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 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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123 views

Montgomery Algorithm

I'm trying to undestand how it works and how to implement the algo described in this paper. The paper shows a methods to compute a modular multiplication where it is used multiplier with a resolution ...
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73 views

Is RSA with SHA1 broken?

I am using CryptSignMessage to sign a string/file. Is using RSASha1 insecure? I know Sha1 is broken as a hashing algorithm, but does that also mean that using it for signing with RSA is broken?
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243 views

Implementing a web app where the server cannot decrypt its own data?

I'm a cryptography novice, but I think that the world needs to move towards an "encrypt everything" mentality as much as possible. As a result, I've been thinking a lot about ways to build a web app ...
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2answers
129 views

Factors of RSA modulus

In the article A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...
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27 views

How to find the factors of the modulus? [duplicate]

In the article "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...
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56 views

ASN.1 encoding off RSASSA-PSS default parameters

I am not totally sure the question belongs to crypto and not stackoverflow but nevertheless... The problem is the encoding of the RSASSA-PSS default algorithm identifier parameters in an X509 ...
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3answers
53 views

private keys for multiple devices [closed]

I have an architecture where: a user can have multiple devices (phones) the server needs to broadcast the payload to all devices through the same channel (basically, all devices listen and receive ...
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1answer
75 views

Strength of RSA with OAEP

In our current system we use an encryption solution based on RSA with OAEP padding. Key size is optional but default 2048. What is the general strength of RSA with OAEP? Are there know attacks that ...
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3answers
446 views

P = NP and current cryptographic systems

I've recently heard some people claiming that if the fact that P = NP is proven, most (all?) the current cryptographic algorithm considered secure like RSA will be unusable in secure systems. My ...
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5answers
469 views

What is the SSL private key file format?

I was researching about how to encrypt with RSA. I understood everything but not the format of the private keys. In the phpseclib (RSA in PHP), you can import your private key (private.key format) ...
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71 views

Why are cryptographically secure hashes required for digital signing (RSA or DSA)?

I know that a cryptographically secure hashing algorithm is required for proper message signing (SHA-1, or I think SHA-2 is the current suggested algorithm). However, why does the hashing algorithm ...
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Why hash the message before signing it with RSA?

The diagram below illustrates the process of digitally signing a message with RSA: As diagram shows, the message is first hashed, and the signature is then computed on the hash, rather than on the ...
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1answer
55 views

How exactly to extract information base 10 from a PGP RSA key pair?

I think I understand the mathematics of RSA ok. I'm not so computer savvy though. How, exactly, can I extract $n$, $e$, $d$, $p$ and $q$ from a PGP RSA public key pair? Is there like a converter ...
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1answer
3k views

RSA 4096 bit key benchmark

How can I benchmark RSA operations on my computer? I want to know about 4096-bit long keys on general computers. How many encryptions and decryptions are possible per second? All benchmarks I found ...
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64 views

RSA - Why should we sign hash rather than raw content? [duplicate]

Apart from obvious performance considerations, is there any mathematical or crypto reasons that imply that we sign a hash rather than a raw content ? I read that it was because the hash must fit in ...
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63 views

Relations between RSA and DLOG, factoring and DLOG

Definition: (The generalized Diffie-Hellman problem) Let $n=pq$ for two large primes $p,q$. Given $x, x^a, x^b,n$, find $x^{ab}\pmod{n}$. (1) Is there a known reduction from the GDH problem ...
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2answers
581 views

How much extra information is in an RSA public key?

I'm trying to calculate the size of an RSA public key in Ruby. I've retrieved the key in PEM format, and once I've decoded the base64 part from the PEM format, I get the size in bytes. What I find is ...
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2answers
214 views

Does RSA operate over a Finite Field (Galois Field)?

Is it correct to say that RSA operates over a Finite Field (Galois Field)? In this case GF(p)? I do understant that the modulo in RSA is not itself a prime number, but all the operations ...
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88 views

Possible to know who is the owner of a message encrypted with RSA public key

Given the scenario in which I want to send 10 messages either to Stalio or Olio. I encrypt these messages with their respective public keys using textbook RSA, before sending the messages to their ...
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47 views

Is basic RSA secure? [duplicate]

I'm pretty new to cryptography, had RSA in my math lectures a few years back and decided to try it myself. I've implemented a rather basic version of RSA using a hash from a passphrase to create the ...
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4answers
246 views

How are random numbers for RSA generated? [duplicate]

The RSA public key encryption requires two very large prime numbers as part of its encryption process that serve as secrets. These are typically generated with cryptographically secure random number ...
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116 views

how to let other people respond to emails only decrypt-able with my private key

First of all I have to say it's a homework question but since I have no one to consult with, I ended up here :) Suppose a case in which you are the manager of a company and all employees encrypt ...
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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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2answers
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OTP from Sony BIOS password recover [closed]

From Dogbert's blog: Sony has a line of laptops ("Vaio") which compete mainly in the high value market segments. They implemented a master password bypass which is rather sane in comparison to the ...
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59 views

RSA Protocol behind Yaksha Security System

So I'm reading over the Yaksha Security System and see it is based on the RSA cryptosystem and a centralized server, easy enough. What I'm slightly confused on is the math behind the related keys. It ...
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RSA Proof of Correctness

Can anyone provide an extended (and well explained) proof of correctness of the RSA Algorithm? And why is it needed? I can't say that this or this helped me much, I'd like a more detailed and newbie ...
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62 views

RSA-blind signatures vs. DSA-blind signatures

I see that the RSA blind signature scheme tends to be implemented more often than others, e.g., DSA blind signatures. Isn't the RSA blind signature scheme a 'lesser' scheme, if you may, compared to ...
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85 views

Probability of factoring keys as a function of bit length

kinda new here, I had a question pertaining to someone being able to factor one's RSA keys through the GCD. Anyways the question goes that there are two people: A and B. A makes his/her private key as ...
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95 views

What are the potential (major) flaws in this security scheme?

