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#set page(
paper: "a4",
numbering: "1",
//numbering: "1",
margin: (top: 2.5cm, left: 2.5cm, right: 2.5cm, bottom: 2cm)
)
#if (context here().page()) != 1 [
#set page(
numbering: "1"
)
]
#set page(
footer: context {
if here().page() > 1 {
align(center)[#counter(page).display()]
}
}
)
#set text(
font: "Times New Roman",
//font: "Times New Roman",
size: 12pt,
)
Marius Drechsler\
Process Essay\
May 17th, 2025
Compare and Contrast Essay\
June 21st, 2025
#align(center, text(size: 17pt, weight: "bold")[
*The Digital Journey of Your Voice*
*Decoding Security: A Comparative Analysis of Symmetric and Asymmetric Encryption*
])
#set align(left)
@ -29,65 +43,64 @@ May 17th, 2025
#show: word-count
Have you ever wondered what happens with your voice when you are talking to someone on the phone?
From the instant the soundwaves leave your throat until they reach the ear of the person you are talking to,
a series of analog and digital processes collaborate to carry your message.
In fact, this whole process can be broken down into three major steps -- sampling, quantisation and modulation.
In the course of this essay, we will investigate each of these steps in more depth to understand how modern
communication works on a technical level.
Modern communication is highly dependent on robust and flexible encryption methods.
These methods are not only needed when transmitting a message, but also to provide secure and reliable infrastructure which is dependent on internet-communication.
To achieve such a high standard of flexibility, two prominent methods for encrypting messages are used: symmetric and asymmetric encryption.
These two kinds of encryption algorithms use different strategies and methods to securely encrypt plain text content.
This essay will investigate the key differences between symmetric and asymmetric encryption algorithms while especially focussing on use-cases, security, performance and complexity.
To start, we will take a closer look at the analoue signal that reaches your phone's microphone.
Every sound wave, like your voice or the tone of a guitar string, is so called time and value continuous.
That means, such a signal has an infinitely accurate value at each imaginable point in time.
However, an electronic device, for example a computer or a phone, cannot understand such an analogue signal, thus we have to first transform it into some kind of electrical signal the device can understand.
In general, we can assume that an electrical device can only process time and value disteet signals.
To transform our original continuous signal into its discreet or rather digital representation, we can make use of the sampling and
quantization steps in our communication process.
The most prominent difference between symmetric and asymmetric encryption is the number of keys used in the encryption and decryption stages.
Symmetric encryption utilizes a single key for both encryption and decryption.
For that reason, both parties that want to encrypt or decrypt a message symmetrically need the same key to decrypt and encrypt their corresponding messages.
On the other hand, asymmetric encryption uses two different keys for encryption and decryption: a public and a private key.
The public is shared openly and is used to encrypt a message for the recipient of the public keys' owner.
The recipient of the encrypted message uses their private key to decrypt the message @symmetric-vs-asymmetric.
The public key can be thought of as a lock that the sender uses so "seal" their message, while the private key is only owned by the corresponding recipient to unlock the message and read its contents.
This fundamental difference in key management not only affects the encryption process but also has significant implications for the security of the encrypted data.
In the sampling process, the analogue signal is transformet into a time discreet and value continuous signal.
Conceptually, an analog-to-digital converter (ADC) takes rapid "snapshots" of the amplitude of the input signal at uniform intervals and records each reading.
The rate at which these snapshots occur is called sampling frequency.
Ideally, we do want to maximize the timespan between each of these snapshots, using the lowest possible sampling frequency so to speak.
The Nyquist Frequency defines this lowest possible sampling frequency as double the frequency of the originating signal @shannon.
For example, if the frequency of our original signal is 1 MHz, the analog-to-digital converter will need to take a snapshot of the signal at a frequency of at least 2 MHz.
At this moment, our signal now is time-discreet and value-continuous.
To convert these time-discreet values into real bits and bytes we will make use of the quantizer in the next step.
The security of both symmetric and asymmetric encryption algorithms depends heavily on the context and application of these methods.
Symmetric encryption heavily relies on the strength of the key and the algorithm used @symmetric-security.
For example, the Data Encryption Standard (DES) algorithm introduced in 1975 uses a key length of 56 bits, which makes it too insecure for modern applications, since the key can easily be guessed by a relatively powerful computer @des.
For that reason, DES has been generally replaced by the Advanced Encryption Standard (AES).
Additionally, since there is only one key for both encryption and decryption, symmetric encryption algorithms are vulnerable if the key is compromised.
This security vulnerability is not present in asymmetric encryption algorithms, as the keys to encrypt and decrypt messages are separated.
The public key is defined as being safely publicly available while the private key can be always kept with its owner @symmetric-vs-asymmetric.
These implications on security also impact the respecting applications for encryption methods. // why? is not explained here.
// hier noch ein concluding sentence um auf das thema use case hinzuweisen
Quanization describes the operation of transforming a continuous value into a discreet form.
Imagine placing random dots in a row on a piece of paper.
A simple quantization process now would be to take a ruler and for each point record which is the next highest marking on the ruler.
In the same sense, the quantizer of an electronic device maps the continuous input vaulues to predefined codewords -- a collection of bits (for example "000", "110" or "011").
Our signal has now fully arrived in the digital domain.
// Note: Maybe expand more what happened up until now
Up to this point we have completeley encoded our analogue message digitally.
During the next steps, the digital signal will be further processed and prepared for transmission.
The use of a certain encryption method heavily depends on the given use case.
While symmetric encryption is mainly used to encrypt large amounts of data, like files or even whole disks, asymmetric encryption is usually used for secure communication over the internet.
