7
votes
1answer
2k views

Sending KCV (key check value) with cipher text

I was wondering why it is not more common to send the KCV of a secret key together with the cipher text. I see many systems that send cipher text and properly prepend the IV to e.g. a CBC mode ...
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 ...
5
votes
1answer
610 views

PBKDF vs HKDF for pretty long key

I'm developing a messenger application with encrypted chats. In the first version of the app I've used PBKDF2 (10000 iterations, SHA1, random salt) to extend a short user password and generate keys ...
5
votes
1answer
2k views

Can Elgamal be made additively homomorphic and how could it be used for E-voting?

Elgamal is a cryptosystem that is homomorphic over multiplication. How can I convert it to an additive homomorphic cryptosystem? How can I use this additive homomorphic Elgamal cryptosystem for ...
4
votes
3answers
568 views

Block cipher fixed points (plaintext equal to ciphertext)

A block cipher is a bijective map from the set of possible plaintexts to the set of ciphertexts, which are the same size and might as well be considered the same thing: $\theta: S\to S$. In this there ...
4
votes
1answer
776 views

Trying to better understand the failure of the Index Calculus for ECDLP

So I'm going to give you guys my understanding and then if you would be so kind as to tell me where I'm off the mark (hopefully I'm not completely wrong). So basically the index calculus for the ...
3
votes
1answer
665 views

Cracking an RSA with no padding and very small e

I have a project wherein I have to crack a given cipher text encrypted using RSA and have been given N and e. Can someone suggest an RSA attack using a very small exponent e(here e=3) and no padding?
2
votes
1answer
108 views

Is it possible to deduce the value of a string when given its hash and multiples hashes of the string + other known strings?

To be clear, I have access to $H(S)$ and as many $H(S||K)$ as I want. Every string $K$ is known. Can I use the extra information to my advantage and try to deduce $S$, without requiring bruteforce? Or ...
10
votes
4answers
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 ...
6
votes
1answer
2k views

RSA with modulus product of many primes

I would like to ask what happens if we build an RSA system with modulus a product of more than 2 primes, for example let $n=p_{1}p_{2}...p_{L}$. I know only the classical RSA system with $n=pq$ with ...
5
votes
2answers
887 views

Hill cipher, unknown letter value

I've been struggling on this problem for a while now : the Hill cipher is well-known to be vulnerable to known-plaintext attack due to its linearity. Given a key matrix $K$ of size $n\times n$, one ...
4
votes
1answer
271 views

Formula for the number of expected collisions

Say we have a hash function that produces $n$ bit outputs. From the birthday problem that after around $\sqrt{2^n}$ different inputs to the has function, we can expect a collision. Say instead that ...
4
votes
1answer
2k views

What is “Implicit Authentication”?

What is “Implicit Authentication” in the context of authentication methods? I searched the Web but could not find any article that describes this. If anyone can describe it, that would be a great ...
3
votes
1answer
324 views

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 ...
3
votes
2answers
628 views

Certificateless cryptography

While reading "Certificateless Public Key Cryptography" by Author Sattam S. Al-Riyami and Kenneth G. Paterson, they have considered generation of private keys by a Key Generation Center (KGC). If the ...
3
votes
2answers
714 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 ...
3
votes
5answers
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 ...
3
votes
1answer
588 views

Generating a cryptographically secure, many-time use, symmetric encryption key

I need to generate a 256 bit encryption key described by the adjectives in the title. Currently I intend to create the key using this RNG. Is this a secure manner of creating the key, given that it ...
2
votes
1answer
2k views

Hill cipher cryptanalysis - known plaintext known key size

Hello I want to know how to go about this problem I know the plaintext "abcdef" and the ciphertext. The key size is 2. I really can't figure out how to find the key for decrypting and encrypting.
2
votes
1answer
344 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 ...
1
vote
2answers
440 views

Attacks against El Gamal private key

El Gamal encryption involves picking $(p,g,b)$ which is our public key. We compute $b=a^x$ $mod$ $p$. Here, $x$ is the private key which we don't know. What are some efficient and strong algorithms ...
1
vote
1answer
403 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 ...
0
votes
2answers
269 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 ...
0
votes
2answers
320 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 ...
22
votes
1answer
27k 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 ...
13
votes
3answers
37k 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 ...
30
votes
3answers
12k 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 ...
17
votes
5answers
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 ...
11
votes
3answers
7k 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 ...
22
votes
1answer
16k 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 ...
15
votes
3answers
9k views

What are preimage resistance and collision resistance, and how can the lack thereof be exploited?

What is "preimage resistance", and how can the lack thereof be exploited? How is this different from collision resistance, and are there any known preimage attacks that would be considered feasible?
3
votes
3answers
991 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?
31
votes
6answers
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 ...
18
votes
6answers
8k views

Is Diffie-Hellman mathematically the same as RSA?

Is the Diffie-Hellman key exchange the same as RSA? Diffie Hellman allows key exchange on a observed wire – but so can RSA. Alice and Bob want to exchange a key – Big brother is watching everything. ...
8
votes
3answers
3k 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. ...
7
votes
1answer
4k 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 ...
27
votes
1answer
4k views

Does the generator size matter in Diffie-Hellman?

For the Diffie-Hellman protocol I've heard that the generator 3 is as safe as any other generator. Yet, 32-bit or 256-bit exponents are sometimes used as generators. What is the benefit of using ...
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 ...
15
votes
3answers
2k views

Why does SHA-1 have 80 rounds?

Why does SHA-1 algorithm have exactly 80 rounds? Is it to reduce collisions? If yes, then why do SHA-2 and SHA-3 have a lower number of rounds?
12
votes
2answers
11k 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 ...
7
votes
3answers
10k 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 $p$ ...
7
votes
4answers
10k views

PBKDF2 and salt

I want to ask some questions about the PBKDF2 function and generally about the password-based derivation functions. Actually we use the derivation function together with the salt to provide ...
6
votes
3answers
633 views

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 ...
6
votes
1answer
13k 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 ...
15
votes
1answer
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 ...
12
votes
1answer
578 views

Choice of multiplication polynomial in Rijndael s-box affine mapping

The Rijndael specification details the design choices for the s-box in section 7.2. They describe the choice of affine mapping as follows: We have chosen an affine mapping that has a very simple ...
11
votes
2answers
8k views

What is difference between PRG, PRF, and PRP

Until what I have gotten is: A PRG is generator is a part of PRF that produces pseudo-random values for the function. PRF is semantically secure and has no worries of being invertible. Fine, then ...
10
votes
0answers
675 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 ...
9
votes
1answer
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 ...
8
votes
0answers
444 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 ...

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