It’s been a few years since I read anything involving crypto. I’ve come across this scheme and I wonder how secure it is: Alice generates an RSA keypair (we assume Alice is using proper random ...
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169 views

Decrypt all RSA ciphertexts if you can break 1% of them

I was given a cryptography question during an interview the other day. Imagine you are given an efficient algorithm which for a given RSA public key (n,e) is able to decrypt 1% of the messages ...
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69 views

Crack RSA with imaginary algorithm [duplicate]

I was given a cryptography question during an interview the other day and I couldn't come up with a valid answer. Imagine you are given an efficient algorithm which for a given RSA public key (n,e) is ...
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1answer
68 views

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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70 views

RSA or Paillier is good? [closed]

I want to implement file storage in cloud using homomorphic encryption. I want to use paillier encryption. Can you suggest the drawback of RSA to store and retrieving the files. Then only i can use ...
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71 views

Does it necessary the public key is prime number in RSA algorithm?

I read some books talk about RSA cryptography but I did not understand something when choosing a public key $e$ Sometimes the condition is $1<e<$$\phi(n)$ Where $\phi(n) = p-1 * q-1$ also ...
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162 views

rsa public and private keys

I have a question about RSA key generation. This is a simple RSA algorithm: Choose p = 3 and q = 11 Compute n = p * q = 3 * 11 = 33 Compute ?(n) = (p - 1) * (q - 1) = 2 * 10 = 20 Choose e such that ...
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166 views

Including a “purpose” designation in a digital signature

A signature of some data can mean many different things, such as: This is a message I sent, this is a certificate I validated,... So I was surprised that common signing schemes don't include a ...
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136 views

Crypto libary with Commutative Encryption

I want to implement Mental Poker in JavaScript as a toy program and lead in to a larger serious project so I did my research and found Massey-Omura cryptosystem and the Shamir three-pass protocol ...
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76 views

Existential Forgery on textbook RSA signatures

Can an adversary who haven't seen the message before forge the signature of that message? The adversary has seen $σ_1 = (m_1)^d \bmod N$ and $σ_2 = (m_2)^d \bmod N$ He forges $m' = m_1\cdot m_2$ $σ' ...
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63 views

RSA Cryptosytsem, choosing $e$ [duplicate]

I am using the RSA crytposytem. I have $p$, $q$ and hence $n$ and $\phi$ however I don't understand how to get $e$ such that $gcd(e,\phi)=1$ Many thanks
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How to compare security parameters of different schemes (Sign-Encrypt, Encrypt-Sign, etc)? [duplicate]

How can one compare the security parameters (confidentiality, integrity, non repudiation, etc.) for different schemes (Sign-Encrypt, Encrypt-Sign, Sign-Encrypt-Sign, Encrypt-Sign-Encrypt)? Are there ...
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145 views

Cracking RSA with Small exponent 5

I have read following questions - Cracking an RSA with no padding and very small e Small Encryption Exponent where in first it says to run out all the possible m options and second says factor ...
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86 views

Generation of strong primes

It seems that this is pretty difficult to find large (above 1024 bits) strong primes, or at least such primes p where (p-1) has a very large prime factor. Is there any information regarding the ...
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131 views

Maximum length in bits of the product n=pq

If p and q are two 1024-bit prime numbers, would the maximum length in bits of product $n=pq$ be ${1024}^2$ or $2^{1024}$? I think it is ${1048576}={1024}^2$? Also, would the least significant bit ...
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63 views

RSA OAEP: prevention of partial decryption of ciphertexts

I'm trying to understand RSA encryption (as a beginner in cryptography). go on this wiki page http://en.wikipedia.org/wiki/Optimal_asymmetric_encryption_padding scroll down to the 2 numbered points: ...
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97 views

Cracking plain RSA by factoring the modulus n

This is the setup: I have both public and private keys of one "instance" of RSA. And I have only the public key of another RSA cryptosystem, but this system has the same modulus as the first one. I ...
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138 views

Python. RSA common modulus attack problem

I have: N = /*500 decimal numbers*/ E1 = 3740453 E2 = 4226171 M^E1 = /*500 decimal numbers*/ M^E2 = /*500 decimal numbers*/ I must use RSA common modulus ...
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2answers
205 views

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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2answers
393 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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54 views

special public keys and modulo n

I just picked up cryptography and have some questions on RSA cryptosystem: Say there are two public keys (n, e1), (n, e2), e1 is coprime to e2. They share the same n. Is it possible to find the ...