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.

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RSA private key d knowing e,n

I need to find RSA private key $(d, N)$ knowing $(e, N)$. It's "own" RSA implementation. As i know $p$ is random 70 bit number, then $q$ is $p-2^{10} < q < p+2^{10}$ $d$ is max 16 bit long with ...
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1answer
149 views

How do we guarantee plaintext is coprime in RSA?

The specifications for RSA state: $P^{\phi(N)} \equiv 1 ~mod~N$ if and only if $P$ and $N$ are coprime. Here $P$ is the plaintext and $N$ is the product of two suitable primes $x_1, x_2$. My question ...
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457 views

The Boneh-DeMillo-Lipton fault attack (RSA CRT)

I am trying to understand the Boneh-DeMillo-Lipton fault attack on RSA CRT signature. Suppose that we sign a message $m$ with RSA-CRT : $d_p = d \bmod (p-1)$ and $d_q = d \bmod (q-1)$ $s_p = ...
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3answers
185 views

Feasibility of finding public key when private key is known

We all know that in a public key cryptosystem, given a public key it is extremely hard to compute private key from it. Is it the same case in reverse? Given a private key, how easy is it to compute ...
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1answer
152 views

Pick faster private exponent

I recently tried to send 1536-bit modulus CSR to COMODO. They refused to sign the certificate. I later found out that it's because NIST mandated 2048-bit modulus on the SSL certificate. I think it's ...
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2answers
534 views

Private RSA key for HMAC key

I am creating software tokens for future request authentication, and I want to use an HMAC for the token to make them tamper-resistant. To ensure I can check the HMAC later I need a secret, persistent ...
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1answer
2k views

Is it true that for RSA with no padding, the length of data must be equal to the length of key?

The question pertains not in terms of security but computing operational functionality, as it how the computation is done. Is it true that for RSA with no padding, the length of data must be equal to ...
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1answer
346 views

Where can I download a database of RSA keys?

I'm looking to do some research into how RSA is used in the wild. I've read through a few papers and it seems other researchers have had no trouble collecting millions of keys to perform analysis on. ...
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1answer
180 views

Why encrypting with private and public keys produce the same result?

Let say $e = 5$, $n = 119$ and $d = 77$. If I encrypt, for example, $m=15$ I get: $$m_1 = m^e=15 ^ 5 \mod 119 = 36\qquad\text{and}\qquad m_2 =m^d= 15 ^ {77} \mod 119 = 36$$. Why? Is it always like ...
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524 views

RSA 896 vs 1024 vs 2048 in Javascript?

I am currently working on a secure messaging website and I had been using RSA 2048 for encryption, decryption and signing of messages but I found it to be EXTREMELY LAGGY so i've moved to 1024. I did ...
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213 views

Which platforms are most vulnerable to Simple Power Analyse Attack

In a "Simple Power Analyse Attack", the difference in power consumption during multiply or square operation is used. In the RSA decryption process with the "Square and Multiply" algorithm, both ...
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2answers
350 views

Chain several RSA encryptions without increasing the message size

I would like to be able to encrypt the output of RSA with RSA again without having the output grow in size over time. In other words, I have some data $D_0$ which I want to encrypt with RSA: $D_1 = ...
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3answers
747 views

RSA finding the inverse of the public exponent

I have a very basic doubt in RSA key generation and its usage. In RSA key generation you choose two large prime numbers of a very large order. Then you multiply them.(eq $p \cdot q = N$) Now, ...
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1answer
86 views

Is there an asymmetric algorithm that can perform double encryption?

I'm looking for any asymmetric algorithm can perform the serial encryption, by serial I mean double or more encryption with different key(same key size). RSA can not do it since the cipher of the ...
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2answers
94 views

Implementing RSA with small integers in CUDA

I have found some researches dedicated for speeding-up RSA calculations using CUDA. But I am wondering how they do that, given that the biggest unsigned int that could be declared in CUDA is 64 bit. ...
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2answers
85 views

How can a message encrypted with the public key be decrypted with the private key? [duplicate]

I've been reading about encryption and have a basic understanding of the concept. What I don't understand, however, is how a calculation with one key can result in a number that, through calculation ...
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1answer
85 views

