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406 votes
13 answers
163k views

Should we MAC-then-encrypt or encrypt-then-MAC?

Most of the time, when some data must be encrypted, it must also be protected with a MAC, because encryption protects only against passive attackers. There are some nifty encryption modes which ...
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74 votes
3 answers
80k views

How does one attack a two-time pad (i.e. one time pad with key reuse)?

My question might appear the same as the question Taking advantage of one-time pad key reuse?, but actually I did read all the answers and none of them helped me with the details I need. I am new to ...
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221 votes
8 answers
104k views

How much would it cost in U.S. dollars to brute-force a 256-bit key in a year?

I am often told that any key can be broken and that it is only a matter of time and resources for any key to be broken. I know that this is technically true. However, I think that there is probably a ...
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  • 2,313
61 votes
1 answer
28k views

Easy explanation of "IND-" security notions?

There are many schemes that can advertise themselves with certain security notions, usually IND-CPA or IND-CCA2, for example plain ElGamal has IND-CPA security but doesn't provide IND-CCA security. ...
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  • 44.7k
125 votes
7 answers
81k views

How big an RSA key is considered secure today?

I think 1024 bit RSA keys were considered secure ~5 years ago, but I assume that's not true anymore. Can 2048 or 4096 keys still be relied upon, or have we gained too much computing power in the ...
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  • 1,517
40 votes
3 answers
94k views

Calculating RSA private exponent when given public exponent and the modulus factors using extended Euclid

When given $p = 5, q = 11, N = 55$ and $e = 17$, I'm trying to compute the RSA private key $d$. I can calculate $\varphi(N) = 40$, but my lecturer then says to use the extended Euclidean algorithm to ...
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137 votes
6 answers
98k views

Should we sign-then-encrypt, or encrypt-then-sign?

Frequently, we want to send messages that are (a) encrypted, so passive attackers can't discover the plaintext of the message, and (b) signed with a private-key digital signature, so active attackers ...
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  • 5,278
110 votes
7 answers
108k views

Taking advantage of one-time pad key reuse?

Suppose Alice wants to send encryptions (under a one-time pad) of $m_1$ and $m_2$ to Bob over a public channel. Alice and Bob have a shared key $k$; however, both messages are the same length as the ...
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  • 1,541
93 votes
2 answers
24k views

What is the "Random Oracle Model" and why is it controversial?

What is the "Random Oracle Model"? Is it an "assumption" akin to the hardness of factoring and discrete log? Or something else? And why do some researchers have a strong distrust of this model?
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  • 4,008
41 votes
6 answers
20k views

Does RSA work for any message M?

I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but ...
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  • 37.8k
14 votes
2 answers
5k views

How reassuring is 64-bit (in)security?

In Feb 2017, CWI and Google announced SHAttered hash collision attack on SHA1, which took $2^{63.1}$ work estimated 6500 CPU years, to achieve. Therefore, 64-bit should be considered now an insecurity....
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  • 6,785
53 votes
6 answers
11k views

Kerckhoffs’ principles – Why should I make my cipher public?

As I understand it, the less people know about the internals of my protocol or cipher, the more secure the protocol is. However Kerckhoffs's principle states that A cryptosystem should be secure ...
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  • 2,526
161 votes
2 answers
159k views

What is the main difference between a key, an IV and a nonce?

What are the main differences between a nonce, a key and an IV? Without any doubt the key should be kept secret. But what about the nonce and the IV? What's the main difference between them and their ...
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  • 5,922
13 votes
1 answer
2k views

Representing a function as FHE circuit

I am actually trying to study homomorphic encryption (on lattices) but I'm facing a problem. Every paper that I have read so far talk about writing the function to evaluate on ciphertexts as a circuit,...
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  • 386
13 votes
3 answers
14k views

Has AES-128 been fully broken?

Has AES-128 been broken over the full 10 rounds? If so, by what means? By a commercial entity? By a supercomputer? If not, why is AES-256 used to replace AES-128 so frequently?
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  • 253
26 votes
1 answer
7k views

What do the signature security abbreviations like EUF-CMA mean?

From time to time, one stumbles across formal security definitions. This includes security definitions for signature schemes. The most common ones are the *UF-* ...
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  • 44.7k
26 votes
2 answers
18k views

Which attacks are possible against raw/textbook RSA?

