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I designed a custom handshake between 2 entities $\rm C$ (client) and $\rm S$ (server) which should meet the following requirements: Requirements: The handshake should make: $\rm S$ know who is $\rm C$, $\rm C$ make sure that he is talking to $\rm S$, ... without letting anyone who is listening the communication line...
In the 1978 RSA paper, it is recommended, among other things, to choose primes $p$ such that $(p-1)$ has a large prime factor $u$. This was motivated by Pollard's p-1 algorithm. Further, the authors state: Additional security is provided by ensuring that $(u−1)$ also has a large prime factor. What was the motivation ...
What is the best CPA distinguisher for the function $F_k:\{0,1\}^{8n}\to\{0,1\}^{16n}$ described below? Let $E_k$ be a $2n\times2n$ matrix with elements in $GF(2^8)$, selected by generating bit strings of length $32n^2$ using a predefined function $PRF_k$, until one is found that is invertible e.g. using Gaussian elimi...
I am trying to learn more about GCM mode and how it differs from CBC. I already know that GCM provides a MAC, which is used for message authentication. From what I have read and from the code snippets I've seen, GCM does an exclusive-or much like CBC, but I'm unsure what the exclusive-or is against. In CBC mode, the ex...
I am wondering if AES only supports 64 character passwords? When using truecrypt, the maximum character limit on passwords is 64 characters; however, when using WinRAR, the limit is 128 characters. What determines the length of passwords I can use with AES?
If I use the output of a cipher, for example a block cipher such as AES and encrypt it again with the same algorithm, I read that this introduces weaknesses into the overall security of the system. Is this the case?
I am attempting to do a final semester project where I implement Diffie-Hellman key exchange on an elliptic curve over an extension field (2^256). Can anybody help me to generate the extension field for this project?
I've read that cracking 128-bit key is currently out of reach of all humanity. However, I can't seem to find any information on what scope of brute force attacks have been performed or are possible at the current time. Can someone provide some information on this subject with quotable reference?
Or more generally, is there a function or algorithm that is slow to calculate/execute, has a reliable execution time, and has a result that can be tested much more quickly than the calculation took?
How can one run a chosen plaintext attack on RSA? If I can send some plaintexts and get the ciphertexts, how can I find a relation between them which helps me to crack another ciphertext?
For instance, what makes MD4 a bad choice for an HMAC? In this case I am asking about MD4 because its less than ideal. I know that a preimage attack can be used to undermine the system, but why? What is the attacker calculating?
Having a "rotating" square Cardan Grill with sides long n cells, how could i determinate the cost of a brute-force attack? How many configurations should be considered to perform an exhaustive search? EDIT FOR MORE DETAIL: This was an exam question so these are all the information given to me, but i think i can suppos...
Since EAX is very flexible with regard to the length of the calculated MAC (what they call "tag" is the MAC value right?), and the EAX paper as well as other documentations carefully avoid suggesting any value for the length of the MAC, is there anything to take into consideration before setting for a value? Is the len...
Is there any freely available verilog implementaion of Diffie-Hellman key exchange? I couldn't find anything using google. So, assuming its not there I started implementing on my own. The code is hosted at https://github.com/nulpoet/verilog_diffiehellman. Behavioral simulation in xilinx works. However it cannot synthes...
The NIST recommended HMAC uses $$\operatorname{HMAC}_k(\mathrm{text}) = H_\mathrm{out}( (k \oplus \mathrm{opad}) \mathbin\| H_\mathrm{in}((k \oplus \mathrm{ipad}) \mathbin\| \mathrm{text}) )$$ Is it feasible to analyze the security and efficiency with different hash function implementations for $H_\mathrm{in}$ and $H_...
I am confused about the hardness of the one-way function behind cryptography -- if someone could factor the large number produced back into two primes quickly then the one-way function would be broken? TIA
I am currently completing a dissertation concerning the encryption of data through a variety of cryptographic algorithms. I have spent much time reading journals and papers but as yet have been unable to find any record of their performance complexity. Would anyone have an idea of the Big-O complexity of the following ...
The actual question is stated at the end of the text. Suppose you have a (grossly inefficient) confidentiality stream cipher with the following components: The keyed function $F_k:\{0,1\}^{8n}\mapsto\{0,1\}^{16n}$ based on vectors with randomized padding multiplied with a key dependent matrix as described in a previou...