Plaintext and ciphertext block sizes

How can you determine the largest plaintext block size and smallest ciphertext size if you used RSA with $n=59768553302699443$ using an alphabet with $27$ characters?
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1answer
199 views

Lattice based attack on RSA

Let $n=pq$ be the RSA module and at least one of $p,q$ is a weak prime.It is proved that the number of such $1024$bit $n$ is at least $2^{759}$. With lattices we can factor these $n$ in a second (I ...
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2answers
98 views

RSA and difference between factors

As I understand, for RSA $n = p \cdot q$. For the key to be safe enough from getting factored, $p$ and $q$ have to be far from each other. How far do they have to be? For example, if I have two ...
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2answers
113 views

Why does the time complexity of RSA encryption and decryption depend on the size of the modulus?

I would think that the time complexity would depend on the exponent, not the number of bits in the modulus. For example, if the exponent were 5, using the "naive" method, we would perform 5 ...
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1answer
134 views

Help understanding basic Franklin-Reiter related message attack

I am trying to understand this attack at the most basic level. I set up the following basic scenario: Let the public encryption exponent, e = 3. Let p, be some arbitrary but known (to the ...
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1answer
77 views

Diffie-Hellman using a different modulus on both sides

For Diffie-Hellman Key Exchange, the used modulus is the same throughout the process. Is it possible to use 2 different for both sides? For example, $A \gets M^{d_1} \pmod{n_1} $ $B\gets M^{d_2} ...
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1answer
87 views

Is there really any way to nullify or avoid MITM attacks?

The question pretty much sums it up. Is there any way to make an attacker who is successfully performing an MITM attack to actually not be able to read or change the messages? Assuming there is no ...
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127 views

Security impact of signing small data using RSA

I have an application which consists of a client and a server. Both have a pair of public and private key (RSA). For communication, both sign their messages and send them to the other part. So a ...
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262 views

Why isn't Rabin-Williams cryptosystem widely used?

I think we all know RSA. And of course we also know DJB (a.k.a. Daniel J. Bernstein). Now some already have noticed that he has an opinion towards cryptographic questions. In his 2008 paper ("RSA ...
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90 views

Retrieve value of private key after encryption with the public key

Is there a way to find an RSA private key after it is encrypted with the corresponding public key? Does there exist an algorithm to recover the private key in this special case?
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446 views

How multiplicative property of RSA can be exploited

It is known that RSA has the multiplicative property $E(m_1) \cdot E(m_2) = E(m_1 \cdot m_2)$ because $m_1^e \cdot m_2^e = (m_1 \cdot m_2)^e \pmod n$ But how can this property be used to break ...
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1answer
169 views

What use is the signature without the message under RSA?

Using RSA for signing & verification, is there a way to take a valid signature for an unknown message, and for someone else to generate a valid signature using a different key against the valid ...
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1answer
568 views

Deterministically generate a RSA public/private key pair from a passphrase (with sufficient entropy)?

Is it possible to deterministically generate public/private RSA key pairs from passphrases? Would giving the (key generating) algorithm data made from key-stretching the passphrase (instead of a ...
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1answer
480 views

Precomputation attacks on RSA

Are precomputation attacks - such as outlined in RFC 3610 chapter 5 - possible on RSA PKCS#1 v1.5 signature generation? If yes, are such attacks taken into account when calculating the cryptographic ...
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1k views

RSA Key Generation Parameters - public exponent, certainty, string-to-key count

I want to know what values are appropriate for the public exponent and certainty when generating an RSA Key (for example using Bouncy Castle RSAKeyGenerationParameters function). What is the ...
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1answer
817 views

Why should a signature use PSS padding in RSA?

Suppose I send a message using AES (private keys already negotiated securely) and I send a hash of this message using RSA (encrypted with private key) with OAEP to verify the authenticity and ...
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257 views

RSA key length choice for TLS when confidentiality not important?

I've a couple of questions about this, the scenario is embedding a key pair in a hardware device which will speak with other hardware devices over tls. computing resources are an issue so i want to ...
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1answer
702 views

Generate key pair deterministically from a particular seed [duplicate]

I've been reading "SQRL Secure QR Login" at Gibson's website, and I'm wondering if there is a way to generate an RSA private/public key-pair based on some cryptographically secure input, so that if ...
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170 views

Does it necessarily mean that an RSA moduli generated with poor randomness is not random?

