# All Questions

627 views

### Hardness of finding mutual discrete logarithms of small generators in $\mathbb{Z}_p$

Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at ...
917 views

### Signal vs Telegram in terms of protocols?

Some time ago, the question was asked in chat, why MTProto (Telegram's protocol) is supposedly worse than Axolotl (Signal's protocol) as both protocols have been the inventions of their respective ...
150 views

### AMD and RDRAND instruction

The latest AMD programmer manuals, dated June 2015, include the RDRAND instruction in the instruction set. For completeness, it lacks ...
621 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 ...
246 views

### How were shift amount constants in MD5 found?

The md5 specification gives a series of 4 rounds to execute over a 16-word block. Each round has a repeating sequence of 4 shift amounts (s in ...
927 views

### Elliptic curve cryptography related key attacks

This question is an extension of Families of public/private keys in elliptic curve cryptography As described above, bitcoin "type 2" deterministic wallets use a root private/public key pair, where ...
67 views

### Default algorithm for scalar multiplication of elliptic curve points by the MIRACL Library

What is the default algorithm used by the MIRACL-Library [1] for elliptic curve cryptography systems to perform scalar-point multiplication with curves of Weierstrass form satisfying the equation : ...
52 views

### K friedman - two texts explanation

I have a question, I read the k friedman test to determine the period of a vigenere cipher text, and I understand something like this: Friedman's K test tries to find out what period of the cipher by ...
129 views

### Santa Claus' secret permutation

This December, $N$ friends play secret santa: they select a random permutation $\sigma$ of $N$ (without fixed point). For Santa Claus, everyone has to bring a gift to the next person in the ...
112 views

### Attacks on elliptic-curve based cryptosystems through solving the Decisional Diffie-Hellman Problem with the Weil Pairing

Are there any examples of practical attacks on cryptosystems set over elliptic curves which utilize the easiness of DDH for certain choices of curves $E(\textbf{F}_q)$, and as such their lack of ...
177 views

### Verbatim of early work on public-key cryptography?

In late 1997, the history of public-key cryptography was turned around with the announcement by the CESG (April 2000 archive) that public-key cryptography was theorized in a 1970 note [1] by James ...
423 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 ...
237 views

### Efficient decoding of irreducible binary Goppa codes and the role of matrix P in McEliece cryptosystem

If we assume that the support for an irreducible binary Goppa code $\gamma_1, ..., \gamma_n$ is publicly known, when is it possible to efficiently decode the code? I know it's possible if one knows ...
53 views

### Performance of ECDSA, ECKCDSA and ECGDSA

It is proven that ECDSA algorithms are faster in key and signature generation compared to RSA. In addition, the signatures are much shorter. However, I would like to know the performance difference ...
110 views

### Efficient way to confirm identity

I am working on a multiplayer game. I have a central server which handles all data transmission and coordinates all games. Clients which involved in a single session send requests to do actions to ...
182 views

### Is there any practical attack to create a printable chosen prefix MD5 collision?

I would like to create two ASCII text messages with the same MD5. Is this possible? If not, is there a similar but less strict attack that could work? Or to rephrase my last question: what are the ...
175 views

### Parallel Pollard's Rho: Number of distinguished points

When using the parallel version of Pollard's Rho algorithm for discrete logs, each processor performs its own random walk to find distinguished points, and reports the starting point and the ...
172 views

### Can a commutative block cipher be indistinguishable from a random one, assuming a random permutation of keyspace?

Define a commutative block cipher with keyspace the finite set $K$, and message space the finite set $S$, to be an application \begin{align} E:K\times S&\mapsto S\\ (k,x)&\mapsto ...
164 views

### Has the distributed project “Number Fields @ Home” project benefited cryptography in any meaningful way?

Is there any new understanding, property, or knowledge that has come from the Number Fields @Home distributed computing project? Has any outcome advanced the study of cryptography, or altered ...
24 views

### OTR AKE protocol implementations security

While looking at the different versions of OTR protocol I discovered a strange thing: there is no trace of the patch for the weaknesses that were noted in “Finite-State Security Analysis of OTR ...
59 views

### Rule 30 Cellular Automaton for Cryptography

Steven Wolfram of Mathematica uses a pseudorandom number generator based on Rule 30 for applications in Mathematica software but I would like to know if a pseudorandom generator based on Rule 30 is ...
49 views

### Proof that perfect privacy implies that the number of keys is at least the number of messages

I was reading a proof to the statement: Perfect privacy implies that $|K| = |M|$ where I am pretty sure that $K$ is the set of keys and $M$ is the set of messages. The proof is the following, ...
41 views

### What is the correct definition of the blowfish F-function?

The Blowfish cipher uses a so called F-function which uses S-Boxes (S[i], i=0,1,2,3) to ...
54 views

### Additively homomorphic cryptosystem with non-interactive zero-knowledge proof of non-negativity

I need a cryptosystem that is additively homomorphic. Paillier preferably, but not neccessarily. Also, for every ciphertext the private key holder must be able to prove non-interactively that the ...
62 views

### Comparison Vigènere vs. Monoalphabetic cipher

I have a question for a class of secure communication, but I have no idea about how to proceed in order to answer it. I'll be very grateful to whom replies to me. Assuming that brute force attack ...
88 views

