# All Questions

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### How to perform AES MixColumns as matrix multiplication in GF(2) (boolean values)?

AES MixColumns is done by multiplying a $4 \times 4$ matrix and a column of the AES state (a vector). Addition and multiplication are done in $\operatorname{GF}(2^8)$. In the paper White-box AES, the ...
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### Naccache–Stern knapsack cryptosystem: How to calculate $p_i ^{s^{-1}} \mod p$?

In the algorithm(link), for calculated n and chosen secret key s, we need to calculate $\sqrt[s]{p_{i}} \bmod p$. As an example in original research paper (link) , For a given $p=9700247$ and ...
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### Explanation of protocol secure under random oracle but insecure with any hash fuction

It is known that there is a protocol that is secure in the random oracle model, but where any real hash function makes the protocol insecure. The proof is constructive, but I could not understand the ...
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### Create a potential input for sha-256 hash given a substring of input?

Let's say I'm given a specific SHA-256 hash. Further assume that the SHA-256 input, that yielded this hash contained a known sub-string. Is there a way to find the input (containing the specific ...
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### How to calculate secret key size of a CP-ABE scheme

How can I calculate the real size of key in a CP-ABE scheme. For example, I have this GSWV scheme: Fuchun Guo, Willy Susilo, Duncan Wong, Vijay Varadharajan: CP-ABE with constant-size keys for ...
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### Step by step conceptual implementation of AUTHENTICATED Diffie-Hellman?

I'm already doing classic DH with pre-shared key in my setup, and it prevents people knowing the same password from eavesdropping on others' traffic. But it doesn't cover situations where a third ...
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### Unclear about the importance of Initialization Vectors

I was reading about Ruby ciphers and found this: Although the key is generally a random value, too, it is a bad choice as an IV. There are elaborate ways how an attacker can take advantage of ...
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### How vulnerable is the one-time-pad (OTP) encryption, if the OTP is used twice, with a random substitution scheme

So I was wondering, I read up about OTP encrption and can see how using an OTP encryption is in itself unbreakable. However, I looked at how OTP is broken if the OTP-key is used on more than one ...
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### Exponent operation over element of G

I found a definition of an exponent operation over the element of $\mathbb{G}$ in this paper (page 4): $$(g^a)^{\% b} = g ^{a \text{ mod } b}$$ I couldn't understand the rest of the paper (Decrypt ...
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### Can “Approximate Hashing” work in a Proof-of-Work context?

Here is a draft of an article claimed to soon appear in a peer-reviewed conference: Matthew Vilim, Uenry Duwe, Rakesh Kumar, Approximate Bitcoin Mining. It is proposed to simplifying a SHA-256 engine ...
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### Create big random number from 2 smaller numbers?

If I have 2 true random numbers from atmospheric noise or a different source. Suppose $x= 299$ and $y= 499$. Is it possible to create a bigger number with $x$ to the power of $y$? Can I use ...
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### Metrics of PRNGs

I am a bit confused on the metrics that can be applied to the output of (deterministic) pseudo-random number generators. I've run output from many RNGs through ENT. The only metrics that really differ ...
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### Possible to generate a one time secret which all nodes on the distributed network can know but cannot pre compute

I have a distributed P2P network. Everyday, I want each node to have a secret which is only valid for that day, while each of the other remaining nodes on the network will be able to calculate the ...
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I am wondering how to solve the problem below: Suppose we have a $MAC$ scheme $I=(S,V)$. There is another algorithm that can find a pair of texts $(m0,m1)$, with $m0≠m1$ such that $S(k,m0)=S(k,m1)$ ...
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### ABE Schemes - Access Structures & Performance

I'm reading this article, CP-ABE with constant-size keys for lightweight devices and in the Table 1, are there these access structure: Threshold, Tree, ($n$,$n$)-Threshold, LSSS, AND gates. I have 2 ...
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### Difference of full codebook and non full codebook

While reading a paper about Dynamic cube attack, I saw two terms: full-codebook and non-full-codebook attacks. What do they mean? What is the difference? Regards
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### Is there a standard for hashing a list of strings?

I'm working in Python, and my goal is to hash a list of strings with a cryptographic hash function such as sha256. It would need the property that a change in any string, or the order of the strings, ...
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### AES key and block size

I am trying to understand $AES$ and I wondered what happens in the case of a $128$ bit block size and a $256$ bit key. All documents I read about $AES$ told me the key expansions algorithm for $128$ ...
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I am trying to devise an encryption scheme such that an adversary can win the following game with probability at most $1/2 + \epsilon$. Adversary gives challenger two plaintext messages $m_1$ and ...
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### How can comparision like (>=,==) be done using homomorphic encryption?

Since we know that Homomorphic encryption allow computation on encrypted data. Let two n-bit integers $(x,y)$ are encrypted using some LWE public key cryptography. For example - if $x'= HEnc(x,pk)$ ...
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### Do any Identity-based Encryption Systems support messaging between domains?

Identity Based Encryption is covered under RFC 5091 (specifying the algorithm), 5408 (specifying data structures), and 5409 (using IBE with Cryptographic Message Syntax). However, every IBE ...
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### Cycling hashing in PBKDF's and their limitations in strength?

I hope this question isn't too similar to one that's already been asked. I also want to point out I know part the answer already, AFAIK: I just want some expert input on this. Let's model a hash that ...
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### Non-numeric Diffie-Hellman?

