections.
Key lengths are not comparable
It is natural to assume that a longer key is always stronger. That holds only within one kind of algorithm.
A symmetric key is attacked by trying every key, so every bit counts in full. An RSA key is attacked by factoring, which is far faster than trying every key, so RSA needs many more bits for the same protection.
| Strength, as symmetric bits | Symmetric key | RSA key | Elliptic-curve key |
|---|---|---|---|
| About 112 | (older ciphers) | 2048 bits | 224 bits |
| About 128 | AES-128 | 3072 bits | 256 bits |
| About 256 | AES-256 | 15,360 bits | 512 bits or more |
Check your understanding
Show the answer
Answer: B. The AES key.
The AES key: about 256 bits of strength against about 112, although the RSA key is eight times as long.
So a 2048-bit RSA key is weaker than a 256-bit AES key, even though it is eight times as long.
Stage: Predict
Comparing the two
Think it through
Before reading the table: which do you expect to be faster, symmetric or asymmetric encryption, and what is each one’s main difficulty?
- Hint 1: Which one was the padlock trick designed to solve?
Show what happens
Symmetric is fast, and its difficulty is getting the key to the other party. Asymmetric is slow, and its difficulty is knowing that a public key really belongs to its owner.
| Aspect | Symmetric | Asymmetric |
|---|---|---|
| Keys | One shared secret key | A public key and a private key |
| Speed | Fast: suits large amounts of data | Slow: suits small amounts of data |
| Main difficulty | Getting the key to the other party safely | Knowing that a public key really belongs to its claimed owner |
| Typical key length | 128 or 256 bits | 2048 bits or more (RSA); 256 bits (elliptic curve) |
| Examples | AES | RSA, and the ECC family |
Do not confuse: Public key and private key
- Share it?Public key
- Yes, with anyone. It is used to encrypt data for its owner, and to check its owner’s signatures.
- Share it?Private key
- No, with nobody. It is used to decrypt data sent to its owner, and to create its owner’s signatures.
“Private key” means the secret half of a key pair. The single key in symmetric encryption is usually called a secret key or shared key, to avoid confusion.
Stage: Predict
Hybrid encryption: using both together
Think it through
Symmetric encryption is fast but cannot share its own key; asymmetric shares keys easily but is slow. How could you use both to send a 40 GB backup?
- Hint 1: Which part is large, and which part is small?
Show what happens
Encrypt the backup with a fast symmetric key, then encrypt just that small key with the recipient’s public key, and send both.
Each family has what the other lacks. Symmetric encryption is fast and cannot distribute its own key. Asymmetric encryption distributes keys easily and is far too slow for large data. Hybrid encryption uses each for what it does well.
Encrypt the data with a fast symmetric key. Encrypt that key with the recipient’s public key.
Step through an example. Alice is the network manager of a fictional school. She must send a 40 GB backup of the school’s files to Bob, at the school’s off-site backup provider. They have never exchanged a secret.
Six steps. Alice uses AES for the backup and RSA for the AES key. The people, school and provider are fictional.
Alice
Step 1 of 6: Generate a new AES key
Alice’s software creates a random 256-bit AES key, to be used for this backup only.
Technical detail: A key used for one exchange is often called a session key or, when it protects stored data, a data encryption key.
Alice
Step 2 of 6: Encrypt the backup with the AES key
AES is fast, so encrypting 40 GB takes minutes. The result is the encrypted backup.
Alice
Step 3 of 6: Encrypt the AES key with Bob’s public key
Alice obtains Bob’s RSA public key and uses it to encrypt the small AES key. Only 256 bits pass through the slow RSA operation.
Technical detail: This is sometimes called wrapping the key. Alice must be sure the public key is really Bob’s, which is what a certificate is for.
Alice to Bob
Step 4 of 6: Send both
Alice sends the encrypted backup and the encrypted AES key together. Mallory, watching the network, sees both and can read neither.
Bob
Step 5 of 6: Decrypt the AES key with his private key
Bob’s RSA private key, which has never left him, recovers the AES key.