### Big block cipher as memory-hard function

I'm wondering, if something like block cipher with big block size is a good memory-hard function? All memory-hard key derivation functions I've seen look more complex than that, which made me ...
47 views

### Reusing same source for single-source randomness extractor

Let $ext$ be a single-source randomness extractor which takes a $d$-bit seed and a $n$-bit source as input and produces a $m$-bit output. Suppose we have a source $X$ with min-entropy $k$. Is it ...
69 views

### Is there a standardized tree hash?

SHA-1, SHA-2, and the standardized version of SHA-3 are all sequential. This is impractical for hashing very large files distributed across machines. Any sequential hash can be straightforwardly ...
37 views

### Is it possible and safe to use SAKKE for signing/verification, rather than for encryption?

Is it safe to use the Sakai–Kasahara key encryption algorithm (SAKKE) for signing/verification, rather than for encryption? (Example at bitbucket.org) In particular, I want many Bobs to be able to ...
46 views

### Can a one-way accumulator be used in place of a digital signature?

Could a one-way accumulator be used in a manner to replace a digital signature? Can it provide a way to: verify that the data has not been tampered with, and verify that the message is in fact ...
138 views

### How to break a columnar transposition cipher?

I'm currently studying for a cryptography exam. I've been given ciphertext that has been encrypted by a columnar transposition cipher. I've been given no shift key length or key word, the only thing I ...
60 views

### Elliptic curve point addition with $Z_1 = Z_2 = 1$

Elliptic curve point addition and point doubling operations using Projective and Jacobian coordinates require fewer field multiplication operations when considering $Z$ coordinates of input points ...
30 views

### Safe generation of $k$ points on a curve such that the mutual discrete logs are hard?

I have a multiplicative group $G$ of prime order $p$ implemented using a twisted Edwards curve (similar to Ed25519). I want to compute a set of $k$ distinct points $P_1,...,P_k$ that generate $G$, ...
208 views

### What is the original SKID3 protocol?

While searching for a mutual authentication protocol I often stumbled upon SKID3. However I encountered different variations of it. The basic structure is the following: (1) A --> B: rA (2) B --> ...
106 views

### Homogenous and heterogeneous Unbalanced Feistel Networks

Unbalanced Feistel networks can be homogenous (F-function identical in each round), or they can be heterogeneous (F-function not always identical in each round). The advantage of heterogeneous UFNs ...
202 views

### Given a 'good' basis for a lattice, how can we solve the CVP?

I'm doing a little bit of reading about lattices. I read that if we can find a 'short' basis for our given lattice, we can solve CVP and SVP very efficiently. However, the paper didn't describe an ...
193 views

### How can I create an RSA modulus for which no one knows the factors?

It's easy to create an RSA modulus where almost no one knows the factors: for example, I can generate two 1024-bit primes $p$ and $q$ and set $n=pq$. If I publish $n$, I will be the only person in ...
295 views

### LT codes with Homomorphic hashing

I have been working on a project implementing LT codes with Homomorphic hashing (inspired from http://blog.notdot.net/2012/08/Damn-Cool-Algorithms-Homomorphic-Hashing and ...
310 views

### Odds of false error detection in a randomness test using the chi-squared test?

Common Criteria classifies the requirements for true Random Number Generators, and specifies how these should be tested against failures (these can occur accidentally, or following deliberate attack, ...
73 views

### How to prove that a function F isn't a pseudo random function

Let $F$ be a length-preserving pseudorandom function. For the following constructions of a keyed function $F' : \{0, 1\}^n \times \{0, 1\}^{n−1} \to \{0, 1\}^{2n}$, state whether $F'$ is a ...
110 views

### Finding the subgroup in isogeny-based cryptography

Isogeny-based cryptography is one of the newest post-quantum cryptography. Hardness of this system is based on finding isogeny between two elliptic curves. Also this is theorem: Elliptic curves ...
30 views

### An MPC protocol from Elgamal is a good solution a homomorphic multiplication?

I want to compute a multiplication between many secret values and then distribute the result to everyone involved. For this, I thought about an MPC protocol built from Threshold Homomorphic Elgamal. ...
62 views

### Zero-knowledge proof for the product of additive Paillier ciphers

Suppose that Alice received the cipher values: $E(x_1), E(x_2), ..., E(x_n)$ that are encrypted using Paillier cryptosystem by $n$ entities with Bob's public key. Alice computes $E(\sum x_i)$ from ...
60 views

### How can I implement decryption for NTRU homomorphic encryption scheme?

I have come across this paper On-the-fly multiparty computation via on-the-cloud Multikey from Fully Homomorphic Encryption by Lopez-Alt et al., where authors describe a NTRU-based homomorphic ...
23 views

### Understanding the definition of HGD

On the section 4.2, page 10, of the paper Order-Preserving Symmetric Encryption, the authors define two subroutines: the first one is called $HGD$ and the second one is $GetCoins$. I have doubts ...
38 views

### Security parameter p =O(n)

In many homomorphic encryption scheme, a security parameter is calculated as p =O(n). How to use the complexity order as values? Is there any specific method with an appropriate example?
55 views

### Why is AES-SIV not used, but AESKW, AKW1?

I'm trying to investigate different key wrapping algorithms for my implementation. I've noticed that AES-SIV is very rarely implemented by most of open source libraries. Most of them implements key ...
50 views

### 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 ...