# All Questions

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### In the SHA hash algorithm, why is the message always padded?

In the SHA hash algorithm the message is always padded, even if initially the correct length without padding; the padding is of the form "1" followed by the necessary number of 0s. Why is it ...
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### 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 ...
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### How does one implement the Inverse of AES' MixColumns

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 ...
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### 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, ...
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### 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 ...
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### What is the difference between CSPRNG and PRNG?

What is the difference between CSPRNG and PRNG? Is there performance differential between them? For example: We use PRNG for key generation which is very expensive and CSPRNG for IV/nonce in block ...
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### RSA leak bits to factor N

Suppose you randomly generate large primes p and q as in RSA, and then tell me N=pq but not p or q. Then, you would like to actually let me factor N, except you should tell me as few bits of ...
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### 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 ...
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### Low Public Exponent Attack for RSA

I'm having trouble understanding the algorithm for finding the original message $m$, when there is a small public exponent. Here is the example I'm trying to follow (you can also read it in the 'Low ...
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### Which risks are associated with deriving multiple keys from the same DH secret Z?

NIST recommends Krawczyk's HMAC-based key derivation function (HKDF) in SP-800-56C (PDF). HKDF shall e.g. be used to create keys from shared secrets after Diffie Hellman key establishment. NIST ...
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### How are timestamps verified?

You put an input and the hash value comes as an output then when someone puts the input the hash function it is applied to see if it is the same hash original value is stored in some database , that ...
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### Why is ciphertext from low entropy plaintext not compressible?

This comes following a discussion with a colleague. My plaintext file plain consists of a about 100,000 lines of "all work and no play...". It's size is: 2.2 MB. ...
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### Does encrypting twice using the same block cipher produce a security weakness?

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. ...
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### Mixing Entropy Sources by XOR?

Assume that I have two sources of entropy (say, a hardware RNG and a CSPRNG) and that the two sources are independent (do not know anything about the internal state of the other RNG). Can I mix them ...
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### Cryptographic system with double keys with reversible order

While reading Shamir, Rivest and Adleman's paper on "Mental Poker", I've met a mention of system such that $E_a(E_b(x)) = E_b(E_a(x))$, without however disclosing details on it, with $E_a(x)$ being ...
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### Is there a “brainwallet” for GPG keys? [closed]

“Brainwallet” is a program that takes a passphrase (hopefully a good one) and deterministically creates a Bitcoin wallet. This wallet can be used for transactions, then deleted from the computer. To ...
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### When do we need composite order groups for bilinear maps and when prime order?

Why we need bilinear groups of composite order? What's the special security property of the composite order group in comparison with one of prime order? To put it in another way when do we need ...
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### Are safe primes $p=2^k \pm s$ with $s$ small less recommandable than others as a discrete log modulus?

I take the definition of safe prime as: a prime $p$ is safe when $(p-1)/2$ is prime. Safe primes of appropriate size are the standard choice for the modulus of cryptosystems related to the discrete ...
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### Proving knowledge of a preimage of a hash without disclosing it?

We consider a public hash function $H$, assumed collision-resistant and preimage-resistant (for both first and second preimage), similar in construction to SHA-1 or SHA-256. Alice discloses a value ...
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The definition of PBKDF2 states that I obtain a derived key (1) by calling a pseudorandom function a bunch of times recursively: $U_1 = PRF(password, salt)$ $U_2 = PRF(password, U_1)$ … $U_n ... 2answers 349 views ### How to determine the order of an elliptic curve group from its parameters? Let$\quad E:\; y^2 = x^3 + ax + b \quad$be an elliptic curve defined over a finite field$\mathbb F_q$where$q = p^n$,$a,b \in \mathbb F_q$and$p \neq 2, 3$. By Hasse's theorem we know that the ... 2answers 1k views ### Measuring entropy for a ciphertext only attack When bruteforcing a password (e.g. the common attacks on DES), where you have ciphertext only, you need a way to assess whether a decrypted plaintext is the right one. I believe the EFF DES machine ... 4answers 4k views ### What are the requirements of a nonce? Sometimes I read that a nonce has to be a random number but I disagree. A nonce just can't repeat itself. You could increase in by 1 every time if you are sure it would never repeat. 3answers 4k views ### How does the key schedule of Rijndael looks for keysizes other than 128 bit? It said in Wikipedia that: [....] Rijndael can be specified with block and key sizes in any multiple of 32 bits, with a minimum of 128 bits. The blocksize has a maximum of 256 bits, but the ... 1answer 868 views ### How realistic is a dictionary attack on a secure remote password protocol (SRP) verifier? I'm deploying a secure remote password protocol implementation and I'm wondering what the consequences are when the client generated verifier gets leaked to an attacker. I've read Thomas Wu's paper ... 2answers 2k views ### RSA and prime difference It is known that the two prime factors$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 ...
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I was looking at the algorithm for Twofish, and I noticed that in some places a XOR is used, but in others, they use "addition modulo-32." What makes modulo-32 special? Why not always use XOR? Why not ...
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### Besides key and ciphertext sizes what are other advantages of elliptic curve versions of various protocols?

There are elliptic curve variants of Diffie-Hellman, ElGamal, DSA and possibly other protocols/algorithms. I know that these elliptic curve variants have smaller key and ciphertext sizes which will ...
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### Why do we need asymmetric algorithms for key exchange?

In SSL protocols, both symmetric and asymmetric algorithms are used. Why is it so? The symmetric algorithms are more secure and easier to implement. Why are asymmetric algorithms usually preferred in ...
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### Does AES-CTR require an IV for any purpose other than distinguishing identical inputs?

I'd like to encrypt files deterministically, such that any users encrypting the same plaintext will use the same key and end up with the same ciphertext. The ciphertext should be private as long as ...
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### ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
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### How does one calculate the scalar multiplication on elliptic curves?

I found this example online: In the elliptic curve group defined by $$y^2 = x^3 + 9x + 17 \quad \text{over } \mathbb{F}_{23},$$ what is the discrete logarithm $k$ of $Q = (4,5)$ to the base ...
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### What is a smart card?

In many cryptographic protocols, some information is transmitted within smart cards. So, what is a smart card? Is it a physical card? What are they used for in cryptographic protocols?
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### Is there a public key semantically secure cryptosystem for which one can prove in zero knowledge the equivalence of two plaintexts?

If Alice encrypts two messages $a$ and $b$, such that $x=E(a)$, $y=E(b)$. Can Alice prove (without revealing $a$, $b$ or the private key) that $a = b$? Obviously the proof must not be too long and it ...
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### Difference between encrypting something and hashing something

What is the difference between encrypting something and hashing something? in what situations would I want one or the other?
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### Relative merits of AES ECB and CBC modes for securing data at rest

I need to store several million Payment Card Numbers (PCNs) securely in a mainframe database (that is, 'at rest'). I assume that any attacker will have access to all of the stored data. I assume the ...
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### Deterministic nonces in CTR mode

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 ...