Bob
Step 6 of 6: Decrypt the backup with the AES key
Bob now holds the same AES key that Alice used, and decrypts the 40 GB backup quickly.
No secret was ever sent unprotected, and the slow algorithm handled only a tiny key.
Check your understanding
Show the answer
Answer: C. The AES key.
The AES key. Bob then uses the AES key to decrypt the backup.
Hybrid encryption is not a special case. It is how encryption is normally done: encrypted email, encrypted files and secure web connections all work this way. Web connections usually agree the symmetric key by a different method instead of encrypting it with RSA; Transport Encryption, Key Agreement and Forward Secrecy explains that and why it is better.
Stage: Explain
Security+ terminology
The CompTIA Security+ SY0-701 exam objectives (objective 1.4) list public key and private key under public key infrastructure, and asymmetric, symmetric, key exchange, algorithms and key length under encryption.
The objectives name no individual algorithm; AES, RSA and ECC are the standard examples used to explain the listed terms. “Hybrid encryption” is not a term in the objectives, though it is how the two listed kinds are used together.
Stage: Apply
Apply it in a new situation
These questions use the lesson in situations it has not shown. For the strongest test of your understanding, come back to them on another day and answer each one at the first attempt.
Apply it
Show the answer
Answer: A. 45
45: each of the 45 pairs needs its own shared key, which is why symmetric keys alone do not scale.
Apply it
Show the answer
Answer: C. Bob’s public key.
Bob’s public key, so that only Bob’s private key can decrypt it.
Apply it
Show the answer
Answer: B. Is the public key really Bob’s?
Alice has to know that a public key really belongs to Bob; otherwise she may lock her letter for Mallory. Later lessons show how that is checked.
Stage: Check
Check your understanding
These questions come from the approved revision bank. They were approved under owner-authorised delegated review: the site owner authorised the review and did not read each question individually.
Show answer
Answer: Getting the shared key to the other party without exposing it
Symmetric encryption uses one shared secret key, and its difficulty is getting that key to the other party safely. Speed is its strength, not its weakness: it is much faster than asymmetric encryption. Key pairs belong to asymmetric encryption, and publishing a symmetric key would defeat it.
Revision sources: Session 9: Cryptographic Algorithms, Public Key Infrastructure and Cryptographic Solutions (Classroom session record) · Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: A symmetric block cipher with 128-, 192- or 256-bit keys
AES is the standard symmetric block cipher, with 128-, 192- or 256-bit keys: one shared key encrypts and decrypts. The algorithm built on large primes is RSA, the elliptic-curve family is ECC, and both of those are asymmetric, using a key pair where AES uses a single key.
Revision sources: Session 9: Cryptographic Algorithms, Public Key Infrastructure and Cryptographic Solutions (Classroom session record) · Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: Bob’s public key
Data encrypted with a recipient’s public key can be decrypted only with the matching private key. Alice therefore uses Bob’s public key, which Bob can share freely, and only Bob’s private key opens the file. Alice does not hold Bob’s private key and should not, and encrypting with either of her own keys would not restrict the file to Bob.
Revision sources: Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: The public key can be shared with anyone without weakening the pair; The private key should stay under its owner’s sole control
A key pair consists of a public key that can be shared freely and a private key that its owner keeps secret and that cannot feasibly be worked out from the public key. Publishing the public key is the point of the design; if the private key could be derived from it, or if both had to be hidden, the scheme would offer nothing over a shared secret.
Revision sources: Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: Factoring the product of two large prime numbers
RSA’s security rests on the difficulty of factoring the product of two large primes: multiplying them is easy, and recovering them from the product is not. Searching a keyspace is a brute-force attack on any cipher, sharing one key is the symmetric distribution problem, and a fixed letter shift describes a classical cipher.
Revision sources: Session 9: Cryptographic Algorithms, Public Key Infrastructure and Cryptographic Solutions (Classroom session record) · Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: False
False. ECC is a family of algorithms based on elliptic-curve mathematics, used for purposes such as key agreement and digital signatures. What the family has in common is the mathematics, which gives strength comparable to RSA with much shorter keys.
