# All Questions

2,089 questions
1k 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 ...
478 views

### Memory-hard password hash in practice?

Dan Boneh, Henry Corrigan-Gibbs, and Stuart Schechter have proposed Balloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks (in proceedings of AsiaCrypt 2016). ...
199 views

### Name of an archaic type of RSA padding (0BBBBBBB…)

In some legacy code, I encountered RSA signature padding in the following format (hexadecimal): 0B BB BB BB BB BB BB ... BB BB <hash> Is there a name for ...
160 views

### Fewest qubits required for the discrete logarithm problem and integer factorization

According to a paper from 2002, the most efficient circuit to factor an $n$-bit integer requires $2n+3$ qubits and $O(n^{3}\lg(n))$ elementary quantum gates, assuming ideal qubits. Later on, according ...
237 views

### Finding $x$ such that $g^x\bmod p<p/k$?

In a Schnorr group as used for DSA, of prime modulus $p$, prime order $q$, generator $g$ (with $p/g$ small), how can we efficiently exhibit an $x$ with $0<x<q$ such that $g^x\bmod p<p/k$, for ...
1k views

### Consequences of AES without any one of its operations

Suppose AES-$128$. There are $4$ operations in AES's encryption, they are SubByte, Shift Row, MixColumns and AddRoundKey. Question: If I remove one of the following opearations, what will happen to ...
444 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 ...
143 views

### Proving multiple products “in the exponent”

I'm trying to come up with a small-sized (non-interactive) proof for a Diffie-Hellman-like statement. I'll start by giving an example. The prover has $g^a, g^b, g^c, g^{ac}, g^{ab}, g^{bc}, g^{abc}$. ...
311 views

### Potential Flaws With Lattice Based Cryptography?

From researching post-quantum cryptographic schemes it seems hash-based and lattice-based algorithms are the most promising (MQ-based seem to be covered by patents and have more potential unknowns ...
123 views

### How exactly does ASKE (Alpha Secure Key Establishment) in Zigbee work?

I am working on Zigbee security. For key establishment, some approaches are given in Zigbee. Some of them are: ASKE (Alpha Secure Key Establishment), ASAC (Alpha Secure Access Control), and SKKE (...
561 views

### Are there attacks against broken RSA signature pad checking with $e = 65537$?

Let's say that an RSA implementation of PKCS #1 signatures fails to validate that the 00 01 FF FF FF ... FF 00 portion of the decrypted signature is exactly as long ...
1k views

### Cracking a PRNG by observing ranks within groups of its output

Suppose that I am generating random numbers with Python's random module, so that there is a known random number generator (Mersenne Twister in this case). I've ...
378 views

### 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 ...
528 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 ...
124 views

### Space complexity of quantum collision search?

Is there a known way to reduce the space complexity of quantum collision search (PDF) beyond what is offered by the built-in time-space tradeoff, while keeping the time complexity significantly below ...
277 views

120 views

### Replacing signer with simulator

Assume we can prove security of digital signature scheme against key-only (no message) attacks. Now we want to prove security against adaptive chosen message attack. We use random oracle model. The ...
191 views

### 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 ...
82 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 $G$, ...
223 views

### Unique GCM/CCM initial counters without recipient side message counters

I am implementing the encryption layer for a communication protocol. The bulk encryption method used is either AES-CCM or AES-GCM. Due to implementation details, encryption of packets is usually, but ...
64 views

### Differences between “NewHope” and “NewHope-simple”

The well-known paper described a key exchange (KE) scheme named "NewHope" on USENIX 2016. The authors then proposed "NewHope-Simple" - a PKE/KEM scheme. They also submitted "NewHope for NIST" - ...
65 views

### Offline Group Key Agreement - Cross Device Syncing

I have a specific use case I am interested in. I have spent the better part of the night reading research papers. I am beginning to believe what I want is not possible so I wanted to confirm here. ...
67 views

### Distributed generation of random integers with prescribed sum

While reading this document I came across the following problem. Assume you have $n$ clients. The clients need to generate random integers in $\mathbb{Z}_p$, say $T_i$ for $i \in \{1, \ldots, n\}$, ...
105 views

### How to build a security model

Probably this question could appear trivial, but when you are building a security protocol (i.e. you can read a lot of papers on IEEE, ACM and so on, that talk about a KMP), most of authors build the ...
145 views

### Relation between Claw-free permutation and Trapdoor

Can someone explain the two definitions in relation to each other? Is a claw-free permutation a permutation without a trapdoor? For your convenience, here's the definition of a "claw-free ...
164 views

### What are the theoretical memory requirements for these factoring algotihms?

Given an $n$ bit integer quadratic sieve takes $L(\frac12,1+o(1))$ time and number field sieve takes $L(\frac13,1.922)$ time where $L$ notation is given in https://en.wikipedia.org/wiki/L-notation. ...
400 views

### Tiny Firmware Authentication

I am developing a product based on the NXP LPC11C24 microcontroller. It will communicate with PC software to perform its function. I am attempting to build in secure firmware update functionality. The ...
170 views

### Can an analog of ChaCha with 64-bit words be defined, and would it be secure?

Blake2b has a lightning fast compression function with more-than-overkill security even against quantum attacks. It seems to be based on ChaCha, but with 64-bit words and different rotation constants....
257 views

### What is the fastest modular reduction algorithm available?

I have been browsing for the fastest and most efficient modular reduction algorithms and came across quite a few. But the one in A Fast Modular Reduction Method (2014) by Zhengjun Cao, Ruizhong Wei ...
301 views

### What level of security is provided when a Feistel Cipher is used as a round function of another Feistel Cipher?

Recently, I was reading: Are there any specific requirements for the function F in a Feistel cipher?, and the answer posted mentions a Feistel Cipher named Turtle, which uses a four-round Feistal ...
52 views

### Time-memory tradeoffs in Shor's algorithm

Can a quantum computer with insufficient qubits to factor an integer of a given size make any progress in factoring it? For example, what if quantum computer is only one qubit short of what is ...
52 views

### Does there exist trapdoor permutation from lattices?

It seems that the lattice functions are either surjective (SIS) or injective (LWE), due to the error that is basically intended to destroy the structure and provide security. I was wondering whether ...
Given an element $g$ in a cyclic group $G$ of known order $m$ its easy to test if $m$ has even or odd order. In other words $\textrm{ord}(g) \pmod 2$ can be computed easily. In some cases where the ...
### on CPA & KPA security of $\boxplus$-Feistel
I am interested to identify the effect of replacing $\oplus$ with $\boxplus$ on basic balanced Feistel structure over $r$-rounds. Given; $F_\boxplus[L,R]= [S,T] = [R,L \boxplus f(R)]$ where $f$ is ...