I am learning about cryptography, purely for my own interest. As part of that, I am implementing a simple one-time-pad toolset in C. Naturally, I need to generate random numbers to create the pad, and they need to be cryptographically strong. I know about rand(), but from what I can tell it is not strong. Is there a st...
I'm currently trying to implement ecdsa and the first problem i met -- multiply an elliptic curve point by a number. As far as i understand X9.62 gives some recommendation for doing it but i haven't managed to find anything. It would be great to see some program like algorithm. P.S. Any help is appreciated. Sorry for...
I am currently studying for an exam and this was a previous question: Give one advantage of using HMACs over using RSA to sign SHA-1 hashes. My thoughts are that it has something to do with the fact that HMAC assumes a private key has already been shared so there is no need to use public-private keys. But wouldn't i...
I'm trying to understand (to reproduce in practice) how does blinded tokens work. Currently i'm lacking examples. According to Wiki the blinded signature protocol is the same as ordinary signature protocol. So maybe it is possible to reproduce it with the help of openssl? I want to reproduce by hand all the steps requi...
I've recently looked a bit at pairing based cryptography and I was wondering what properties the groups involved should have in order to be useful for cryptographic purposes? Has anything more exact been formulated? As an example, we could just take the pairing $\mathbb{Z}_p\times \mathbb{Z}_p\to \mathbb{Z}_p,\;\; (x,y...
For a fair channel, sender sends a bit b and receiver gets it with probability 1/2 and gets b's flipped value with probability 1/2. It is trivial to build a fair noisy channel from 1 out of 2 oblivious transfer since sender only needs to input b and b's flipped value and receiver randomly choose one. Now I wonder if w...
Probably the simplest cipher is the xor cipher with a single integer. One can extend this to use more than one integer by several means. I'm wondering if there is any benefit to doing more than this: Let $x_n$ be the $n$th data byte to encrypt and $p_k$ be the data stream (password or whatever) to encrypt with and $p_k...
In RSA, a message is encrypted by $m^e \pmod N$. $N$ is the modulus, $m$ is the message and $e$ is the public exponent. (I know that $m$ should not be greater than $N$.) My question is, can $m^e$ be greater than $N$ (obviously, before taking the modulus)? In that case is there a possibility like $ m_1^e=m_2^e \pmod N$...
Using $n$-bit ECDSA, a signature has a size of $2·n$. It is possible to recover the public key from this signature, which shows that there is a publicly visible redundancy in the signature. Is it possible to exploit this redundancy to reduce the signature size to $n$ bits, sacrificing key recovery? I suspect it's not p...
I want to encrypt a file with AES in CTR mode. I have a 256 bit master key and the file. Given these, the encryption must be deterministic, so I can't use a random nonce in the usual way. Fortunately the master key will be unique¹. My original plan was to simply set the nonce to 0. Assuming no collision happens when de...
I am looking to understand if there are any hard figures on which digital signature schemes are most commonly in use today. I'm only really interested in what is employed recently (ie. last couple years), as opposite to what was adopted say ten years ago, and especially what's employed in systems in which the bandwidth...
It is my understanding that while a practical solution to the factoring problem will definitely break RSA, it has never been proven that the security of RSA is equivalent to factoring. In otherwords, theoretically, someone could mathematically break RSA without breaking the factoring problem. Are there any problems for...
I am trying to wrap my head around the benefits of salt in cryptography. http://en.wikipedia.org/wiki/Salt_(cryptography) I understand that adding salt makes it harder to precompute a table. But exactly how much harder do things get with salt? It seems to me, like when you add salt, the number of entries in your precom...
I am looking at implementing NTRU, but I noticed that while the encryption/decryption algorithm seems to be mature and well-documented, there is comparatively little information about how to sign using NTRU (and the proposed method apparently leaks information about the private key). My question is, why can't I just si...
I have a personal project in mind in which I plan to use cryptography in order to let the users be confident in the fact that, even if all data get's stolen, it would be virtually impossible to crack in the next few decades. I would like some advice on the way I planned it until now: All data resides in two key/value s...
Given a CBC ciphertext and IV, how can I find the encryption key? We are limited with an 8 chars key, each char in the range of [a..h], so I can generate every possible key (these are only $8^8 = 2^{24}$ (about 4 million) different possible keys). How would I go about finding the correct one though?
