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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Is 512-bit RSA still safe for signature generation?

The standard CSP on Windows XP only supports RSA up to 512-bit, which means that it's the maximum key size I can use for authenticity verification of updates. The public key is embedded in the ...
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289 views

Is it possible to attack RSA with a WalkSat derivative?

We consider a large $n$-bit number $N$. We want to find a factor, if it admits any. For $m$ taking values from $1$ to $n$, perform the following three steps (actually, for each $m$, perform many ...
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513 views

How exactly are GPG keys mathematically related, and prime numbers inside of GPG general

Before anyone suggest it, I've yet to pick up "Applied Cryptography" I'm planning on picking it up the next time I visit amazon. I know that the keys are somehow mathematically related, and I know ...
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Is there a way to systematically calculate the public exponent $e$ in RSA?

I'm learning RSA in one of my classes and we were given a problem: $p = 5$, $q = 11$ I have done the following steps: $n = 5 \cdot 11 = 55$ $\phi = (5-1)\cdot(11-1) = 40$ I know that to ...
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321 views

RSA assumption and cryptography

The RSA assumption states that it is hard to find $m$, given $c = m^e \bmod{n}$, $e$, and $n$ (for appropriate choice of $n,e$). Suppose that there exists an algorithm, $D(c,e,n)$, that finds $m$ in ...
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In RSA, why does $p$ have to be bigger than $q$ where $n=p \times q$?

In openSSL – during RSA key generation – if $q$ is bigger than $p$, they exchange them. Why is that?
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How does this happen in RSA malleability?

I don't understand how the $E(m)$ turns into $E(mt)$. I mean, I don't know how does that transformation happen and how does the equation occur. $$E(m) \cdot t^e \bmod n = (mt)^e \bmod n = E(mt)$$ ...
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599 views

How does one deal with a negative “d” in RSA?

I'm trying to write my own RSA implementation using the textbook approach — which I know is not optimal — of picking primes $p$ and $q$, then computing Euler's totient $phi$, then randomly picking an ...
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What is the meaning of “trapdoor” in cryptography?

I do not really understand the meaning of a "trapdoor" in cryptography, so here are my questions: What is the meaning of trapdoor and how can I convert a word or string using a trapdoor in ...
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Is RSASSA-PKCS1-v1_5 a good signature scheme for new systems?

Is RSASSA-PKCS1-v1_5 a good signature scheme to recommend that people use in new systems? Is it believed to be secure and represent the state-of-the-art in RSA-based signatures? I understand that ...
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646 views

ABC Conjecture's Impact on RSA Encryption

A recent proof of the ABC Conjecture has been released by one Shinichi Mochizuki. Now, I'm not well versed in mathematics but it would appear that this proof implies that finding prime factors could ...
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519 views

Why RSA uses {d,n} as private key instead of {e,n}?

While studying the RSA algorithm I referred to some books and some sites such as RSA (wikipedia) and all of them chose {d,n} as the secret (private) key and release {e,n} as the public key but as d ...
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Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA. (Note: I do realize that in practice this is done through an intermediate symmetric key, but ...
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229 views

Can RSA signing be implemented on top of RSA encryption/decryption?

I need to use RSA-SHA256 signing. Unfortunately not all Microsoft CryptoAPI providers support that. It's possible that I might get a handle to a CryptoAPI provider that can just encrypt/decrypt with ...
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159 views

Perfect Forward Secrecy in TLS

I read that TLS does PFS using Diffie Hellman. However, DH can be used even without certificates - so how is DHE-RSA better than plain DHE? Is DHE a insecure algorithm, that DHE-RSA is needed?
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434 views

Textbook-RSA meet-in-the-middle attack against other RSA based schemes?

A “meet-in-the-middle” (not “man-in-the-middle”!) attack on textbook-RSA was presented to me. The only requirements for it was that the attacker gets the output of RSA and the public key, and that the ...
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218 views

Why is verification using DSA slower than verification with RSA?

We read in literature that verification of a digital signature is slower using DSA than if we used RSA. Why is this? DSA parameter generation: choose prime number $p$ choose prime number $q$ such ...
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phi(P*Q) = (P-1) * (Q-1)

I was trying to understand RSA when I encountered the Euler Function. I do understand this: $\phi(P)$, where $P$ is a prime is $P-1$. However it seems that for a number $N$ such at $N=P\cdot Q$ where ...
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990 views

How to decrypt this RSA-like cipher

Suppose we have a RSA-type Modulus $n = pq$ with $p,q$ prime. We also pick a random public exponent $e$ with $\gcd(e,\varphi(n)) = 1$ and compute the private exponent $d$ with $de \equiv 1 ...
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898 views

Is RSA of a random nonce with no padding safe?

Consider the following protocol: Bob has a private RSA key $B_{priv}$, and Alice knows the public key $B_{pub}$. Alice wants to send confidential messages to Bob (no integrity intended). To send a ...
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334 views

Which attacks are possible against raw/textbook RSA?