The PKCS#1 standard defines multiple padding schemes for signature generation/verification (EMSA-PSS and EMSA-PKCS1-v1_5), and encryption/decryption (EME-OAEP and the less safe EME-PKCS1-v1_5). Which ...
36 votes
4 answers
41k views

Why is CBC with predictable IV considered insecure against chosen-plaintext attack?

I just learned that using CBC encryption with an IV which is predictable is not secure. From what I understand, using certain plain texts, and then guessing the IV that it uses, the attacker can ...
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  • 461
24 votes
1 answer
16k views

What are the odds of collisions for a hash function with 256-bit output?

There are some related questions on the net but I did not understand their solutions. I am reading in a textbook about methods of finding a collision. It states to consider a collision for a hash ...
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  • 387
6 votes
1 answer
2k views

Multiple AES Key Derivation from a master key

I need cryptography advice regarding this issue. Kamus is a service that encrypts secrets for applications running on Kubernetes. When using AES (actually, Rijndael) symmetric encryption, Kamus uses ...
user avatar
88 votes
8 answers
13k views

Guarding against cryptanalytic breakthroughs: combining multiple hash functions

Assume I want to design a protocol (or data format or similar) including some cryptographic hash, and want it to be as future-proof as possible, i.e. I want to avoid that breakthroughs in cryptography ...
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23 votes
4 answers
5k views

Is it feasible to build a stream cipher from a cryptographic hash function?

A few years ago I devised a symmetric-key system that worked like so: ...
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  • 1,465
56 votes
6 answers
48k views

Why is AES resistant to known-plaintext attacks?

At least it's my understanding that AES isn't affected by known-plaintext. Is it immune to such an attack, or just resistant? Does this vary for chosen-plaintext?
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58 votes
3 answers
48k views

Definition of textbook RSA

What is the definition of textbook or "raw" RSA? What are some of the properties of textbook RSA? How does it differ from other schemes based on RSA?
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  • 1,903
24 votes
2 answers
12k views

Is RSA encryption with a private key the same as signature generation?

It is often said that RSA encryption of a cryptographic hash with a private key is the same as signing (signature generation). And that verification consists of decryption using a public key. Is RSA ...
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  • 85.8k
17 votes
2 answers
23k views

Is it possible to obtain AES-128 key from a known ciphertext-plaintext pair?

I have a file, which was encrypted with AES-128 in ECB mode. I know the format of the original file and know that all files in this format have the same headers. So, I have an encrypted block and the ...
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66 votes
3 answers
103k views

Why shouldn't I use ECB encryption?

I'm using Java to generate encrypted strings, and I get this warning at build time: ECB encryption mode should not be used So I'm wondering why I shouldn't use ECB and what I can use instead?
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  • 786
57 votes
2 answers
20k views

What makes a hash function good for password hashing?

Using a cryptographic hash to store e.g. passwords in a database is considered good practice (as opposed to storing them plaintext), but is subject to attacks on said cryptographic hash, assuming the ...
user avatar
  • 673
87 votes
4 answers
99k views

What are the practical differences between 256-bit, 192-bit, and 128-bit AES encryption?

AES has several different variants: AES-128 AES-192 AES-256 But why would someone prefer use one over another?
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  • 3,176
22 votes
5 answers
8k views

Using CBC with a fixed IV and a random first plaintext block

What if, instead of using CBC mode in the normal way with a random IV, I used this approach: Use a fixed IV (like a block of 0's). Before encrypting, generate a random block and prepend it to the ...
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46 votes
4 answers
30k views

Security strength of RSA in relation with the modulus size

NIST SP 800-57 §5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength $s$ in bits: ...
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58 votes
2 answers
17k views

Why is $H(k\mathbin\Vert x)$ not a secure MAC construction?

If $H(m)$ is a secure hash function, can't we implement a MAC using $H(k\mathbin\Vert m)$? However, it seems the more widely used MACs, such as NMAC and HMAC (both originally defined in Keying hash ...
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36 votes
4 answers
8k views

Why is plain-hash-then-encrypt not a secure MAC?

It seems that even in MAC-then-encrypt systems like SSL, something like HMAC is used rather than a plain hash. Why? Suppose we use some stream cipher; then why can't we use $Encrypt(m | H(m))$ as ...
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  • 1,091
51 votes
2 answers
7k views

What security authorities and standards reject $e=3$ in RSA, when, and with what rationale?