I can't really understand MixColumns in the Advanced Encryption Standard, can anyone help me how to do this? I found some topics on the internet about MixColumns, but I still have a lot of questions to ask. Ex. $$ \begin{bmatrix} \mathtt{d4} \\ \mathtt{bf} \\ \mathtt{5d} \\ \mathtt{30} \\ \end{bmatrix} \cdot \begin{bma...
I am confused about how keys in RSA asymmetric encryption are generated and what the implications for open communications are. Textbooks say the one-way function is merely two primes (with some critical constraints) -- so how do the two primes generated get turned into keys? Does this mean that having a public key is...
I'm a total noob when it comes to cryptography but I believe this falls under the "zero knowledge" category. I have two associated pieces of information: tag — known by both parties. Unique per scenario. identity — known by only one party. Potentially associated to multiple tags. Comes from a pool known by both partie...
I just read Offline anonymous electronic money systems and their cryptographical base , which asks for anonymous offline systems. The OP claims eCash is such a system, and the answer claims that fairCash is such a system. I've added security as a third requirement, since an insecure system seems useless to me. When eva...
I need a way to distribute knowledge among multiple parties - lets start with two. The idea is while the knowledge is originally created by one party I need to transform it into a situation where no party can access the information without the other's help. I actually have an idea about how to solve this but cryptograp...
I have written a C implementation of the Berlekamp-Massey algorithm to work on finite fields of size any prime. It works on most input, except for the following binary GF(2) sequence: $0110010101101$ producing LFSR $\langle{}7, 1 + x^3 + x^4 + x^6\rangle{}$ i.e. coefficients $c_1 = 0, c_2 = 0, c_3 = 1, c_4 = 1, c_5 = 0...
I am looking to see if this one-way communication protocol is secure. Assume Alice wants to send Bob a message (and doesn't need Bob to reply in the same session/channel - think email). Bob knows Alice's public key $A_{public}$, and Alice knows Bob's public key $B_{public}$. Assume ideal cryptographic primitives for th...
I have a question about RCON here is my illustration... this is the 128 bit key.. [2b] [28] [ab] [09] [7e] [ae] [f7] [cf] [15] [d2] [15] [4f] [16] [a6] [88] [3c] and then I will get this.. [09] [cf] [4f] [3c] and then I will put down the first 8bit(1byte) where it is the 09: [cf] [4f] [3c] [09] after that I will cha...
I have heard a lot about the biclique cryptanalysis research on AES, which as far as I know is the closest anyone has got to breaking AES. Exactly how close did they get? Does this attack propose a credible risk to my using AES today? Exactly how hard would it be to extend their work to fully break AES?
I created a basic file encryption method, that seems pretty secure to me (based on an answer below, it seems to be an implementation of the Vigenère cipher) , but one of my colleagues claims that it can be cracked if you know the length of the password. The way the encryption works, is that it reads the byte value of ...
I am confused. How can I encrypt a file using 128-bit Advanced Encryption Standard? Do I need only to encrypt the file name and it's content or is there something that I need to do to encrypt it? Is there something that I will need to extract to the file to encrypt it? For example, I want to encrypt an MS Word file or ...
I'm looking into blind signature schemes for use as digital cash. I have come across blinded RSA, and Lucre(DH based). Are there other schemes available, and how do they compare? I suspect there should be a elliptic curve scheme, which might have better performance than the other schemes. In particular I'm interested i...
I know that Elgamal algorithms have fallen out of fashion, and they are not included in any widespread cryptographic standard nowadays. However, they are still present in several popular crypto libraries (bouncy castle, botan, cryptopp, etc). One disturbing thing I found is that such libraries have no or very limited t...
Let's assume a simple algorithm like the Skein hash function. Is it possible, given the algorithm, to construct a proof that it does not have a particular distinguisher, something like: $P(xyz)$ is the probability that $xyz$ is truly random over some alphabet, Given $\vert y \vert = l$, for some fixed length l, $z = f(...
I'm trying to find faster ways to solve this: http://cryptogram.org/solve_cipher.html Actually lists of common words are good, but they are often limited to 1000 words. I found this, but I'm not sure which one to use, but the word list still seems too large. Do you know lists of 10k, 20k, 30k words, or tools that sorts...