It may seem that this is a programming question, but I just need advice on the cryptography side of the question. I want to implement the Diffie-Hellman key exchange algorithm on iOS (since no free ...
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### Recommendation for lightweight algorithm for partial message encryption

I have designed a specific client and server program, which sends a file from client to server in 32k chunks. I want to encrypt only part of the data. More specifically: in each 32k chunk passing ...
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### Elliptic ElGamal Public Key Cryptosystem doubt

I need an example of Elliptic ElGamal Public Key Cryptosystem. I have been trying with some values but I don't get the right solution. I have $p=13$, the elliptic curve $E:y^2=x^3+11x+7$ and a point ...
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### What is the viability of a hybrid vigenere cipher?

So a vigenere cipher's main weakness is that you can use frequency analysis on each alternated alphabet, and thus crack the cipher with relative ease... But that implies that you know what the ...
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### Multi Party System with n-1 adversaries

Novice here. Is there a MPC function where no information is leaked even if all parties are not trustworthy ?
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I am using Android's keystore to generate a key which is protected by fingerprint authentication. This key can be used to encrypt any secrets. In my case, I want to encrypt a user password (which is ...
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### Would it be better to use HKDF or SCrypt for deriving a child key?

Okay so I'm trying to derive a child public key from an EC public key. I've come up with a couple ideas and now I'd like to know which is more secure. Mp: The master key pair, this includes a ...
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### How to check the integrity of a key received through mail using symmetric encryption?

I would like to provide access to encrypted data through a cloud service provider, using a pay-as-you-go model. This means that we will sometimes need to revoke a user's access to the data. To ...
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### Can the original message be retrieved from a public/private key signature?

When I sign a message (which has potentialy low entropy) using a private key and I send it without the original message, can the original message be retrieved from the signature(s)? I want to prove – ...
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Suppose a client (Alice) goes to an HTTPS website (Bob) over TLS 1.2. Alice sends Client Hello with some random number $r_a$. Bob sends Server Hello with another random number $r_b$. Suppose they ...
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### What is a good algorithm to scramble data in a 2-D grid

I want to know if there exists an algorithm i can use where the input is a string of data and the output is a scrambled version of the same but in a 2 D array ie given something like: |1 2 3 4 5 6 ...
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### bcrypt collision probabilities assuming same password and work factor?

What is the likelihood of 2 bcrypt hashes colliding if they use the same work-factor and input? Are bcrypt's salts large enough to prevent this from happening?
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### How to store keypair generated by RSA in a textfile?

I'm trying to write an encryption decryption program using Openssl-RSA. There are only two operations. User stores the data and retrieves it whenever he needs. To decrypt something, we need the ...
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### Deletion complexity in a RSA accumulator

My question is about the existence of a dynamic RSA accumulator with deletion of an element in O(1) time. Do you know some practical implementation?
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### How do different block sizes affect the throughput of GPU implementations of AES?

I am confused about the effect of different block sizes on AES performance. As you can see here, there is a huge gap between the throughput of different block sizes. As far as I know, every 16 bytes ...
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### Is there short period in AES 128 key schedule?

I am wondering if for some particular keys the AES 128 key schedule lead to a periodic pattern for the round keys. The key schedule is only 10 rounds, but I am also wondering in the general case where ...
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### Cryptography of numbers

Is there any algorithm capable of encrypt securely (symmetric) N numeric digits in a numeric message of M digits (N < M)? I am especially interested in a specific case in which N = 10 and M = N + ...
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### Few questions about CBC MAC

I want to use CBC MAC. First I hope to find some implementation of block cipher which I will use in CBC mode, which I understand is CBC MAC. But I have two questions: 1) If the length of the message ...
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### Probabilistic RSA, IND CPA

Suppose we have classic RSA scheme. Let $n=pq$, $e$ public, $d$ secret. Then message(M), not empty(not 0), is encrypted by choosing random $r$ and computing $A=(r^e)^e$ and $B=(Mr)^e$ $(A,B)$ is ...
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### Continuous stream of strong randomness from limited entropy?

I need a continuous (infinite) strong random generator, but I've only got limited entropy as seed. I know there's already a contradiction there, but I'm looking for a practical approach. Suppose I ...
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### Finding collisions for the DES F-function

It's known that for a given subkey, the F-function of the DES is not injective (see Is the DES F-function injective for a given subkey?). I am interested in efficiently finding collisions for this ...
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### S boxes in Blowfish

I know how the s-boxes in blowfish are initialized, but how is the output sorted, I mean which bit from the input goes where in the box ? and what do mean they have 256 entries if they are 32-bit ...
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### RSA: must $d$ be an integer?

I am only taking baby steps in RSA. If $p=11$, $q=7$ and $e=3$, $$\phi(n) = 10*6 = 60$$ Then: $$d = (2 (\phi(n)) + 1 ) / 3 = 121/3$$ Should $d$ be kept as a non-integer or is such a $d$ invalid? ...
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### Rogue CA Certificate MD5 Collision Control

Papers from Marc Stevens et al show that X509 certificates that rely on MD5 signatures can break the assumed security model, that is, it allows for a forged certificate to have the same signature as a ...
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### Bilinear map assumpion

Is there an assumption that says from a tag $k\cdot e(g,g_1)^{rx}$ ($k,r$ are secret) it is difficult to forge it with some x': $k\cdot e(g,g_1)^{rx'}$, as long as you cannot solve DL in ...
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### how to calculate maximum data size of an RSA signature

I am reading a content, and am not sure if I follow how they come up with the maximum data size which can be signed by an RSA key. The author states: "...if you are trying to sign a message using a ...
Let $f$, $g$, and $h$ be hash functions that each map binary strings of length $2n$ to binary strings of length $n$. Suppose that $h(x) = f(g(x)||g(x))$. Prove that if $f$ and $g$ are collision ...