In 2012 a group of researchers collected a large amount of RSA moduli and calculated their greatest common divisor in order to find common factors between them. By finding a common factor they could ...
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1answer
1k views

How is text converted to a number for RSA? [duplicate]

According to http://en.wikipedia.org/wiki/RSA_%28algorithm%29#Key_generation the key length is the number of bits in n. So how can a message of many megabytes (millions of bits) be modded by a 1024 ...
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1answer
69 views

Comprehension question on a signature protocol based on the RSA assumption

We have the following two-party protocol between Alice and Bob. Alice sends messages $m_1, m_2, \ldots \in_R \mathbb{Z}_n^*$ to Bob and Bob signs these values by calculating $v_1, v_2, \ldots \in_R ...
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1answer
95 views

What is the most secure way to let Alice “input” her private key, transfer it to the server and decrypt the message?

What is the most secure way to let Alice "input" her private key, transfer it to the server and decrypt the message? (Then destroy the private key on the server) Every connection is using SSL. ...
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1answer
575 views

using Post-quantum asymmetric ciphers instead of RSA

We can't trust RSA to encrypt our Emails so what is best post-quantum cryptography system as alternative for RSA which provide good security and don't be breakable? because McEliece cryptosystem looks ...
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232 views

RSA keys finding when messages are known

I have this situation, where, in a game, people send messages to each other (game moves etc...) These messages need to be encrypted, and should only be readable by the destination person. I am using ...
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1answer
610 views

How are the primes used to generate RSA keys?

I am confused about how keys in RSA asymmetric encryption are generated and what the implications for open communications are. Textbooks say the one-way function is merely two primes (with some ...
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1answer
71 views

Preserving Confidentiality and Integrity in a Public channel

Let's say I've got two people that are trying to talk in a public channel $A$ and $B$ and they want to preserve their confidentiality and integrity. Which cryptographic algorithm would they want to ...
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1answer
86 views

Attack on textbook RSA with small messages

We learned in class that if Alice wants to send a small message $m$, such that $m < N^{\frac{1}{e}}$, so we can break the system using $e$-th square of $m^e$. But what if Alice knows this flaw and ...
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2answers
94 views

How do you communicate the hash function used with RSA signing?

When it comes to RSA signing, I understand why you need to hash the data before signing it, but don't you need to communicate what hash algorithm you use to whoever will need to verify the signature? ...
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1answer
165 views

RSA 1024 bit forge a new matching signature from a chosen message

I have an RSA signature scheme with 1024-bit key where I know the following: Public modulus $N$ Public exponent $e=3$ A lot of signatures Summary: To compute a signature, an MD5 hash is ...
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58 views

Why can we ignore $y$ when using the extended Euclidean algorithm to calculate an RSA decryption exponent?

I have a follow-up question about the extended Euclidean algorithm, as applied to RSA key generation, described in this answer. Let us say we have $p=5$, $q=11$ and $e=17$, so that $N=55$ and ...
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229 views

RSA signatures without padding

Suppose I have a message $M$ for which I generate an RSA-2048 digital signature as follows: $H = H(M)$, $H(M)$ being the SHA-256 of the message $M$ $S = H^d \bmod N$ Assume $N = pq$ is properly ...
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1answer
196 views

Given only RSA public key parameters, what security issues might I be able to detect?

I'm attempting to automate some checks against a large list of .NET assemblies, and want to include a test to see if the RSA parameters used to sign the assemblies are sensible. However, since I don't ...
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1answer
189 views

RSA public key exponent generation confusion

Quote from Wiki: $e$ having a short bit-length and small Hamming weight results in more efficient encryption — most commonly $2^{16} + 1 = 65537$. However, much smaller values of $e$ (such as $3$) ...
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275 views

2048-bit RSA Decryption

If a message is encoded with 2048 bit RSA. The ciphertext is $M^e mod N$. In some cases, the message is short, $ M \approx 10^{20} $. With a high probability, $M$ can be written as $M = ab$ with $a, b ...