If we have a hash function $h(x)$ and then a hash function $H(X) = h(h(X_0) || h(X_1))$ where $X_0$ is the first half of $X$, $X_1$ is the second half of $X$ and $||$ is concatenation. Then assuming we can easily find a collision for $H$, then it would be easy to find a collision for $h$ as well - Therefore finding a c...
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure. However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem instance...
Possible Duplicate: How can I do a brute force (ciphertext only) attack on an CBC-encrypted message? My question is about a cipher text only attack - I have as input only the initialization vector and one cipher text. I know the key domain: letters "a-h", and the padding is zero's (don't know if that helps). Problem...
This question is an extension of Families of public/private keys in elliptic curve cryptography As described above, bitcoin "type 2" deterministic wallets use a root private/public key pair, where subsequent keys take advantage of the fact that in elliptic curve cryptography the public key for a private key + a fixed n...
My understanding is that a KDF is a function that takes a master secret and generates multiple keys. It is secure as long as the keys are "independent". If this is true, the following definition would generate a secure KDF, right? Assuming we have access to a completely random function, $R: \mathcal{K} \rightarrow \ma...
Assuming I already have a D, P, Q, etc of an RSA key: How do I now sign a message? If it matters – the message is around 100 bits. I don't know much about cryptography, but I can get these numbers generated by a computer. Unfortunately, in my scenario – I can't use the built-in functions to use these numbers.
I'm trying to decrypt a message that is encrypted using a LUC encryption scheme and running into roadblocks. I know that with RSA if Alice and Bob use the same public modulus but different encryption exponents, with $\gcd(n_A,n_B)=1$ then you can find the plaintext $M$. I'm provided $R$ (public modulus), $n_A$ (Alices...
I'm conceiving an application that uses cryptographic tools and concepts for securing data. I know that's difficult and risky, therefore I prefer to ask around before implementing anything. When using generic length-extension for hash functions, such as SHA256d where, if I'm correct, "d" stands for the number of times ...
A lot of hash functions, including the SHA-2 family(but not the SHA-3 candidates and SHA256d) are vulnerable to length extension attacks. But when is this property a problem? I guess certain naive MAC implementations might have issues. Are there also some situations where length-extensions cause problems for unkeyed ha...
I am considering attacks on Two-Key Triple-DES Encryption assuming $2^{32}$ known plaintext/ciphertext pairs (that's a mere 32GiB of ciphertext) by the method devised by Paul C. van Oorschot and Michael J. Wiener: A Known-Plaintext Attack on Two-Key Triple Encryption (in proceedings of Eurocrypt 1990), or another publi...
IPSec recommends rekeying SA's figuring in both time and amount of data sent. Even when using AES-256 in CBC mode, the key and IV commonly get re-negotiated after 100MB. My case isn't using IPSec, the above is just for comparison. Assuming a plaintext is encrypted and stored to disk using AES-256 in CBC mode, is ther...
I need MGF1 and OS2IP functions, as defined in the PKCS #1 v2.1: RSA Cryptography Standard. Is there anything available in OpenSSL, or any other open C library?
EDIT: Just wondering why was this question closed as a duplicate of a question asked almost 2 years after this one... I've seen an example of how to sign using RSA. Besides the signing itself (s = m^d mod n) it also hashes and adds an IV. Why is that needed?
I can't understand what CFB really is. It said in Wikipedia that CFB is same as CBC, but I find that CFB is more difficult than CBC. Can someone explain to me how CFB works. Such as how Initialization Vector(IV) work inside the Encryption Algorithm process together with the Key, and also how does the ciphertext messag...
Some cryptographic algorithms are as strong as the size of their key is, while other have some weaknesses that limit their strength (such as SHA-1). How strong is the ECDSA algorithm, and does that strength depend on anything (for example, the curve used and so forth)?
The abstract of the Biclique Attack paper claims: The first key recovery attack on the full AES-128 with computational complexity $2^{126.1}$. What does $2^{126.1}$ mean in this context? And where does this value come from?
I'm trying to implement parameters generation for ECDSA according to SEC1 v2.0: Input: The approximate security level in bits = t is {80, 112, 128, 192, 256} Output: Elliptic curve domain parameters over Fp: T = (p, a, b, G, n, h) Here's the 2nd step of the algorithm: Select elements $(a, b)$ is $F_p$ to determine...
