# All Questions

2k views

### Why are RSA key sizes almost always a power of two?

I know that other bit sizes are possible, e.g. this HTTPS server seems to have a 9000 bit key https://www.ssllabs.com/ssltest/analyze.html?d=qqq.gg, but it's very rare that one sees a key not of size ...
484 views

### For a given plaintext-ciphertext pair, how many valid AES keys are there?

For $PT\in \mathbb{M}$ and $CT\in \mathbb{C}$, let $\mathbb{F}=\{f|f:\mathbb{M}\rightarrow\mathbb{C}\}$ be the collection of all functions from $\mathbb{M}$ to $\mathbb{C}$. Then AES encryption under ...
135 views

### How can I instantiate a generalized hash function?

I've come across a bunch of "strange" hash function notations, such as the following ones and now I don't know how to choose / instantiate them. Can you please explain me what this notation means and ...
2k views

### Approach towards anonymous e-voting

I want to implement an internet-based e-voting system. Voters shall be able to cast their vote for one out of n possible candidates. Each candidate has his own ballot-box kept by and at a trustworthy ...
453 views

### Does CBC encryption of a hash provide authenticity?

Given a message $M$ and a cryptographic hash function $H$, let $f(M) = E_K(M || H(M))$ where $E_K$ is AES-128-CBC encryption with PKCS#5 padding. Take $H = \textrm{SHA-256}$ if it matters. In other ...
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### Building a combined encryption scheme from two encryption schemes that's secure if at least on of them is secure

Any thoughts on how this can be done? Let $\Pi_1 = (\mathrm{Gen}_1, \mathrm{Enc}_1, \mathrm{Dec}_1)$ and $\Pi_2 = (\mathrm{Gen}_2, \mathrm{Enc}_2, \mathrm{Dec}_2)$ be two encryption schemes for ...
760 views

### Making counter (CTR) mode robust against application state loss

Counter (CTR) mode, which is a block cipher mode of operation, has some desirable qualities (no padding, parallel encryption and decryption), but at the cost of failing badly when non-unique counter ...
370 views

### Proof of correctness of a homomorphic ElGamal sum

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...
293 views

### Factors of RSA modulus

In the article A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...
369 views

### Homomorphic Encryption: how does the equality test on ciphertexts work?

Let's suppose we have a asymmetric crypto-system $H$ which is homomorphic with respect to some function $F$. Alice encrypts a message $m$ with her private key $e$ in the crypto-system $H$ and ...
6k views

### Is truncating a SHA512 hash to the first 160 bits as secure as using SHA1?

I am from a web development background (I don't know an awful lot about cryptography or how the algorithms themselves work), so I am asking this question in simple terms. Consider a hash of the word '...
11k views

### How can one securely generate an asymmetric key pair from a short passphrase?

Background info: I am planning on making a filehost with which one can encrypt and upload files. To protect the data against any form of hacking, I'd like not to know the encryption key ($K$) used for ...
41k views

### Difference between stream cipher and block cipher

A typical stream cipher encrypts plaintext one byte at a time, although a stream cipher may be designed to operate on one bit at a time or on units larger than a byte at a time. A block cipher ...
6k views

### Galois fields in cryptography

I don't really understand Galois fields, but I've noticed they're used a lot in crypto. I tried to read into them, but quickly got lost in the mess of heiroglyphs and alien terms. I understand they're ...
4k views

### How were the DES S-box values determined?

It seems like the S-boxes in DES have essentially random values. How were these chosen?
7k views

### Is there a simple hash function that one can compute without a computer?

I am looking for a hash function that is computable by hand (in reasonable time). The function should be at least a little bit secure: There should be no trivial way to find a collision (by hand). For ...
14k views

### Why is public-key encryption so much less efficient than secret-key encryption?

I'm currently reading Cryptography Engineering. After giving a high level explanation of the difference between secret-key encryption and public-key encryption, the book says: So why do we bother ...
20k views

### What is the difference between CBC and GCM mode?

I am trying to learn more about GCM mode and how it differs between CBC. I already know that GCM provides a MAC which is used for message authentication. From what I have read, and seen code ...
3k views

### What is the post-quantum cryptography alternative to Diffie-Hellman?

Post-quantum cryptography concentrates on cryptographic algorithms that remain secure in the face of large scale quantum computers. In general, the main focus seems to be on public-key encryption ...
20k views

### HMAC-SHA1 vs HMAC-SHA256

I have three questions: Would you use HMAC-SHA1 or HMAC-SHA256 for message authentication? How much HMAC-SHA256 is slower than HMAC-SHA1? Are the security improvements of SHA256 (over SHA1) enough ...
8k views

### What is the relation between RSA & Fermat's little theorem?

I came across this while refreshing my cryptography brain cells. From the RSA algorithm I understand that it somehow depends on the fact that, given a large number (A) it is computationally ...
2k views

### Why should I use Authenticated Encryption instead of just encryption?

There are various different modes of operation for block cipher use, some of which provide "encryption" and some of which provide authenticated encryption. Why should I use an authenticated ...
1k views

### What are the differences between proofs based on simulation and proofs based on games?

what are the main pros and cons of proving the "security" of a crypto scheme under simulation proofs instead of game based proofs?
4k views

### Is sharing the modulus for multiple RSA key pairs secure?

In the public-key system RSA scheme, each user holds beyond a public modulus $m$ a public exponent, $e$, and a private exponent, $d$. Suppose that Bob's private exponent is learned by other users. ...
5k views

### Advantages using Diffie-Hellman or ElGamal

For what kind of usage should we prefer using Diffie-Hellman in order to exchange keys instead of ElGamal, and most important why should we use one or the other? I do not see a clear difference ...
7k views

