Questions tagged [rsa]

An asymmetric (e.g. public-key) cryptosystem, based on modular exponentiation with big exponents and modulus. RSA can be used both for signature and encryption with proper paddings.

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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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229 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 ...
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243 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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171 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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533 views

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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651 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 ...
8
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303 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 ...
5
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52 views

Finding the period of a function with a single output qubit - impact on RSA

In this paper,May and Schlieper claim that one can find the period of a function $f()$ by embedding $h \circ f = h(f(x))$ for input $x$. This would have the immediate consequence of reducing the ...
5
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220 views

Is there an efficient way to verify the union of two RSA accumulators?

More specifically, say we have one RSA accumulator $A_{S_1}$ accumulating set $S_1$ and another RSA accumulator $A_{S_2}$ accumulating set $S_2$. Does there exist a sublinear method to securely verify ...
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3answers
233 views

Decrypting small integers under RSA

Let $(n,e)$ be an RSA public key. Suppose $c = m^e \pmod n$, where $c>1$ is a very small integer. For concreteness, say $c=2$ or $c=4$. Is it hard to find $m$ under the RSA assumption (or any of ...
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The security of blind RSA signatures with modular exponentiation as padding

It is known that (blind) RSA signature implementations should apply some sort of padding to messages before signing or blinding them. Does blind RSA signature with modular exponentiation as a padding ...
4
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100 views

Why do one-way accumulators use rigid integers as the modulus?

In the paper that introduced one-way accumulators, the author's justify their use of rigid integers as the modulus with the following: The advantage of using a rigid integer $n = pq$ is that the ...
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Computing cost for a trillionaire to compute GNFS in RFC 3766

RFC 3766, Section 4.1 discusses picking $n$ to achieve some target cost for employing the GNFS, i.e., $T$ is known and $N$ is unknown in the below equation: $$T = \kappa \cdot \exp{\left(c \cdot (\ln{...
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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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160 views

Is MITM possible after key exchange phase done successfully in RSA?

Is MITM attack theoretically possible after public/private key pair exchange is done successfully. Say Alice and Bob have genuine public keys of each other. Is MITM possible further during ...
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50 views

Multi-users RSA problem

Rivest and Kalisky's RSA problem considers various notions on security of the RSA One-Way Trapdoor Permutation. They do it only from the perspective of a single user. What's the state of the art in ...
3
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1answer
38 views

Update non-member witness in RSA accumulator

According to study of "Universal Accumulators with Efficient Nonmembership Proofs", I don't understand exactly how to update non-member witness in construction 4.2. In the addition step, I understood ...
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95 views

How do I recover RSA primes from the modulus and the coefficient?

The RSA private key contains 2 primes (of about 4096 bits each), and I only know their product (called modulus) and the modular inverse (called coefficient). How do I recover the RSA primes from the ...
3
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70 views

RSA calculate $d$ using Chinese Remainder Theorem with $d_p$, $d_q$ and $e$

Suppose for a RSA system I have the following variables given: modulus $n$, expononent $e$, $d_p$ and $d_q$Where, $d_p = d\bmod(p-1)$ and $d_q = d\bmod(q-1)$, Is it possible to find the private ...
3
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1answer
140 views

RSA Accumulators with auxiliary information or known trapdoor information

In "Universal Accumulators with Efficient Nonmembership Proofs" by Jiangtao Li1, Ninghui Li2, and Rui Xue3 section "How to compute witness with the auxiliary information" the authors write: "The ...
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97 views

RSALib prime generation - derive number of primes

I'm working on factorizing a ~450 bit key that I know has been generated with RSALib and thus is vulnerable to ROCA. Now reading the original paper, I can see that the primes are generated in the ...
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531 views

How to determine the correct padding to use for rsa signing?

Before today I didn't know the difference between RSA padding for encryption and for signing, I think this answer describes it pretty succinctly, however, I don't know if there is an optimal padding ...
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666 views

RSASSA-PSS p1v2.1 (rfc 4056) signing

I'm signing mails with the RSASSA-PSS (p1v2.1) certificate. When I click Details, it shows "Signature Algorithm: RSASSA-PSS". openssl x509 -text shows ...
3
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410 views

RSA - factorizing $N$ to get $p$ and $q$

I need to decrypt a message encrypted using RSA. I only know the public keys $n$ and $e$. I need to get the private key $p$ and $q$ in order to get the decryption exponent $d$. Now to do so, I know ...
3
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171 views

IND-CCA1 RSA padding?

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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179 views

How much plainext could be known without reducting security of RSA?

It is known, for example, that exposing 50% of most significant bits of RSA private exponent does not provide security risk (when a small public exponent it used). So how to qualify security ...
2
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1answer
75 views

Hard-core bits from RSA assumption

I am trying to understand better the hard-core bit property from the RSA assumption. The paper by Hastad and Naslund shows that every single bit is hard-core. By the result itself, two or more bits ...
2
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95 views

Fixed point in RSA encryption

Some papers count the number of the fixed points in the RSA encryption algorithm. They're a minimum of 9 and the real number depends on the smoothness of primes $p$ and $q$. It very unlikely that a ...
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52 views

One-Way Trapdoor Permutation more secure than RSA at same width?