It said in Wikipedia that: [....] Rijndael can be specified with block and key sizes in any multiple of 32 bits, with a minimum of 128 bits. The blocksize has a maximum of 256 bits, but the keysize has no theoretical maximum. How would the key schedule look for these other key sizes, like a 136-bit key?
How can I process Initialization Vector inside the Block Cipher Encryption box (using for example AES) together with the Key? Will I encrypt the Initialization Vector like a block of plaintext? So I can generate a keystream, which I will then XOR to the plaintext to generate ciphertext?
just a follow up question with this question.. How does the key schedule of Rijndael looks for keysizes other than 128 bit? A 256-bit key can still encrypt a block of plaintext in 128 bit? but in this tutorial, to encrypt 128-bit plaintext, It need 128-bit of secret key also.. can someone provide me a clear explanati...
Assume that you want to compare several cryptographic primitives (say, encryption schemes), and choose one. You need to consider several complexity measures, such as the key length, encryption time, decryption time, etc. In order for the comparison to be fair, all primitives in question must provide the same level of s...
I found this question on the game programming site and was intrigued. I came up with an answer off the top of my head but I'm no cryptanalyst so it is probably not water-tight. This is how my idea goes: each of the two peers generates a random number. each peer creates a salted hash of its number and sends it to the...
I would like to create a publicly available tool that is used to generate a password that gives a limited time access to a resource. My idea is to digitally sign the current date with a private key entered by the user, generating a message that is sent to the resource that verifies it with the public key. If valid, the...
Several websites ( such as Is there a secure cryptosystem that can be performed mentally? ) briefly mention RC4-52 as a modification of standard RC4. RC4-52 has only with 52 instead of 256 elements in the state array, so encryption or decryption (or both) can more easily be executed manually (literally "by hand") with ...
I'm looking for a one-way hash function that can be performed by A on an encrypted piece of data E(D) provided by B, without the performer A able to figure out D or H(D). This similar to HMAC(Message, Key), except the output hash cannot be known by A. Usage: B encrypts data D => E(D) B sends E(D) to A A contains a se...
I was not able to understand why we practically need a CPA security in Cipher Block Chaining, which insist on having a random IV. Let's say if the encryption is not CPA secure, i.e. the adversary can identify two ciphertext are same and conclude the two plaintext would have been the same. Of what use is this informatio...
I run a baseball league and would like to do silent auctions for free agents. This would require teams to enter their highest bid and the highest bidder at the end of the auction period would win. Unfortunately, my league, my code, my server, I have access to the information if I choose to look at it. I'd like to no...
Can $n=pq$ be part of two different pairs of RSA keys? If such keys exist, say $(e_1,n)$ and $(e_2,n)$, how are they related? What will be the security concerns for the two users?
I want to combine two or more keys to create a single encryption key that relies on all of them. What is the proper method for doing that? Simple XOR? Using hash functions? Something else? I personally used this: k = md5( key1 || key2 ). Note: || means concatenation. I used md5 because I use 128-bit encryption and ...
What is the complexity of ECB in terms of Time and Memory? and also in OFB? I can't find it in the internet, so I decided to ask it in here.
For a file encryption program, I was told to use Output Feedback mode (OFB) instead of ECB (Electronic code book) mode. Which attacks can I avoid by this choice?
Although this has been extensively discussed around here, I'm curious whether my approach makes sense, or I should just stick to "the standard version". I'm implementing some homomorphic encryption primitives (Paillier, Okamoto–Uchiyama etc) and, at the moment, I'm using GMP as the big number library (this may change i...
Let's say I have a long sentence, like "The quick brown fox jumped over the lazy dog." Let's further say that I need to keep this string encrypted, so I use an HMAC. Let's further further say I want to be able to do prefix searches for this string, so I also store all possible prefixes of this string, for example: $\op...
From Dogbert's blog: Sony has a line of laptops ("Vaio") which compete mainly in the high value market segments. They implemented a master password bypass which is rather sane in comparison to the rest of the bunch: The randomly generated master password is only stored in RAM, e.g. it's lost after the next reboot ("o...