In RSA, some security authorities and/or standards allow the public exponent $e=3$, others require or recommend $e>2^{16}$ (or perhaps some other minimum). I gathered the following: PKCS#1 allows $...
user avatar
  • 125k
3 votes
1 answer
904 views

Discrete Logarithm: Given a p, what does it mean to find the discrete logarithm of x to base y?

My understanding is that $a^b \bmod p$ is the discrete logarithm problem. Given the question is worded this way, are we trying to find $ \log_y x \bmod p$. For instance, if we are trying to compute ...
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69 votes
1 answer
54k views

Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5?

I've studied that the Bleichenbacher's CCA attack on PKCS#1 v1.5. is a base to many versions of attacks in the area. I'm trying to understand that attack, but every explanation I saw starts with the ...
user avatar
  • 2,020
12 votes
1 answer
17k views

Bit Flipping Attack on CBC Mode

To perform a bit flipping attack, the previous block is modified by using XOR. This results in an altered plaintext. However, now the ciphertext of the previous block is altered, hence it will result ...
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  • 161
24 votes
4 answers
5k views

Attacks of the MAC construction $\mathcal{H}(m\mathbin\|k)$ for common hashes $\mathcal{H}$?

Consider a common practically-collision-resistant hash function $\mathcal{H}$ (e.g. SHA-1, SHA-256, SHA-512, RIPEMD-160), perhaps based on the Merkle–Damgård construction as are the first three. We ...
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  • 125k
31 votes
3 answers
5k views

Are common cryptographic hashes bijective when hashing a single block of the same size as the output?

It's been said that CRC-64 is bijective for a 64-bit block. It the corresponding statement true for typical cryptographic hashes, like MD5, SHA-1, SHA-2 or SHA-3? For example, would SHA-512 be ...
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  • 1,797
18 votes
4 answers
5k views

Is SHA-256 secure as a CTR block cipher?

Generate a 256-bit random nonce. XOR it with a 256-bit reusable symmetric key. This is x. We represent numbers in simple binary instead of a counting function. <...
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  • 565
26 votes
4 answers
6k views

What makes Quantum Cryptography secure?

This is my current understanding of how Quantum Cryptography works: (The first bit is Quantum Key Distribution) Alice sends a beam of photons to Bob through a quantum channel such as an optical fiber. ...
user avatar
  • 373
21 votes
2 answers
15k views

How bad it is using the same IV twice with AES/GCM?

I understand that initialization vectors (IV) should not be used twice when using AES/GCM. I am using a counter as an initialization vector. Every time I send out a new packet (I am developing an UDP ...
user avatar
  • 1,381
6 votes
2 answers
2k views

What is a multi-target attack?

What exactly is a multi-target attack? How does the attack work on different cryptographic schemes (block ciphers, hash functions, elliptic curves)? How can it be avoided?
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  • 6,129
12 votes
4 answers
5k views

Disadvantages of AES-CTR?

On paper, it sounds *very* good to me: secure fast (in my tests it's somewhat slower than ECB (but without most of the weaknesses, more on that below) but faster than every other alternative I tested,...
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20 votes
4 answers
13k views

What tests can I do to ensure my random number generator is working correctly?

In the past I have used the Chi-squared test to check the statistical randomness of my generator. Is this a good test to use? Are there other tests?
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  • 1,887
9 votes
1 answer
2k views

What are the rules for using AES-GCM correctly?

When using AES-GCM I know that I am supposed to use a new initialization vector every time I call the AES-GCM algorithm with the same key. What are other rules must be followed to use AES-GCM ...
user avatar
  • 471
70 votes
4 answers
39k views

How can I use asymmetric encryption, such as RSA, to encrypt an arbitrary length of plaintext?

RSA is not designed to be used on long blocks of plaintext like a block cipher, but I need to use it to send a large (encrypted) message. How can I do this?
user avatar
  • 3,176
32 votes
2 answers
19k 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 ...
user avatar
46 votes
5 answers
9k views

Is there a secure cryptosystem that can be performed mentally?

I, myself, do not plan on getting into a situation where I would be unable to use a computer in order to communicate securely. However, I can think of many practical situations in which mental ...
user avatar
  • 1,465
23 votes
4 answers
32k views

Is using the same IV in AES similar to not using an IV in the first place?

So if I understand how an IV works with AES, I'm supposed to generate a different IV for every message because using only a key, I will get the same encryption if the message was encrypted twice (...
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  • 333

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