### Why does nobody use (or break) the Camellia Cipher?

If Camellia is of equivalent security and speed to AES, concerns arise. First of all, assuming the above, why is Camellia so rarely used in practice? Why aren't there any breaks in Camellia? Does ...
14k views

### How cryptographically secure was the original WW2 Enigma machine, from a modern viewpoint?

If cryptanalysts today were to crack the original Enigma machine, “how fast” or “how easily” could they do it? What methods would they use? The original cracking was significantly helped by operator ...
4k views

### Is TrueCrypt's multiple/cascading encryption safe?

Is TrueCrypt use of cascading encryption safe? Is it useful? TrueCrypt is arguably one of the most popular and widely used encryption applications in use today, yet it seems to use a very ...
12k views

### Why is TLS susceptible to protocol downgrade attacks?

A recent blog post from Ivan Ristić (expert extraordinaire on all things SSL) says: all major browsers are susceptible to protocol downgrade attacks; an active MITM can simulate failure conditions ...
710 views

### Who first published the interest of more than two prime factors in RSA?

Multi-prime RSA is now a well known technique (described here): it uses $k>2$ distinct secret prime factors in the public RSA modulus, with the advantage that, using the CRT, we can gain a speed ...
483 views

### Security of RSA for paranoids with padding?

RSA for Paranoids (RSAP) (in cryptobytes v3n1), also known as Unbalanced RSA, is a variant of RSA proposed in 1995 by Adi Shamir, as a mean to increase the RSA public modulus size while keeping ...
1k views

### Using a Non-Random IV with modes other than CBC

The weakness CWE-329 is an interesting problem with CBC mode. However, does this same weakness affect the other modes of operation that rely upon an IV such as: PCBC, CFB and OFB? My gut feeling is, ...
1k views

### Correct way to map random number to defined range?

Say that we have a secure random number generation that outputs 32 bit random numbers, so it's output is a true random number between 0 and a MAX. What is the best way to map this random number to a ...
15k views

### How to solve MixColumns

I can't really understand MixColumns in Advanced Encryption Standard, can anyone help me how to do this? I found some topic in the internet about MixColumns, but I still have a lot of question to ask....
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### Finding roots in $\mathbb{Z}_p$

Is there an efficient way (algorihtm) to compute the solutions of the congruence $x^n\equiv a \pmod p$? $n\in \mathbb{N}$ $a\in\mathbb{Z}_p$ $p$ is a large prime number Note that: By efficient I ...
561 views

### Is it possible to match encrypted documents using user-defined search terms?

Suppose I am storing a number of encrypted documents in a database. I would like to make it possible to identify the subset of documents whose contents match user-specified search terms without a) ...
6k views

### What is a white-box implementation of a cryptographic algorithm?

What is a white-box implementation? Does a white-box implementation have specific properties?
3k views

### What stops the Multiply-With-Carry RNG from being a Cryptographically Secure PRNG?

Despite the fact that Marsaglia's MWC PRNG (multiply-with-carry random number generator) is considered to be "the mother of all RNGs", it does not seem to be considered to be a CSPRNG (...
2k views

### How does HOTP keep in sync?

My understanding of HOTP is that each password is unique and based on a counter. $$PASSWORD = HOTP_1(K,C)$$ Where $C$ is an incremental counter. What I wish to know, is how you keep the client ...
3k views

### From hash to Cryptographic hash

After reading some excellent papers on SipHash, I understood that good non-cryptographic hashes such as MurmurHash and CityHash are not secure for MAC usage, due to a certain type of DDos attack ...
2k views

### Why was ISO10126 Padding Withdrawn?

Wikipedia mentions ISO10126 Padding has been withdrawn, but doesn't say why. Also there were no news reports about this, as far as I can see. Why was it withdrawn? Are there security flaws? Is there ...
1k views

### How to account for moore's law in estimating time-to-crack?

It seems to be common practice (at least in some communities) to tack on the phrase "with current computing power" when estimating the absurdly long time it would take to, for example, brute-force an ...
4k views

### Is it possible to validate a Public Key in RSA?

If I have a 1024-bit number, and someone is telling me that it is in fact a valid RSA public key, is there any way I can quickly validate that it is indeed so (without cracking RSA)? (I suppose I am ...
4k views

### Why is MixColumns omitted from the last round of AES?

All rounds of AES (and Rijndael) have a MixColumns step, save the last round which omits it. DES has a similar feature where the last round differs slightly. The rationale, if I recall correctly, ...
824 views

### Why is the salt used only once in PBKDF2, while the password is used often?

The purpose of PBKDF2 is to create a derived key (DK) from a master password (PW) and a salt, often using a function like HMAC-SHA256. I have read that the salt should be as random as possible. But ...
17k views

### Why is padding used for RSA encryption given that it is not a block cipher?

In AES we use some padded bytes at end of message to fit 128/256 byte blocks. But as RSA is not a block cipher why is padding used? Can the message size be any byte length (is the encrypting agent ...
320 views

### Collision or second preimage for the ChaCha core?

Daniel J. Bernstein's ChaCha core is an evolution of the Salsa20 core. Both are functions over the set of 512-bit bitstrings, partitioned as sixteen 32-bit words. Can we exhibit collisions, or second-...
1k views

### Replacing the Rijndael S-Box?

The Rijndael S-Box design generates a permutation cycle of type $2+27+59+81+87$. What effect would replacing that permutation with a cycle of type $256$ have on the security of AES?
It is known that the two prime factors $p$ and $q$ of an RSA modulus $n$ should not be too close to each other, otherwise an attacker may factor the modulus. In other words, \$\Delta = \left| p - q \...