The classical One-Way Trapdoor Permutation is RSA. The permutation that it implements on a set of $n$ elements¹ is invertible by an adversary knowing only the public key with work $w$ conjecturally² ...
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41 views

How to extract message in Bleichenbacher 1998 attack

Im trying to understand the Bleichenbacher 1998 attack, but i am having trouble wrapping my head around the bounds-part. So as far as i understand, the idea is the following: We have a ciphertext $...
2
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1answer
86 views

Short padding + known prefix RSA attack

Suppose I have a message in the form of: $m = \text{prefix} \mathbin\| \text{secret} \mathbin\| \text{padding}$ We have: $e=3$ $n$ $n_\text{padding}$ (length of the random padding, <$1/4$ of $m$)...
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242 views

WebCrypto SubtleCrypto RSA sign/verify AND encrypt/decrypt?

I have a project where I'd like to use public-key cryptography in both typical sign/verify situations and encrypt/decrypt situations. For example, I'd like to create a self-signed X.509 certificate ...
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25 views

What are some examples of out of bound channels that work over the Internet in practice?

If I want to verify a public key (be it RSA, PGP, etc.) with another client over the Internet only, what are some viable out-of-bound channels for verification? Which channels have been used in ...
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72 views

Recursive RSA encryption

I have a ciphertext $C$ encrypted with public key $pub_C$, which contains ciphertext $B$ and $pub_B$, $$C= E_{pub_C}(B\mathbin\|pub_B)$$ Ciphertext $B$ is encrypted with $pub_B$ and contains $pub_A$ ...
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43 views

RSA: Blinding versus fixed-time computation

For RSA, what is the standard solution against timing attacks? I know about RSA blinding as one solution. Another solution is to always compute both the squared value and square-and-multiply values, ...
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65 views

Concept for a RSA “repeater”. Is it sensible?

I have been using RSA signed/encrypted mailing a lot recently. Naturally, I wanted to use RSA mailing also on my phone, not only on my computer. However, I feel uneasy having my private key on my ...
2
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1answer
142 views

Using YubiKey to store a PIN-protected secret for disk encryption

I want to store a secret on YubiKey and use it for disk encryption. It's crucial that it be PIN protected. There are a limited number of PIN tries, and after three attempts the YubiKey would be ...
2
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0answers
130 views

What are the known attacks on $\phi$-hiding assumption? How to chose its parameters?

$\phi$-hiding assumption states the following. Sample 2 random primes $e_0$ and $e_1$ in the range $[5, 2^{\lambda/4}]$. Sample $N = pq$ of length $\lambda$ ($p$ and $q$ are large primes of length $0....
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192 views

Sharing RSA private key between SSH and SSL services. How bad is it?

An appliance uses a curious way of obtaining ssh-rsa host keys: There is a single configuration option "management certificate" that sets RSA private keys both for HTTPS and SSH management. ...
2
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534 views

RSA most significant bit oracle attack

I have been reading up on RSA attacks and came across a problem that could be called a most-significant-bit (MSB) oracle attack. For the sake of clarity, let's define RSA primes $(p, q)$, private key ...
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223 views

Chinese Remainder Theorem and Elgamal

I am studying an encryption scheme which is Elgamal-like where I think CRT can help optimise the encryption and decryption but I am not sure if I am applying CRT the correct way. I have a cyclic ...
2
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0answers
28 views

What are SNFS-safe limits for an RSA moduli optimized for simple modular reduction?

I consider $n$-bit RSA moduli $N$ having high-order bits starting by with $k$ bits at 1, then $k$ bits at 0, then $m-2k$ bits at ...
2
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279 views

Where shoul I store private/public keys and how should I share it?

I'm new in terms of encryption and I have to encrypt the data between two Java Spring applications, one have serves as MVC framework and other as Web Service, I'm implementing an asymmetric encryption ...
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66 views

Asymmetric encryption property required in an authentication protocol

We want to choose an asymmetric encryption scheme for use as follows: A device holds its private key, with the corresponding public key known and trusted by all. The device also holds a small $b$-bit ...
2
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0answers
174 views

What kind of RSA padding mode is it?

1: I have a HTTPS server and I added hooks in RSA decryption procedure to dump error RSA input(client key exchange). 2: I get some RSA input that I couldn't check padding successfully(It's usual) and ...
2
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0answers
333 views

RSA signatures that allow hash to move around in block

I'm looking at a broken RSA signature padding implementation in a real device. It's a very-badly implemented version of PKCS #1-like encoding, but before PKCS added the DER-encoded hash identifier. ...
2
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0answers
59 views

Does secure LWE implementation leak bit information?

We know RSA leaks one bit about the factors and improper yet secure implementations of Discrete Logarithm leak one bit about the discrete logarithm. Does LWE leak any information?
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186 views

Textbook RSA: Public key used to decrypt ciphertext and checked against known plaintext

In textbook RSA with no padding schemes, is it possible to forge a ciphertext that decrypts to a known plaintext when the ciphertext is encrypted using the private key and decrypted with the public ...
2
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118 views

RSA - find d,e with restrictions

For academic purposes, assuming $n, p, q$ with $n\approx 2^{4096}$ and $p,q\approx 2^{2048}$. I need to find ($e,d$) such that: $e$ is smaller than $2^{64}$ $d\approx 2^{4096}$ and will have as ...
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0answers
143 views

Estonian e-voting, vote verification system

I believe I do understand the basics of how the Estonian e-voting system works, but I'm stuck at their vote verification system. In order to get the vote verified, a client needs to encrypt all of the ...

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