# All Questions

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### Present an attack for the combination of OTP and textbook RSA

Let $N=p \times q$ where $p$ and $q$ are two primes. Compute $\Phi (N) = (p-1)(q-1)$. Choose $e$ s.t. $1 < e < \Phi(N)$ and $gcd(e,\Phi(N))=1$. Compute $d = e^{-1}(mod \ \Phi(N))$. ...
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### How can I design a cryptographically secure, key-dependent s-box?

I would like to design a cryptographically secure, key-dependent s-box, but I am not sure how. Mainly, because I am unsure about the difference in design compared to a random s-box. What is the ...
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### Roots in modulo field

I have a point $(X,Y)$ on an elliptical curve $E(a,b)$ where $a=-3$ and $B$ is a large number that is in hexadecimal from -51BD. To compress this point oficially in a program, we know that every $X$ ...
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### Is there a way to systematically calculate the public exponent $e$ in RSA?

I'm learning RSA in one of my classes and we were given a problem: $p = 5$, $q = 11$ I have done the following steps: $n = 5 \cdot 11 = 55$ $\phi = (5-1)\cdot(11-1) = 40$ I know that to ...
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### How could Fully Homomorphic Encryption support power operations?

Fully Homomorphic Encryption (FHE) enables arbitrary functions computed on encrypted data, because it supports both addition and multiplication. But I wonder if FHE supports power operations. For ...
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### How do I convert the definition of E-521 into a curve definition a la Bouncy Castle?

I am currently trying to create an ECCCurve for E-521. Unfortunately, it is not currently a named curve in the library I am using, so I will have to define it manually. I am using the definition of ...
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### How to calculate the maximum output size for data encrypted with a RSA Private Key?

I have an an encryption algorithm I am working with that looks like this: prv_key_enc(sha1_hash(data)) Where, the RSA parameters are: RSA/ECB/PKCS1Padding 1024 ...
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### How is HKDF-Expand better than a simple hash?

Why do we need HKDF-Expand if we can simply hash the pseudorandom key to make it longer? The docs (in the link) say: The second stage "expands" the pseudorandom key to the desired length... ...
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### Weaker Notion of Target Collision Resistance

I'm reading the paper “Collision-Resistant Hashing? Towards Making UOWHFs Practical” which states: While it might be easy to find a collision $M,M'$ in $F_K$ by making both $M,M'$ depend on $K$ ...
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### Dependence on Keyed Hash Function

I'm reading the paper “Collision-Resistant Hashing? Towards Making UOWHFs Practical” which states: With an ACR hash function $F$ the key $K$ is announced and the adversary wins if she manages to ...
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### How can an encryption scheme be indistinguishable with multiple messages but vulnerable to an adaptive chosen-plaintext attack?

In order to be indistinguishable with respect to multiple messages, wouldn't the scheme need to be nondeterministic? How would this then possibly be vulnerable to an adaptive CPA?
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I'm performing ElGamal encryption algorithm and using the additive homomorphic property so the product of two ciphertexts is the encryption of the sum of the plaintexts. The problem is that I need to ...
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### How large should a Diffie-Hellman p be if the messages are encrypted?

How large should the prime $p$ and generator $g$ values be in a Diffie-Hellman handshake if the messages are encrypted. If the key that encrypted the Diffie-Hellman messages becomes compromised, ...
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### Nonce role on stream ciphers

Modern stream ciphers usually predicts the usage of a nonce (also termed as IV) in the cryptosystem. The cost of initializing the cipher with the nonce varies from algorithm to algorithm (for ...
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### Discrete logs on elliptic curve with embedding degree 3 with the 'MOV' attack

The curve $E(\mathbb{F}_{47}):y^2=x^3+x+38$ has order $61$ and $61|47^3-1$ so the embedding degree of $E$ is $3$ and therefore the MOV attack, presumably using some sort of distortion map and a ...
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### using Post-quantum asymmetric ciphers instead of RSA

We can't trust RSA to encrypt our Emails so what is best post-quantum cryptography system as alternative for RSA which provide good security and don't be breakable? because McEliece cryptosystem looks ...
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### Is it safer to encrypt twice with RSA?

I wonder if it's safer to encrypt a plain text with RSA twice than it is to encrypt it just once. It should make a big difference if you assume that the two private keys are different, and that the ...
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### Why is a non fixed-length encryption scheme worse than a fixed-length one?

I have the following definition (highlights by me): An (efficient secret-key) encryption scheme $(Gen,Enc,Dec)$, where $Gen$ and $Enc$ are PPT algorithms and $Dec$ is a Deterministic Polytime ...
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### What exactly is addition modulo $2^{32}$ in cryptography?

EDIT: I've been confusing this the whole time. What I've been wanting to say this whole time is addition modulo $2^{32}$ not addition modulo 32 as the question originally said. Thanks for pointing ...
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### Shortcuts / practicality of brute forcing block cipher (AES) + ECB with known plaintext

I know the plaintext (26 bytes long) and cryptotext of block cipher (suspected to be AES) in ECB mode. I can generate hundreds or thousands of such samples, but the samples are not arbitrary. What are ...
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### Entropy of system data - use all and hash, or trim least significant bits?

I'm working on a background entropy collector for key generation that monitors hardware and produces an entropy pool. Here's my list of sources: Mouse position Keyboard timings (i.e. time between ...
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### How to get the keyword from a keyword cipher?

I was given a ciphertext and now I am trying to break it via looking for the keyword. This is a keyword cipher. So: PlainEnglish: ABCDEFGHIJKLMNOPQRSTUVWXYZ If ...
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### Shannon entropy calculation: is $H(A|R·A) = H(A)$?

Suppose I generate a random $m×m$ matrix $R$, where each of its elements belongs to $\mathbb Z_n$. I ensure that $R$ is invertible in $\mathbb Z_n^{m×m}$. Now I take a non-random $m×m$ ...
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### Salts, how does the script know what the salt is?

I am new to PHP programming and trying to grasp the idea of hashing and encryption for protecting passwords, credit card details and such. I've done a lot of reading about MD5 which I think I ...
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### A mathematical explanation of the DES encryption system

I need a mathematical explanation of what does the DES encryption system really do. This means I need more explanation than the one that offers FIPS, which is more an explanation for computer ...
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### Proving an encrypted message contains (but does not 100% consist of) a plain-text message?

I have keypair (u,r), and two pieces of data, X and Y. I reveal X publicly but keep Y secret. Y has high entropy. I then concatenate X and Y, into Z. I encrypt Z, into "encrypt(Z,u) = Q". r is ...
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### NTRU Encryption

It's using Euclidian inverse. Can you show it step by step? $$N=7, q=11, a = 3+2X^2 -3X^4 +X^6$$ the inverse of $a \pmod {11}$ is $$A=-2+4X+2X^2 +4X^3 -4X^4 +2X^5 -2X^6$$ How do we compute $A$?
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### Proving the semantic security of the One Time pad

Currently hearing a lecture on cryptography, and the professor gave us the definition of semantic security, which is roughly the following (formally not quite complete, but you get the idea): ...
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### Sharing an encrypted file between a group of people

Is there any way to share an encrypted file with a group? In the other words, can I encrypt a file with a public key so that each person in a group decrypt it with his/her private key? Is there any ...
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### DES-X , computation load and storage

The passage said that the computational load to attack DES-X can be reduced to approximately $2^{(56+64)}=2^{120}$ steps,and the storage of data sets should be $2^{64}$. But I can't figure why ...
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### Homomorphic Encryption Notation Question

What does the following notation mean in a homomorphic encryption scheme? ENC(x;r) What does x and ...