A fitting example for secure internet communication is secure web browsing, using Transport Layer Security (TLS) @tls.
TLS uses asymmetric cryptography to ensure that the web server is correctly authenticated against the user.
This method provides assurance that the user is genuinely interacting with the designated server.
Another example is encrypting or decrypting e-mails using the Pretty-Good-Privacy (PGP) system --- encrypting and decrypting e-mails with the public and private key respectively @pgp.
PGP can also be used to digitally sign content.
As with TLS authentication, asymmetric cryptography makes it possible to generate digital signatures of content using the private key.
Subsequently, this signature can be verified using the corresponding, publicly available, public key.
To optimize the use of both encryption methods, hybrid encryption methods can be used.
Using hybrid encryption methods, a strong symmetric encryption key can be shared with another party securely using asymmetric encryption methods.
The symmetric key can then be used to encrypt and decrypt larger amounts of data, for example to securely transfer large files over the internet.
A broadly used method of using hybrid encryption methods is called "Diffie-Hellman (DH) key exchange".
Using the DH key exchange, a symmetric key can be securely exchanged on a public channel using the public-private key model of asymmetric encryption @dh-key-exchange.
The reason for the use of different encryption methods for different use cases is heavily influenced by the underlying performance of these algorithms.
A digital signal in its raw form is very inefficient to transmit because of the limited underlying bandwidth.
Because we need to transport our message over some kind of communication channel, the amount of information we can transport in a fixed period of time is limited.
The first step in solving this issue is using compression by removing irrelevant and redundant information from the signal.
A popular example for a compression method is called Huffman Coding @huffman.
Conceptually, the Huffman Code consists of multiple codewords of varying length where symbols with a higher probability of occurrence are assigned to the shorter codewords, thus reducing the overall size of the message.
Since the assignment of symbols to codewords is based on their probability of occurrence, this method of compression requires information about the statistics of the incoming symbols.
If these statistical information are not known, other compression methods such as the Lempel–Ziv–Welch algorithm can be used.
Furtheremore, compression algorithms specifically tailored for different signal sources can be used, for example PNG for pictures, MP3 for audio or MPEG for video signals.
With the analogue message digizited and compressed for easier transport over our communication channel, we will now need to prepare our message on a physical level for it to be able to be transmitted using a radio wave or a data cable.
The performance of an encryption algorithm can be defined as its speed of operation.
To measure the performance of an algorithm, the time for both encryption and decryption is measured.
Symmetric encryption algorithms are generally considered faster due to the use of simpler encryption algorithms, like AES @aes-performance.
AES also uses shorter keys than the, for example, asymmetric RSA algorithm @rsa, which also contributes to the higher performance @performance-comparison.
The underlying reason for these differing performances in asymmetric and symmetric encryption algorithms can also be attributed to their complexity.
Currently, the message to be transmitted can be represented as a set of codewords like "00 01 10 11".
To prepare our message digital and compressed message for transmission over a physical channel, digital modulation -- like amplitude modulation -- is used.
This works by defining a specific signal amplitude for every possible codeword, which is called Amplitude-Shift Keying (ASK) @modulation.
The simplest form of ASK is called On-Off Keying (OOK), where we will either transmit a wave -- and signaling a binary 1 -- or not transmit anything -- and signal a 0.
In our example we may define four sine functions with varying amplitutes as the modulated signal that is being transported over the physical communication channel.
Because we defined four different Amplitude-Shifts, this type of modulation is called "4 ASK" @modulation.
Signal modulation is not limited to changing the ampliude of our transmission signal, thus we can also alter the phase or frequency of the signal.
Depending on the type of communication channel we may want to choose a different modulation type using either one or a combination of different modulation parameters.
For example, a popular modulation type that uses a combination of amplitude shifts and phase shifts is called "Amplitude-Phase-Shift Keying (APSK) @modulation.
Using modulation, we prepared our signal on a physical level to instruct a communication interface -- like an antenna or an optical transmitter -- to finally transmit our message.
The implementation and use of symmetric encryption algorithms is significantly less complex than that of asymmetric methods.
Due to the use of the same key for encryption and decryption in symmetric methods, the process of encrypting and decrypting data is simpler than that of asymmetric methods.
Symmetric algorithms like AES also use a special structure to encrypt content called "Block Cipher Structure".
Here, AES splits up the content to be encrypted into fixed-size blocks of data, which then can be processed in parallel, allowing for even higher performance.
Asymmetric encryption methods, on the other hand, require the previously introduced set of keys (public and private) to encrypt and decrypt data.
The asymmetric RSA algorithm, for example, utilizes computational intensive exponential calculations to encrypt plain text content @rsa.
In conclusion, both symmetric and asymmetric encryption methods have different strengths in various application areas.
While symmetric methods benefit from their high efficiency in encrypting large amounts of data, asymmetric methods are more suitable for secure information exchange, for example over the internet.
Hybrid cryptography represents an exciting solution to the weaknesses of both systems by combining both encryption types. By exchanging symmetric keys via asymmetric cryptographic methods, large amounts of data can already be securely transmitted over the internet today.
As final step, the receiver of the message has to process the received signals in exactly the reverse order to create a comprehensible message.
The most important prerequisite for this to work is that both sender and receiver have agreed on the same transmission and reception conditions.
The receiver will first need to use the correct modulation type to convert their received signal back to a set of codewords.
Going on, they will decompress the message based on the used compression algorithm and use a Digital-to-Analog Converter (DAC) to transform the digital message back into sound waves which will be output by the speaker of their phone.
This whole process now happens at such a high speed that makes it possible for us to talk to a person on the other side of the world.
//Essay has a total of #total-words words.