All Questions

25
votes
0answers
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 ...
14
votes
0answers
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). ...
13
votes
0answers
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 ...
12
votes
0answers
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 ...
11
votes
0answers
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 ...
11
votes
0answers
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 ...
11
votes
0answers
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 ...
10
votes
0answers
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 $g^a, g^b, g^c, g^{ac}, g^{ab}, g^{bc}, g^{abc}$. ...
10
votes
0answers
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 ...
10
votes
0answers
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 (...
10
votes
0answers
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 ...
10
votes
0answers
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 ...
10
votes
0answers
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 ...
10
votes
0answers
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 ...
10
votes
0answers
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 ...
10
votes
0answers
277 views

What might be assumed about a PRF if the key has been chosen?

The defining feature of a PRF $f:\{0,1\}^k\times\{0,1\}^s\mapsto\{0,1\}^*$ is that, if the first parameter is selected at random, it should be indistinguishable from a function $g:\{0,1\}^s\mapsto\{0,...
9
votes
0answers
184 views

Do trinomials weaken the Alternating Step Generator?

The Alternating Step Generator was proposed by Christoph G. Günther: Alternating step generators controlled by de Bruijn sequences, in proceedings of Eurocrypt 1987. It's perhaps the conceptually ...
9
votes
0answers
192 views

What was the BassOmatic cipher, and what made it so weak?

According to Wikipedia, this homebrew cipher was originally used in PGP, before Phil Zimmermann replaced it with IDEA. Supposedly, insecurities in the algorithm were pointed out to him, leading to ...
9
votes
0answers
448 views

Why does Telegram roll its own crypto?

Telegram recently updated its symmetric-key encryption scheme MTProto, which seems to fix some known vulnerabilities. Nevertheless, I still do not understand why they roll their own crypto. What ...
9
votes
0answers
57 views

Decision R-LWE parameters for spherical error with worst-case hardness

In Peikert et al.'s most recent work (STOC 2017) a direct reduction of worst-case lattice problems to decision R-LWE is achieved for $\alpha q \ge 2 \cdot \omega(1)$ (Theorem 6.2), where $\alpha q$ is ...
9
votes
0answers
527 views

Yaos Millionaire Problem: Why distance >= 2?

I'm currently reading about Yao' Millionaire Problem: http://research.cs.wisc.edu/areas/sec/yao1982-ocr.pdf Alice and Bob want to know which of them is richer. Let $j \in \{1, \cdots 10\}$ be Bobs ...
8
votes
0answers
148 views

Bleichenbacher RSA1024 signature forgery, closed-form solution

Hal Finney's writeup (Bleichenbacher's RSA signature forgery based on implementation error) shows a formula for RSA3072. I tried to replicate the attack for RSA1024 and failed, since the first term of ...
8
votes
0answers
269 views

Security proof in (Ciphertext-Policy) Attribute-Based Encryption

I am having hard time understanding the security proof in Attribute-Based Encryption, especially in Ciphertext-Policy Attribute-Based Encryption. To do reduction in CP-ABE scheme, how do I check that ...
8
votes
0answers
109 views

Software timing attack using Kocher method

What's the minimum number of random sample points needed in Kocher's timing attack, so that we can determine enough valid measurements of $A_{i,r}$ and $D_{i,r}$? I'm working from this paper: Volker ...
8
votes
0answers
872 views

CPA-security of a pseudorandom permutation encryption scheme

Let $F$ be a pseudorandom permutation, and define a fixed-length encryption scheme $(Gen, Enc, Dec)$ as follows: on input $m \in$ $\{0,1\}^{n/2}$ and key $k \in \{0,1\}^n$, algorithm $Enc$ chooses ...
8
votes
0answers
864 views

Rationale for use of right-shift (rather than rotate) in SHA-2?

The SHA-2 hashes in FIPS 180 define $\Sigma$ and $\sigma$ bijections of words, with $\Sigma$ used in the round function, and $\sigma$ used in preparing 48 words of message schedule from 16 words of a ...
8
votes
0answers
297 views

Is the key schedule of Serpent a circle?

The creation of the prekeys for Serpent works by XORing some previous values with a counter and a fixed value. Every word is 32 bits big and 4 words form a round key (after applying a S-Box, but this ...
8
votes
0answers
271 views

What are the current limitations (and capabilities) of Functional Encryption used for access control?

I'm trying to make my way in Functional Encryption used for access control. I read a lot of papers such as "How to Run Turing Machines on Encrypted Data", "Functional Encryption: New Perspectives and ...
8
votes
0answers
463 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 http://blog.notdot.net/2012/...
7
votes
0answers
121 views

GCM with reversed poly

These slides talk about how GCM can be sped up if one uses $x^{128}+x^{127}+x^{126}+x^{121}+1$ as the reduction polynomial instead of $x^{128}+x^7+x^2+x^1+1$. When one is doing that one needs to ...
7
votes
0answers
144 views

Adding bit constants to the key schedule to reduce rounds?

Bit constants are often added to the key schedule to reduce slide attacks. I have reviewed David Wagner's work, where he showed that the increased rounds in a Feistel network do not help if you have ...
7
votes
0answers
187 views

Index calculus over elliptic curve over function field

According to my understanding there are some pretty solid seeming roadblocks to carrying out an index calculus on an elliptic curve over a finite field. The general strategy is to take points over $E(\...
7
votes
0answers
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 ...
7
votes
0answers
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 ...
7
votes
0answers
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 $G$, ...
7
votes
0answers
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 ...
6
votes
0answers
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" - ...
6
votes
0answers
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. ...
6
votes
0answers
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 $i \in \{1, \ldots, n\}$, ...
6
votes
0answers
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 ...
6
votes
0answers
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 ...
6
votes
0answers
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. ...
6
votes
0answers
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 ...
6
votes
0answers
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....
6
votes
0answers
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 ...
6
votes
0answers
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 ...
5
votes
0answers
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 ...
5
votes
0answers
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 ...
5
votes
0answers
55 views

Parity of the order of a element

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 ...
5
votes
0answers
120 views

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 ...

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