48
votes
6answers
36k views

How can I generate large prime numbers for RSA?

What is the currently industry-standard algorithm used to generate large prime numbers to be used in RSA encryption? I'm aware that I can find any number of articles on the Internet that explain how ...
55
votes
3answers
25k views

How should I calculate the entropy of a password?

If part of the password is a whole regular English word, does the entropy of that part depend on the number of English words in existence, the number of English words known by the choosing algorithm, ...
46
votes
7answers
51k views

Should I use ECB or CBC encryption mode for my block cipher?

Can someone tell me which mode out of ECB and CBC is better, and how to decide which mode to use? Are there any other modes which are better? Edit: This question was asked long back when I was ...
37
votes
1answer
36k views

What is the difference between PKCS#5 padding and PKCS#7 padding

One runtime platform provides an API that supplies PKCS#5 padding for block cipher modes such as ECB and CBC. These modes have been defined for the triple DES, AES and Blowfish block ciphers. The ...
53
votes
5answers
20k views

Is AES-256 weaker than 192 and 128 bit versions?

From a paper via Schneier on Security's Another AES Attack (emphasis mine): In the case of AES-128, there is no known attack which is faster than the 2128 complexity of exhaustive search. However, ...
27
votes
2answers
12k views

Impacts of not using RSA exponent of 65537

This RFC says the RSA Exponent should be 65537. Why is that number recommended and what are the theoretical and practical impacts & risks of making that number higher or lower? What are the ...
10
votes
4answers
6k views

Why is it important that phi(n) is kept a secret, in RSA?

Why is it important that $\phi(n)$ is kept a secret, in RSA?
37
votes
3answers
8k views

What are the benefits of the two permutation tables in DES?

Why do we use a permutation table in the first step of DES algorithm and one at the end of the algorithm?
16
votes
2answers
6k views

Using the same secret key for encryption and authentication in a Encrypt-then-MAC scheme

Is it a weakness to use a single shared secret for protecting messages using a Encrypt-then-MAC scheme? Assuming a system is using AES-256-CBC and a SHA1-HMAC and the same secret key for both ...
13
votes
4answers
3k views

Why is RSA encryption key based on modulo $\varphi(n)$ rather than modulo $n$?

While calculating RSA encryption key we take modulo $\varphi(n)$ rather than modulo $n$. I can’t understand why it’s done this way.
13
votes
3answers
2k views

Can you create a strong blockcipher with small blocksize, given a strong blockcipher of conventional blocksize?

Suppose I want a strong 20-bit blockcipher. In other words, I want a function that takes a key (suppose the key is 128 bits), and implements a permutation from 20 bits to 20 bits. The set of ...
10
votes
2answers
584 views

How to derive two keys from one password

What is the best way to generate two independent symmetric keys from one user-entered password or passphrase? Would using both scrypt and pbkdf2 achieve this?
13
votes
2answers
7k views

Why is asymmetric cryptography bad for huge data?

I've been told that asymmetric cryptography requires that the message to be encrypted be smaller than its key length. Why is this? I know about hybrid encryption, which uses symmetric encryption to ...
15
votes
1answer
3k views

What is a tweakable block cipher?

Pretty simple question - but I can't seem to find much information about it. What exactly is a tweakable block cipher? How do they differ from traditional block ciphers? What is the 'tweak'? Is it ...
10
votes
4answers
924 views

Creating a small number from a random octet string

I'm trying to figure out the best way to generate a cryptographically secure random number between 0 and 200 (inclusive) from a cryptographically secure random string of bytes (ie. read from /dev/...
9
votes
3answers
6k views

What should be the size of a Diffie-Hellman private key?

I'm implementing the SRP-6 protocol, which relies on discrete logarithms for it's security (essentially Diffie-Hellman). The RFC documents state: The private values $a$ and $b$ SHOULD be at least ...
8
votes
3answers
2k views

Desirable S-box properties

What desirable properties should an S-box have? My current standard selection process is to just pick them at random and verify that they fit the following criteria: The probability that any random ...
6
votes
2answers
1k views

Can a computationally unbounded adversary break any public-key encryption scheme?

