# All Questions

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### 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 ...
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### 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 ...
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400 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 ...
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### The aftermath and considerations of the new record of 30750-Bit Binary Field Discrete Logarithm - 2020

Granger et al. recently published a paper about breaking a record for discrete logarithm on the Binary field Computation of a 30 750-Bit Binary Field Discrete Logarithm, Robert Granger and Thorsten ...
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### 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 ...
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### 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 ...
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322 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 ...
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### Has Telegram security been significantly improved with MTProto 2.0?

Telegram messenger's original encryption scheme, MTProto 1.0, has been shunned by most cryptographers for a number of reasons, like being vulnerable to IND-CCA attack; being unorthodox in general, ...
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### 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 ...
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### 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 ...
520 views

### The backdoor of Telegram on Diffie-Hellman Key Exchange and possibly other examples?

Diffie-Hellman Key-Exchange (DHKE) should be used carefully during the end-to-end encryption. A man-in-the-middle (MITM) attack is possible. Standard DHKE The simple protocol on the multiplicative ...
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262 views

### RSA key such that pi deciphers to your name per RSA-OAEP

Can you efficiently construct an RSA public/private key pair with $8k$-bit public modulus such that $C=\left\lfloor\pi\,2^{8k-2}\right\rfloor$ deciphers per RSA-OAEP to your name as a bytestring in ...
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### How Significant is the New Quasi-Polynomial-Time Attack on Fixed Characteristic Discrete Logarithms?

There is a new paper by Kleinjung and Wesolowski on eprint that claims and proves a new attack on the discrete logarithm problem in finite fixed characteristic fields in quasi-polynomial time. ...
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### 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 ...
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### 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 ...
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### Requirements for security against multi-target attacks, for McEliece and other code-based cryptosystems?

This question is potentially relevant to NIST post-quantum cryptography standards, involving code-based cryptosystems such as McEliece, BIKE and HQC. For these cryptosystems, it seems that an attacker ...
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### RSA factorization with special primes

Suppose that primes for RSA modulus are generated using formula: $P_i(x,y) = \operatorname{next\_prime}(x^{z_i}+y^{z_i}) = x^{z_i}+y^{z_i}+d_i$ where $x,y$ are unknown random numbers with size 128 ...
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### 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 ...
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### Do CCM and EAX provide key commitment?

In an interesting paper called "Partitioning Oracle Attacks" by Julia Len, Paul Grubbs & Thomas Ristenpart an attack is presented on 1.5 pass AEAD schemes that utilize GMAC (GCM, AES-GCM,...
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### Why does the Signal protocol use AES/CBC instead of AES/GCM?

AES/GCM has obviously proved itself to be better than AES/CBC. Unless the key is re-used with the same initialization vector (see disadvantages of GCM). More information on its advantages against CBC ...
287 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 ...
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213 views

### How to build a security model

What are the minimal components to build a security model proof for a protocol? This question might seem trivial, but having read many papers-- from the IEEE, ACM, etc., that talk about a KMP-- I ...
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94 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 ...
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### 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 (...
594 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 the ...
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### 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 Feistel ...
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### What is the origin of the phrase "Don't roll your own crypto"?

The phrase is well-known and widely used, it is often attributed to Bruce Schneier and is indeed relevant to his Schneier's Law. However, I wasn't able to find this specific wording among Schneier's ...
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### 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. ...
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360 views

### Share Conversion between Different Finite Fields

Let us have any linear secret sharing scheme (LSSS) that works on some field $Z_{p}$, where p is some prime or a power of a prime e.g., Shamir Secret Sharing, Additive secret Sharing. The problem at ...
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### 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 ...
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### 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 ...
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85 views

### How inefficient are current Indistinguishability Obfuscation (IO) candidates?

Since last year, IO finally seems to be within our reach. Several papers (https://eprint.iacr.org/2020/1003, https://eprint.iacr.org/2020/1024 and https://eprint.iacr.org/2020/1042) proved the ...
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### 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" - ...
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### 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 a quantum computer is only one qubit short of what is ...
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959 views

### Key size, performance, and security tradeoffs for AES GCM / CCM

AES can be used with 128, 192 or 256 bit keys and each one appears to have a performance vs security trade-off (What is the effect of the different AES key lengths?, What are the practical differences ...
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### 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 ...
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### 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 $g$ has even or odd order. In other words $\textrm{ord}(g) \bmod 2$ can be computed easily. In some cases where the ...
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### 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 ...
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### Are there conventions for signing JSON as a tree, to allow proofs of signed subtrees?

Given some JSON with a chosen encoding, you can obviously cryptographically-sign the whole thing as a binary blob. However, it might be useful if the logical structure of the JSON-compatible object ...
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### Replacing signer with simulator

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