The PKCS#1 standard defines multiple padding schemes for signature generation/verification (EMSA-PSS and EMSA-PKCS1-v1_5), and encryption/decryption (EME-OAEP and the less safe EME-PKCS1-v1_5). ...
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296 views

What kind of machine can generate 100-400 digits prime number? RSA

The 64 bit machine's biggest number can be 2^63 (9,223,372,036,854,775,807). So what kind of a monstrous machine can generate 100-400 digits prime number? I probably don't understand something, so ...
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338 views

Openssl & RSA : how many public exponents are possible?

I would like to know if it is possible to set the public exponent we want with "OpenSSL RSA" or if it is really limited to 2 possible exponents: 3 65537 If yes, why ?
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Please punch holes in this authentication scheme

Folks, I am undertaking a crypto course in Uni. Our professor asked us to try and design some authentication schemes which are resistant to active attacks. This was just a in class exercise to get us ...
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252 views

It is reasonably safe to leave a SSH private key with a 30+ character passphrase public?

I'm curious about exploring uses for a distributing a single RSA private key with a passphrase instead of trying to secure the private key and distribute the public key. With the private key (and ...
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207 views

RSA Key generation Public exponent too big

I'm currently writing a paper about RSA (a self-chosen subject). I'm writing about the key-generation in RSA, and I have problem finding the public exponent e. I have chosen p = 61 and q = 53. Then ...
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710 views

Why do we need in RSA the modulus to be product of 2 primes?

I think I roughly understand how the RSA alorithm is working. However, I don't understand why we need the $N$, which we use as a modulus, to be $pq$ for some large primes $p, q$. I vaguely know it ...
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How to sign a message using RSA?

Assuming I already have a D, P, Q, etc of an RSA key: How do I now sign a message? If it matters – the message is around 100 bits. I don't know much about cryptography, but I can get these numbers ...
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For which RSA moduli, precisely, is $e=d$ for all $e$?

This question shows that there are at least two valid RSA moduli $n$, namely $35$ and $91$, such that for any $e$ coprime to $\lambda(n)$, $$e^2\equiv1\mod\lambda(n)\text.$$ Reading the linked ...
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Chosen plaintext attack on textbook RSA decryption

Let $(n,d)$ be an RSA private key and $(n,e)$ the corresponding public key. Generate a secret random $r$ from $(\mathbb{Z}/n\mathbb{Z})^*$ Compute $C’ = C (r^e) \bmod n$ Submit $C’$ as a chosen ...
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RSA private exponent primality

I know that the public exponent is always a prime, but what about the private exponent? Is it always a prime too?
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Publicly exposed hash of private key

Would exposing a cryptographic hash function's digest (e.g. SHA-3) of RSA private key data compromise the key? If so, what are the possible (cryptanalysis-) vectors for attacking the key if an ...
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467 views

How does OAEP improve the security of RSA?

The heart of OAEP algorithm used for RSA encryption are the cryptographic hash functions $H$ and $G$. Does everybody (so also an adversary) know these functions? If YES: How does it help the ...
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risk of attacker decrypting RSA ciphertext without public or private key

As I describe in my previous question I am trying to decide if it's worth it for me to use the Offline Private Key Protocol in creating some long term private archives, instead of just going with a ...
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Is it safer to encrypt twice with RSA?

I wonder if it's safer to encrypt a plain text with RSA twice than it is to encrypt it just once. It should make a big difference if you assume that the two private keys are different, and that the ...
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383 views

What is the strength of unpadded RSA?

I would like to use unpadded RSA for homomorphic encryption in a toy P2P game, for things like fair coin flips and shuffling. How many bits of security does unpadded RSA have, in relation to its key ...
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383 views

What algorithm does PGP use to encrypt email?

I know it uses RSA/DSA to create keys, but does it use that same algorithm for the actual cipher?
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Is xgcd faster than Fermat for calculating $d$ in RSA?

I want to calculate $d$ from $e$ when generating RSA keys. What is faster? Calculating $\operatorname{xgcd}(e,p)$ and $\operatorname{xgcd}(e,q)$ and CRT. Or calculating $e^{p-2}\bmod p$ and ...
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190 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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123 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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121 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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237 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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438 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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How to calculate the maximum output size for data encrypted with a RSA Private Key?

I have an an encryption algorithm I am working with that looks like this: prv_key_enc(sha1_hash(data)) Where, the RSA parameters are: RSA/ECB/PKCS1Padding 1024 ...
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Why can ECC key sizes be smaller than RSA keys for similar security?

I understand how ECC is based on the discrete log problem and RSA on integer factorization. I've read several references that show how a solution to either of these problems can typically be adapted ...
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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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At what stage is DHE and RSA used during the SSL/TLS handshake?

At what stage of the SSL/TLS handshake is the DHE and RSA used and what is the purpose of using a pre-master secret when you could just use RSA to exchange the symmetric key (i.e. AES) for further ...
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301 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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155 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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What makes RSA secure by using prime numbers?

I am just learning about the RSA algorithm. Looking at the first two steps: Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$. I have some probably stupid questions: Why do $p$ ...