Revision sources: Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: False
False. Key lengths are not comparable between kinds of algorithm. A 2048-bit RSA key is rated at roughly the strength of a 112-bit symmetric key, well below a 256-bit AES key, because attacking RSA does not require trying every possible key.
Revision sources: Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: Encrypt the backup with a new AES key, then encrypt that key with Bob’s public key
In hybrid encryption, such as AES and RSA used together, the data is encrypted with a fast symmetric key, and that key is then protected with the recipient’s public key. Encrypting 40 GB directly with RSA would be extremely slow. Anything produced with Alice’s private key can be processed by anyone holding her public key, so it restricts nothing to Bob. Sending the AES key unprotected leaves the distribution problem unsolved.
Revision sources: Session 9: Cryptographic Algorithms, Public Key Infrastructure and Cryptographic Solutions (Classroom session record) · Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Show answer
Answer: The symmetric key that encrypted the data
Hybrid encryption encrypts the data with a fast symmetric key and then protects that key with the recipient’s public key. The public-key operation therefore handles only a small key, which is what makes the scheme practical for large data. Private keys are not sent or wrapped in this exchange: each stays with its owner.
Revision sources: Symmetric, Asymmetric and Hybrid Encryption (Supplementary Study Guide explanation)
Study and revision
Practise through the Cryptography & Data Protection topic. Questions cover the key-distribution problem, AES, which key encrypts for a recipient, what RSA rests on, ECC as a family, comparing key lengths and hybrid encryption; five flashcards recall the main points. Most are learning-only. The questions that have been verified against CompTIA Security+ SY0-701 objective 1.4 are also in the Security+ practice track; that does not mean the lesson covers the whole of an objective, and the lesson does not establish practical experience.
One earlier concept is practised here as well. “Cryptographic mechanisms and PKI” holds one question and one flashcard on the two key models. They were written before this lesson existed, from NIST’s definitions and not from course evidence, and both are approved items of the seed bank: the question is mapped to objective 1.4, and the flashcard is verified for it. That concept still records no course evidence of its own; the course evidence for this subject is recorded on this lesson’s main concept.
Stage: Consolidate
What to remember
- Symmetric encryption uses one shared secret key; AES is fast, but the key has to reach the other party safely.
- Asymmetric encryption uses a key pair: data encrypted with the public key opens only with the private key.
- RSA rests on the difficulty of factoring; ECC gives the same strength with shorter keys.
- Key lengths compare only within one kind of algorithm.
- Hybrid encryption encrypts the data with a symmetric key, and that key with the recipient’s public key.
Key terms
- Symmetric encryption
Encryption in which the same secret key encrypts and decrypts. It is fast and suits large amounts of data.
- Asymmetric encryption
Cryptography that uses a mathematically related pair of keys: a public key that can be shared and a private key that is kept secret.
- Key pair
The two related keys used in asymmetric cryptography: a public key and a private key. What one does, only the other can undo.
- Public key
The half of a key pair that can be given to anyone. It encrypts data for the key’s owner and verifies the owner’s signatures.
- Private key
The half of a key pair that its owner keeps secret. It decrypts data sent to the owner and creates the owner’s signatures.
- Hybrid encryption
Encrypting data with a fast symmetric key, then protecting that key with the recipient’s public key.
Common misunderstandings
Neither replaces the other. Symmetric encryption does the bulk work because it is fast; asymmetric encryption solves key distribution. Real systems use both.
Only within one kind of algorithm. A 2048-bit RSA key is weaker than a 256-bit AES key.
Anything produced with your private key can be processed by anyone with your public key, which is everyone. For confidentiality, encrypt with the recipient’s public key.
ECC is a family of asymmetric algorithms built on elliptic curves, used mainly for key agreement and signatures.
Further reading
- NIST FIPS 197: Advanced Encryption Standard (AES): the standard itself.