Public/private key algorithms such as RSA encrypt a message with a private key but only decrypted with another (mathematically related) key. Can the public key decrypt the messages encrypted with the private key and the private key decrypt messages encrypted with the public key? If the algorithm is based on multiplyin...
Using small private exponents with RSA improves performance. However, it has been shown (Wiener, 1990) that if $\log d \leq \frac14 \log N$, the private exponent $d$ can be reconstructed from the public key $(N,e)$. Smart, Inc. uses special private keys designed such that they are: Larger than the minimum bound recomm...
Is there a known non-trivial system with plausibly secure public key encryption where: the time function is efficiently computable; the [pubkey,privkey] pairs are generated with time(privkey) = 0; when encrypting under pubkey, the encryptor chooses a value of t in the appropriate range; given privkey0 and t such that ...
This is a replication of this question on Stack Overflow. There's class Random in .NET runtime which is designed for use as a cheap fast source of pseudo-random numbers for simulation - very fast, seed can be passed in explicitly, emits easily reproducible sequences. This class is often misused for generating passwords...
A = hash("blue" + X); B = hash("pink" + X); If A and the literals are known and X is unknown, are there attacks on B aside from the attacks on directly on hash()? In other words, is B safe? Would it be better to reverse the concatenation? A = Hash(X + "blue"); B = Hash(X + "pink"); If it matters, I am using hash=sha...
From page 318 in Stinson's "Cryptography: Theory and Practice", question 7.3: Suppose that Alice is using ElGamal Signature Scheme. In order to save time in generating >the random numbers k that are used to sign messages, Alice chooses an initial random value >$k_0$, and then signs the $i$th message using the value $k...
I was wondering how many possible private/public keys exist? If a million people – for whatever reason – would try to generate 5 keys each in the same minute (on the same date and time) is there a high chance of collision? I believe GUID would suffer from that problem as many bits are reversed for date/time (and GUID v...
I want something like this, but in a digital sense: You and others walk into a room. Everyone knows who each of you are and everyone is doing their best to figure out what piece of paper each person is taking. Fortunately the all the paper is in a box. You bring your own envelope, shuffle the papers blindly and put on...
Is there such an algorithm that would allow to upgrade the encryption of an RSA-encrypted message without revealing the plaintext to the untrusted user? Basically, such an algorithm would probably be split in two parts. The algorithm would take the old private key and the new public key and generate a sort of intermed...
I don't understand how disk encryption (e.g. TrueCrypt) is supposed to resist frequency analysis. If blocks can be randomly accessed (which they can), doesn't that mean that frequency-domain information (e.g. contiguous free space) is exposed? The only safeguard I know against this is chaining, but if they use chaining...
I got an answer in the related question about Mixcolumn for encryption, but how about decryption? what will I do? Because it said that I will used this: During decryption the Mix Column the multiplication matrix is changed to: 0E 0B 0D 09 09 0E 0B 0D 0D 09 0E 0B 0B 0D 09 0E How does one implement this maxtrix mult...
Suppose Alice sends messages to Bob by encrypting the messages with Bob's public key. Eve knows that the data is encrypted using RSA, but does not know the public key. Can Eve figure out the public key just by observing the encrypted messages? And if so, approximately how much data would it take for Eve to discover the...
Wikipedia has a nice section regarding the speedup of the RSA decryption using the Chinese Remainder Theorem here. I need to understand the implementation of a similar speedup for the encryption algorithm of a more complex homomorphic encryption scheme (DGK) and, for some reason, I'm unable to get my head around the wa...
I try to get the full reasoning behind the above statement. First, after reading articles here and at wikipedia i understand that using an IV only once is good practice. For stream ciphers not doing so will result in compromising security because of Cipher1 xor Cipher2 = Plain1 xor Plain2 For block ciphers using the ...
I'm building a system that has to take file paths, and generate a unique name for each one. I'm planning on using SHA1 as the hash function. My question is: do I have to deal with possible collisions (2 different paths producing the same SHA1 value) or can I assume it won't occur?
This question at StackOverflow mentions that DSA cannot be used for encryption. But both RSA and DSA can be used to generate public and private keys, right? Then why can't I use the DSA public key to encrypt?
My intuition tells me it's a trade off between speed and security, but how did the standardisation process select these three seemingly arbitrary key lengths (namely, AES-128, AES-192, AES-256).