Assume there is a public-key encryption scheme $(KeyGen, Enc, Dec)$ with perfect correctness (i.e., for all messages M and valid key-pairs (PK,SK), we have $Dec_{SK}(Enc_{PK}(M))=M$). Will there ...
10
votes
3answers
1k views

Converting a stream cipher into a block cipher

The well-known Counter-Mode (CTR) mode of operation for a block cipher essentially converts any block cipher into a stream cipher. Is there a way to do the reverse? In other words, given a "good" ...
2
votes
4answers
1k views

RSA with composite numbers

It has been said that RSA uses a modulus product of two prime numbers for security reasons. But does RSA even work correctly if we allow composite integers instead? I think that the answer is "NO". ...
15
votes
3answers
2k views

Why does the padding in Merkle–Damgård hash functions like MD5 contain the message length?

I understand the need for padding in MD5. But why do we append the message length to the padding? I heard it strengthens the hash but how? Please provide an example if possible and how it applies to ...
6
votes
2answers
4k views

In RSA, why is it important choosing e so that it is coprime to φ(n)?

When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$. I know that a common choice is to have $e = 3$ (which requires a good padding ...
6
votes
2answers
2k views

Why can't the IV be predictable when its said it doesn't need to be a secret?

I heard multiple times not to reuse the same IV and IV should be random but doesn't need to be secret. I also heard if the IV is something like sequential numbers or something predictable I should ...
6
votes
1answer
1k views

Why doesn't preimage resistance imply the second preimage resistance?

Let the preimage resistance be defined as »given a hash value $h$, it is hard to find any message $m$ such that $\operatorname{hash}(m)=h$«, and let the second preimage resistance be defined as »given ...
5
votes
1answer
947 views

Why can ECC key sizes be smaller than RSA keys for similar security?

I understand how ECC is based on the discrete log problem and RSA on integer factorization. I've read several references that show how a solution to either of these problems can typically be adapted ...
5
votes
2answers
1k views

DES — Can I recover the key when I have both ciphertext and the plaintext?

Given a message and DES encrypted form of said message, is it possible to efficiently compute the key used to encrypt the data?
4
votes
1answer
404 views

Is knowing the private key of RSA equivalent to the factorization of $N$?

Given the RSA modulus $N$ the fastest method to factor it is of sub-exponent order. But, now if I know the private key $d$ of RSA, does that mean I can factor $N$ efficiently?. It intuitively seems ...
3
votes
2answers
881 views

Is there a length-preserving encryption scheme?

Is there a length-preserving encryption scheme, that preserves the lengths of input sizes such that the length of the input plain text is same as length of the output cipher text ?
10
votes
2answers
1k views

Why RSA can't handle numbers above 76?

I'm going to encrypt the characters Zhu, and decrypt them using RSA. I'm using the public key $\{e, n\}$ and private key $\{d, n\}$. The values of $e$, $d$ and $p$ ...
4
votes
1answer
431 views

Relation between attack and attack model for signatures

I would like to know: What is the relationship between an attack and an attack model. For example, let $\Pi$ be the Lamport signature scheme. This signature has its security based on any one-way ...
4
votes
2answers
2k views

Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA. (Note: I do realize that in practice this is done through an intermediate symmetric key, but ...
3
votes
4answers
593 views

Verify product without revealing multipliers

Situation: Several participants contribute encrypted random numbers. These numbers will be used to generate community-agreed random (by simple multiplication). Question: Is there any way to detect ...
3
votes
1answer
495 views

What does the expression $1^n$ mean as a function argument?

In a paper about predicate encryption or attribute based encryption, the setup function is mentioned with the $setup(1^n)$ or $setup(1^l)$. I want to know what is meant here. Is it multiples of ones ...
2
votes
1answer
209 views

Mathematical formula for switching the key for OTP?