- NIST SP 800-57 Part 1: Recommendation for Key Management: includes the table of comparable key strengths.
- NCSC: advice and guidance by topic, filtered to cryptography: the UK National Cyber Security Centre’s published guidance on using cryptography.
- CompTIA Security+ SY0-701 exam objectives (PDF): objective 1.4.
Lesson sources and acknowledgements
Sources and scope
- Covered in Session 9 (see the Session 9 Learning Log): symmetric encryption and AES; asymmetric encryption, RSA and ECC, key pairs and key distribution, and prime numbers as the foundation of RSA; and hybrid encryption using AES and RSA together.
- Accuracy qualifications: ECC is a family of algorithms, not one algorithm; RSA encryption and RSA signing use the keys for different purposes; key lengths are not comparable between kinds of algorithm.
- Independently checked: AES against NIST FIPS 197; the comparable key strengths against NIST SP 800-57 Part 1; and the Security+ wording against the published SY0-701 objectives. These are external references, not course evidence.
- Supplementary explanation: every definition, the strongbox and padlock analogies and their limits, the key-count arithmetic, the 61 and 53 example, the account of ECC, the two comparison tables, the school backup walk-through and the misunderstandings. These were developed afterwards and are my explanations, not the tutor’s words. The diagrams are original.
- Guided version (published 1 November 2026, awaiting the site owner’s editorial review): the strongbox and open-padlock opening questions, every question asked in the lesson with its feedback and hints, the application questions and the closing summary are supplementary explanation written for the Study Guide. The settings are fictional. The questions in the lesson’s steps are not revision-bank items; those in “Check your understanding” are, unchanged.
- No practical work is claimed. Alice, Bob, the school and the backup provider are fictional. I have not generated keys or encrypted a backup as part of this lesson.
The standard symmetric block cipher, with 128-, 192- or 256-bit keys.
A fixed, step-by-step method for carrying out a task. In cryptography, the published method that a cipher or a hash function follows.
Cryptography that uses a mathematically related pair of keys: a public key that can be shared and a private key that is kept secret.
A cipher that encrypts data in blocks of a fixed size. AES is a block cipher that works on 128-bit blocks.
An algorithm that turns plaintext into ciphertext, and back again, under the control of a key.
The security objective of restricting information to authorised people, systems or processes.
A secret value that controls what a cipher does. The same algorithm with a different key gives a different result.
The practice of protecting information by transforming it, so that only the intended parties can read it or trust it.
A method by which two parties each contribute a value and both compute the same shared secret, without the secret itself being sent.
A value produced with a private key that only the signer should hold, which anyone can check with the matching public key to confirm who signed some content and that it has not changed since.
A family of asymmetric algorithms based on the mathematics of elliptic curves, used for key agreement and digital signatures.
A digital signature algorithm from the elliptic-curve family. It signs and verifies; it does not encrypt.
Transforming data with a cipher and a key so that it cannot be read without the right key. Decryption reverses it.
Encrypting data with a fast symmetric key, then protecting that key with the recipient’s public key.
The rule that a cryptographic system should stay secure when everything about it except the key is public.
Getting a cryptographic key to the party who needs it without exposing it on the way.
Any method by which two parties come to share a secret key over a network that others can observe.
The number of bits in a key. Each added bit doubles the number of possible keys.
The two related keys used in asymmetric cryptography: a public key and a private key. What one does, only the other can undo.
The certificate authorities, certificates, software and policies that bind public keys to identities and manage certificates through their lives.
The half of a key pair that its owner keeps secret. It decrypts data sent to the owner and creates the owner’s signatures.
The half of a key pair that can be given to anyone. It encrypts data for the key’s owner and verifies the owner’s signatures.
Uncertainty and potential harm to an organisation’s objectives, considering what could happen, how likely it is, the consequences and the organisation’s context.
An asymmetric algorithm whose security rests on the difficulty of factoring the product of two large prime numbers.
Encryption in which the same secret key encrypts and decrypts. It is fast and suits large amounts of data.
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