10
votes
0answers
686 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
0answers
457 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 ...
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Why was ISO10126 Padding Withdrawn?

Wikipedia mentions ISO10126 Padding has been withdrawn, but doesn't say why.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 Why was it withdrawn?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 ...
7
votes
3answers
5k views

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 ...
5
votes
2answers
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 ...
2
votes
1answer
6k views

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 ...
14
votes
2answers
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, ...
12
votes
2answers
795 views

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 ...
11
votes
2answers
808 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 ...
10
votes
3answers
308 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 ...
9
votes
5answers
585 views

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 ...
8
votes
1answer
2k 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 ...
7
votes
1answer
5k views

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 ...
7
votes
2answers
701 views

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 ...
7
votes
4answers
5k views

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 ...
6
votes
2answers
2k views

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. ...
6
votes
4answers
3k views

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. ...
5
votes
1answer
705 views

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 ...
5
votes
1answer
331 views

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 ...
5
votes
0answers
318 views

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 ...
4
votes
3answers
768 views

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 ...
15
votes
2answers
501 views

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 ...
12
votes
6answers
1k views

Why does PBKDF2 xor the iterations of the hash function together?

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 ...
10
votes
2answers
380 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 ...
10
votes
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 ...
9
votes
3answers
1k views

How is the One Time Pad (OTP) perfectly secure?

The Wikipedia entry on One Time Pads (OTPs) states that if this cipher is used properly; ie, the keys are truly random and each "part" of the key is independent of every other "part", it's ...
8
votes
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.
8
votes
3answers
5k views

Encryption with “constant” initialization vector considered harmful

I try to get the full reasoning behind the above statement. First, after reading articles here and at wikipedia i understand that using an IV only once is good practice. For stream ciphers not doing ...
8
votes
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 ...
8
votes
1answer
871 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 ...
7
votes
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 ...
7
votes
1answer
1k views

Why Addition Mod 32?

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 ...
7
votes
5answers
7k views

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 ...
6
votes
2answers
610 views

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 ...
6
votes
1answer
2k views

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 ...
5
votes
1answer
2k views

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 ...
5
votes
4answers
8k views

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 ...
4
votes
1answer
1k views

Mapping of message onto elliptic curve and reverse it

I would like to perform a variant of Elliptic Curve ElGamal in java using the BouncyCastle libraries. I currently face the difficulty of mapping a message $m$ onto the elliptic curve $E_p$. I have so ...
4
votes
1answer
919 views

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?
4
votes
3answers
433 views

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 ...
4
votes
2answers
3k views

How can I do a brute force (ciphertext only) attack on an CBC-encrypted message?

Given a CBC ciphertext and IV, how can I find the encryption key? We are limited with an 8 chars key, each char in the range of [a..h], so I can generate every possible key (these are only $8^8 = ...
3
votes
1answer
389 views

How do you test the security of your cipher?

I got asked this question and I didn't know what to answer. How do you test the security of your cipher? What comes to my mind now would be to test it with famous attacks: padding attacks, ...
3
votes
2answers
3k views

Attacking 2DES efficiently

Meet in the middle on 2DES uses $2^{56}$ memory. Given the fact that the attacker has only $2^{45}$ memory. How can the attacker adjust the attack so even with this memory limit, it will still be more ...
3
votes
1answer
1k views

Is RSA of a random nonce with no padding safe?

Consider the following protocol: Bob has a private RSA key $B_{priv}$, and Alice knows the public key $B_{pub}$. Alice wants to send confidential messages to Bob (no integrity intended). To send a ...
2
votes
2answers
354 views

Why is MAC using nonce+message+hash(nonce+message+identifier) not the standard?

Given that we know that nonce + message + hash(nonce + message + mac-key) all inside the encryption makes it possible to detect if any bits of the message have been ...
2
votes
1answer
838 views

How can I calculate the Rijndael SBox?

I would like to implement the Rijndael subBytes() operation using calculation instead of tables, because I like to play with this on different wordsizes, as an ...
14
votes
5answers
4k views

What is the difference between a stream cipher and a one-time-pad?

A (synchronous) stream cipher is an algorithm which maps some fixed-length key to an arbitrary-length key-stream (i.e. a sequence of bits): $C : \{0,1\}^k \to \{0,1\}^{\infty}$. This key-stream is ...
12
votes
1answer
581 views

RSA with probable primes

I am a bit of a newbie to RSA encryption, so please be patient. I understand that for a 4096 bit RSA, the numbers p and q should be prime. And to have the best security, the p and q should both be ...
11
votes
1answer
790 views

How random are commercial TRNGS

I'm thinking about buying a USB TRNG. How do I evaluate its randomness? I'm sure some are better than others but which is which? Are thermal-noise better than radio-noise TRNGs?
11
votes
1answer
4k views

Is AES-256 a post-quantum secure cipher or not?

We know Grover's algorithm speedup brute-force attacks two time faster in block ciphers (e.g brute-forcing 128 bit keys take $2^{64}$ operations not $2^{128}$). That explains why we are using 256 bit ...

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