Instead of generating the random key for the one time pad cipher over and over again, is there a mathematical formula that allows you to switch the key to a new key? The new key must be as random and ...
30
votes
6answers
10k views

Is Convergent Encryption really secure?

Recently a company called Bitcasa demonstrated a product of cloud storage. they indicated that they would use "Convergent Encryption" to secure your data and de-duplicate, essentially one copy of the ...
19
votes
4answers
17k views

Recommended skills for a job in cryptology [closed]

First let me apologize if this is an ill posed question. Let me also note that I do not in any way seek a comprehensive answer, simply your thoughts on what makes for a valuable asset to a company ...
23
votes
1answer
30k views

How does RSA signature verification work?

I understand how the RSA algorithm works for encryption and decryption purposes but I don't get how signing is done. Here's what I (think) I know and is common practice: If I have a message that I ...
29
votes
5answers
6k views

How can we reason about the cryptographic capabilities of code-breaking agencies like the NSA or GCHQ?

I have read in Applied Cryptography that the NSA is the largest hardware buyer and the largest mathematician employer in the world. How can we reason about the symmetric ciphers cryptanalysis ...
47
votes
1answer
3k views

Why does my SSH private key still work after changing some bytes in the file?

I (for a test) just randomly altered a private RSA key by opening it up in Vim and changing a few bytes. It is the private part of an SSH key pair used for logging in on a remote system. Puzzlingly, ...
24
votes
2answers
8k views

What is entropy?

We discuss a lot of topics and use measures of entropy to determine how difficult it is for an attacker to be successful. What does entropy mean in the context of cryptography? How is entropy ...
8
votes
2answers
14k views

How much computing resource is required to brute-force RSA?

It's been over 30 years since Rivest, Shamir and Adleman first publicly described their algorithm for public-key cryptography; and the intelligence community is thought to have known about it for ...
28
votes
4answers
112k views

How secure is AES-256?

The cipher AES-256 is used among other places in SSL/TLS across the Internet. It's considered among the top ciphers. In theory it's not crackable since the combinations of keys are massive. Although ...
17
votes
3answers
2k views

Is using slow password hashing on the client side easier attackable than on the server side?

As we know, one should use a slow password hashing algorithm instead of a fast one for storing passwords, to hinder brute force attacks when the database is compromised. The problem with this is that ...
9
votes
2answers
11k views

What makes RSA secure by using prime numbers?

I am just learning about the RSA algorithm. Looking at the first two steps: Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$. I have some probably stupid questions: Why do $p$ ...
16
votes
1answer
1k views

Mapping points between elliptic curves and the integers

My primary question is: Is there an easy way to create a bijective mapping from points on an elliptic curve E (over a finite field) to the integers (desirably to $\mathbb{Z}^*_q$ where $q$ is the ...
12
votes
4answers
3k views

Why is the IV passed in the clear when it can be easily encrypted?

The initialization vector (IV) is exclusive or'd against the plain text before encryption for the first block sent in order to prevent an attacker from learning that duplicate message blocks are being ...
21
votes
1answer
5k views

Why can't one implement bcrypt in Cuda?

I had heard that although it's easy to implement message digest functions like MD5, SHA-1, SHA-256 etc. in CUDA (or any other GPU platform), it is impossible to implement bcrypt there. bcrypt is ...
20
votes
3answers
1k views

Purpose of outer key in HMAC

From what I know, the HMAC constructions has two strength: It's resistant to length extensions Since the key is consumed before the message, the attacker does not know the initial state, preventing ...
16
votes
9answers
5k views

RSA with small exponents?

Just to establish notation with respect to the RSA protocol, let $n = pq$ be the product of two large primes and let $e$ and $d$ be the public and private exponents, respectively ($e$ is the inverse ...
15
votes
3answers
3k views

How practical are side-channel attacks and how much of a concern are they?

I see a lot of research in very sophisticated side-channel attacks on crypto systems. Most (but definitely not all) seem to follow a trend, namely, the crypto system does something very dumb like ...

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