# All Questions

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### How to correctly encrypt data with proper authentication using AES-256-CBC in php?

I have been using the openssl function for encrypting data with AES-256-CBC in php. I have been able to encrypt it using an unique IV (by generating with openssl_random_pseudo_bytes)for each new ...
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### Why reveal MAC-keys after using them?

As far as my understanding goes MACs are used to determine whether the received message comes from a source that has access to a MAC-key which is known by both parties. Some crypto protocols reveal ...
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### Why gcd(r,(p-1)/r) needs to be 1 in benaloh cryptosystem

I recently discovered the benaloh cryptosystem. I am working with the system as it is discribed in the following link: https://en.wikipedia.org/wiki/Benaloh_cryptosystem However I need some help in ...
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### TPM's monotonic counters

I am reading the TPM Design Principles v1.2 §17 and do not feel I fully understand the example they give on how the counters would work. Apparently monotonic counters are used to prevent replay ...
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### Is EFS vulnerable to Chosen plaintext attack?

I have some backed up files encrypted with EFS and I lost the EFS certificate thus unable to decrypt the files. I understand that EFS uses the user certificate public key to encrypt the symmetric key ...
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### High-level overview of system architecture of LUKS/cryptsetup (how it works vs. how to setup) [closed]

I've been searching (unsuccessfully) online for a high-level overview of how LUKS/cryptsetup disk encryption works. I am reading through the cryptsetup source code to try to understand what is going ...
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### HD (Hierarchical Deterministic) Keys using Safe Curves?

Bitcoin's HD (Hierarchical Deterministic) Keys as described in BIP32 allow for a master key to be created (a private key and a chain code) such that a tree of both public and private keys can be ...
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### Why SIVP Is Worst Case Problem?

I just started to study lattice cryptography. I'm now studying worst-case to average-case reduction for SIS. In previous question, "worst means any and average means random". And I wonder why ...
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### Seeking an implementation of the Satoh algorithm for elliptical curve point counting

I would be very grateful if someone has an implementation of the Satoh algorithm (Fast Elliptic Curve Point Counting). Can someone point me to practical algorithm implementations or provide some ...
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### Cost of attack on DSA with attack on DLP

Are there any (recent) estimates of cost of attack on DSA by solving the discrete logarithm? I'm especially interested in attacks that use Pollard's rho algorithm. Are there any optimized ...
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### Does Coppersmith's method always finds non-trivial factor of integers of the form $n=a(2^k b+1)$ assuming $1 < a<2^k b +1$ and $b < n^{1/4-0.05}$?

Crossposted from mathoverflow. Got an argument and numeric evidence that pari's implementation of Coppersmith's method finds non trivial factor of integers of certain form under some assumptions very ...
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### Public key exponent coprime with totient proof

I read this question a while back (In RSA, why is it important choosing e so that it is coprime to φ(n)?). I was wondering whether there is a proof that shows that a public key exponent e that is ...
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### How does darkmail (DIME) work to hide email metadata?

While Email encryption can protect the content of an email, the metadata are still readable and can be used to gather important information about the sender and the receiver. There were several news ...
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### Implementation specific differences between RDRAND and RDSEED

I've read Intel's The Difference Between RDRAND and RDSEED and Intel Digital Random Number Generator (DRNG) Software Implementation Guide, but I have some open questions that are specific to usage in ...
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### Lattice attacks against Multilinear Maps [CLT13]

I am currently studying an article on a construction of Multilinear maps. There are some attacks on the scheme presented by the authors and I got stuck at the one in section 5.1. I will try to ...
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### How about a homomorphic integer sorting in a MPC context?

I want to implement the ATV-FHE scheme as described by Adriana López-Alt, Eran Tromer, Vinod Vaikuntanathan: On-the-Fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption ...
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### Brute force attack multiple stream cipher

Assume that a scheme used to secure a specific system $Π=(Gen,Enc,Dec)$ which is thought have indistinguishable multiple encryption in the presence of an eavesdropper. For any adversary $A$ that can ...
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### What followed findings of A. Lenstra et al. concerning shared factors of practical RSA moduli?

A. Lenstra et al. had a paper in 2012 "Ron was wrong, Whit is right", in which one reads: "What surprised us most is that many thousands of 1024-bit RSA moduli, including thousands that are contained ...
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### Elliptic Curve Blind Signature Implementation

I have seen this prior post: Elliptic Curve based blind signature implementation Currently I'm sizing up how difficult it would be to attain Elliptic Curve Blind signatures for an application I'm ...
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### Which precautions to protect against side-channel attacks on ARX ciphers?

In recent crypto there has been a trend to design ciphers using only the ARX set of instructions - i.e. additions (modulo $2^{32}$ or $2^{64}$), rotations (by a fixed constant) and XORs, examples ...
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### Is this a correct way of use symmetric encryption?

If I want to encrypt some block of text in AES, but at the time of decryption I don't have a way to check if the symmetric key is the correct one. So I: Generate a randomKey, and use that to encrypt ...
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### Is there a standard notation for a message concatenated with its signature?

I'm wondering what's the standard (or canonical) notation for "a message along with its signature", i.e. $$\mathit{Message}~\Vert~\sigma_k(\mathit{Message}) \text.$$ Here the duplicated ...
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### Which is/are the strongest known Fully Homomorphic Encryption scheme(s)?

As it is discussed here that the highest security any homomorphic encryption scheme is at most IND-CCA1, Is there any known fully homomorphic encryption scheme that achieves this security level? Out ...
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### How to test a FHE implementation?

I want to implement a FHE scheme based on NTRU, namely the scheme described here https://eprint.iacr.org/2014/039.pdf . How to test the security of my implementation ? Do I have to implement the ...
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### Unknown authenticated encryption mode

I'm running through a protocol specification (LoRaWAN, pdf), and I'm puzzled by the crypto. The data is encrypted and authenticated in the following way: a unique 128-bit key is used; the plaintext ...
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### Discrete Logarithm problem with inverse

Let $\mathbb G$ be a cyclic group of order $q$. The Discrete Logarithm Problem (DLP) is, given $g, g^x \in \mathbb G$, to compute $x \in \mathbb Z_q$. I'm interested to know if there is a known ...
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### Fast forwarding hash functions

We know that a good hash function is a one way/trapdoor function. Easy to calculate one way, harder to work out a previous state. I was wondering if anyone knew a good hashing system that allowed ...
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### Are there MD5 collisions for inputs of different length?

There are many examples of MD5 collisions (some of them can be found here Are there two known strings which have the same MD5 hash value?). But as far as I know two inputs should have the same length ...
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### Probabalistic Polynomial-time Algorithms & One-way functions

I've been reading up on probabilistic polynomial-time algorithms and one-way functions, and I was hoping to get some guidance on the topic. A textbook I'm reading states the following for one of the ...
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### Combining md5 collisions to create more collisions

Given X1 and X2 such that md5(X1) = md5(X2) and Y1 and Y2 such that md5(Y1) = md5(Y2), and knowing the following property of md5: if md5(a) = md5(b), md5(a|s) = md5(b|s) is there a way to find ...
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### ElGamal Signatures

I know various applications of RSA signatures. I wonder, is there any real-world applications of ElGamal signatures and encryption?
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### How does the ring settings of enigma change wiring tables?

EDIT: The model I'm trying to make is "Enigma 1". I learned initially about it from a book called "Code Book" and then looked at it in detail from its wikipedia page. The site wont allow me too add ...
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### How to use “proof of knowledge” to verify the result of modular exponentiation

I am thinking about regarding proof of knowledge as the inverse of result verification in server aided computing. For example, a user asks the server to compute $R=x^y \bmod z$. Normally, the user ...
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### Authenticate encrypted seed for KEM + AEAD hybrid cryptosystem

Say I want to encrypt something using RSA / KEM and an authenticated cipher. I encrypt using the following scheme: generate random seed z using ...
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### What is the impact of a server not fully verifying the data in the Client Finished packet of a TLS connection?

F5 BIG-IP devices suffer from a vulnerability in which not all bytes of the Finished packet in a TLS connection are validated. The sort-of technical description can be found here. F5 don't consider it ...
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### Small subgroup attack on Diffie-Hellman

I am trying to understand the small subgroup attack on Diffie-Hellman. I will present the attack and try to explain why it works. Let be a group $\mathbb{Z}_p^*$ where $p$ is a large prime, so the ...
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### Are there simpler FHE methods than Craig Gentry's original paper?

Craig Gentry's 2010 paper on FHE is very cool, and I'm planning on implementing a basic proof of concept FHE. I was wondering though, are there any simpler methods that have been discovered since ...
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I've found a way to complete a task which I'd solve with passwords or by sending keys over the wire (otherwise) by using RSA's homomorphic property. I'm restricted to RSA (any padding; for hardware ...
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### Worst case to average case in Ring LWE

I am currently trying to understand this Ring LWE article and I have a question. I don't understand how to apply Lemma 5.11 in order to get the worst case to average case reduction in Lemma 5.12, as ...
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### Generating random vector for Full Homomorphic Cryptography

The site below explains that part of doing homomorphic encryption, you need to generate a vector of random numbers that have the property that its dot product against a randomly generated bit vector ...
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### Can convergent encryption be turned into deterministic authenticated encryption with HMAC?

If you take a convergent encryption algorithm and replace the hash $H$ used to derive the key with HMAC-H, keyed with a secret key $k'$, does the resulting algorithm provide you with deterministic ...
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### Is modular Barrett reduction usable for Ed25519?

I currently try to implement Ed25519 following this draft. I have implemented every field operation except the reduction by the group order $q$ (in chapter 5). I looked for a reduction algorithm and ...
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### Words having weight near to minimum distance

I am studying the NP-Problem of the codes Syndrome Decoding. The formulation is show below. Input: a binary matrix $H$ of dimension $r \times n$ and a bit string $S$ of length $r$. Property: there ...
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### Example: pre-image resistance to second pre-image resistance

It is possible to convert a pre-image resistant function $f:\{0,1\}^{n}\rightarrow \{0,1\}^{n}$ to a second-preimage resistant function? I am thinking to use a pseudo-random generator and construct ...
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### Blinding to mask private key operations

Blinding is often used to mask private key operations when the underlying problem is integer factorization. For example, its used in both RSA and Rabin-Williams signature schemes. This presumes ...
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### Proving existence of an encryption scheme that has indistinghuishable multiple encryptions in the presence of an eavesdropper, but is not CPA-secure [duplicate]

I got stuck in trying to find a solution to the 3.7 exercise of the Katz-Lindell book. The exercise also assumes the existence of a pseudorandom function. The problem is that a multiple messages ...
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### What happens if no final subtraction is done in Montgomery multiplication?

I'm doing Montgomery arithmetic modulo $N = 2^{255}-19$ for the Curve25519, picking $R = 2^{256}$ for Montgomery. After multiplying two numbers $0 <= A,B < N$ in the Montgomery representation ...
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### Establishing encryption key using shared secret

I need to establish some security on a network of 8 bit microcontrollers. very limited RAM, CPU and packet sizes. I have zeroed in on a shared secret based scheme. Setting up shared secret is out of ...
I've been thinking about a geometric picture for El-Gamal. The idea is to understand the set $\{(my^{x},g^x) \mid x \in Z_p\}$ (the set of encryption of $m$ for fixed $g$ and $y$) by taking the ...