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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Timing attacks against RSA, DH and AES

I have been reading about “Timing Attacks on RSA: Revealing Your Secrets through the Fourth Dimension” by Wing H. Wong. I was wondering if this attack is feasible while signing with RSA and, if yes, ...
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162 views

Rabin/RSA four possible messages?

Given this encryption method: $$f_{N,e} : Z^{*}_{N} \to QR(N)^{*};\quad f_{N,e}(x) = x ^{2e} \bmod N$$ I need to show that, for any $x_{0} \in Z^{*}_{N}$, there are four elements $x \in Z^{*}_{N}$ ...
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226 views

Diffie-Hellman exchange

So for a Diffie-Hellman problem, I am given the prime $p$ for the Diffie-Hellman exchange. I am also given $g$, secret number for machine as $A$, secret number for station as $B$, a Diffie-Hellman ...
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680 views

RSA problem if i choose two specific small prime numbers?

I know that rsa normally is made to make it with big integers, but i trying to make the algorithm myself (with the help of wikipedia) and I´m making it with small numbers to track the problems easily. ...
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281 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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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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90 views

Is it secure to choose d in a RSA key pair?

An RSA key pair consists of the private key $(n,d)$ and a public key $(n,e)$ such that $de \equiv 1 \bmod{\lambda(n)} $. Usually one chooses a small $e$ and computes $d$ by inverting it modulo $\...
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324 views

Message exchange with textbook RSA

I am working on this exercise but can't work out the answer to the question b. I have solved the question (a) by decrypting the ciphertext $C = 2$ using the formula: $$ M = C^d \bmod n = 2^{17} \bmod ...
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124 views

What is RSA key normalization?

How can I understand the term RSA key normalization? What exactly is done in the process?? Please explain.
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543 views

two public keys with same passphrase insecure? | can two hashes be compared?

Suppose someone had generated a 2.048-Bit RSA GPG/PGP key pair and published the public key on the usual key servers. Then he withdraws this key and generates a new one in 4.096-Bit RSA using the same ...
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262 views

Large primes p and q for RSA

I am writing a high-school paper on textbook RSA (the mathematical aspect only). Many definitions of the RSA method start off with saying that one should: Generate two large random (and distinct) ...
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130 views

Three different numbers with x³=x mod p

p is a prime greater than 2 and $a \in \mathbb{Z}_p$. Why are there exactly three solutions for a³ = a mod p? Obviously 0 and 1 are both in $\mathbb{Z}$ and valid solutions, but that still means, ...
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355 views

What is h in this RSA variant?

I am trying to implement a proposed improved algorithm of RSA . Here the author has increased the number of exponents. However I am unable to understand what $h$ is in the Key generation step. Can ...
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89 views

find solutions that solve the equations

I am implementing a timing attack on RSA for school and I need to generate two sets of messages $Y$ and $Z$ for which holds: $ (Y^d \mod N) \cdot Y < N $ and $ (Z^d \mod N) \cdot Z > N $ where ...
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2k views

Is it possible to use the RSA algorithm, or a variant, for software licensing?

I'm almost a newbie about RSA encryption, so my question could it be banal. I'm beginning to create a licensing system for my software. I need to distribute a crypted license file to many customers. I ...
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94 views

Really simple RSA style public private key generator

I am giving a talk to high school students and would love to do a real life encryption/decryption demonstration. I am not too familiar with the maths but is it possible to create like a 5-10 bit ...
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52 views

Computing the cardinality of the co-domain of specific modular exponentiations

Consider the following function: $f: \mathbb{Z}_n \rightarrow Y,~x \mapsto x^e \bmod n$, where $n = p \cdot q$ is an RSA modulus and $gcd(\varphi(n),e) \neq 1$ (different as required for a public ...
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111 views

Why is RSA encryption version 1.0 not specified in an RFC?

I saw that there are three RSA encryption versions, as follows: RSA encryption version 1.5 (RFC 2313) RSA cryptography specification version 2.0 (RFC 2347) RSA cryptography specification version 2.1 ...
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2k views

Is ECB mode safe to use with RSA encryption? [duplicate]

Firstly, bear with me, I'm relatively new to cryptography. In a recent static analysis scan of our application, one of the findings complained that we are using ECB: A mode of operation of a block ...
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773 views

Use cases and implementations of RSA CRT

I discovered the chinese remainder theorem (CRT) version of RSA cryptosystem which is used in many crypto libraries (OpenSSL, Java...). The use of this theorem improves the speed of decryption so, ...
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204 views

How is the following different than RSA Signing of a document?

If the goal is to demonstrate that you are who you say you are, I think the following will work: Bob wants to know that you are Amy. Bob encrypts a number using Amy's public key and then asks her what ...
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172 views

Brute force RSA cracking

Suppose one had a complete list of primes up to $2^{n+1}-1$. Then wouldn't one be able to crack an $n$-bit RSA public key in time $O(\pi(2^{n+1}-1))$, making RSA insecure? Thanks, René
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379 views

modulo operations in crypto algorithms

Am not a mathematician. Every crypto specification I see uses the modulo operation. For example RSA - If $e$ is the public key and $m$ is the plaintext with a modulus $n$ - the cipher text is $c = ...
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Why is it a security problem that two RSA moduli are not co-prime?

I found this security problem, for example: Alice has an RSA public key: $e = 37$ and $\phi$ (totient, $N_A = (pa-1)(qa-1)$) is $55$, so the key is $(37, 55)$. Bob has an RSA public key: $e = 37$ ...
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617 views

Possibility of factorisation of rsa modulus due to vulnerability in java implementation code

Below is my implementation of the RSA algorithm. Actually I'm choosing the private key (d) instead of public key (e) and computing the public key.It is working fine but I want to know if this is a ...
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99 views

Tweaking textbook RSA to make the encryption a Pseudorandom function

Lets say I want to tweak/alter the textbook RSA encryption function to create a pseudorandom function by pre-processing the input. Suppose I do something simple like add 2 to the input before ...
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5k 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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454 views

Does RSA-OEAP have integrity and authenticity properties?

RSA-OAEP is IND-CCA2 secure (indistinguishable under an adaptive chosen ciphertext attack). Does it also have the INT-CTXT (integrity of ciphertext) and INT-PTXT (integrity of plaintext) properties? ...
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188 views

RSA encryption input range - plaintexts that map to ciphertexts?

According to the wiki article on the RSA encryption function, the valid range of input $m$ is $0 \leq m \lt n$. However I have found that the following values of $m$ always return themselves when ...
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167 views

Idea for secure password hash-likes, is this feasible/usable/workable?

(Hand moved from stackoverflow.com,due to suggestion) Since breaking password hashes has become a new passtime for scriptkiddies, I thought of the problem and came up with a novel(?) idea. store ...
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88 views

RSA message integrity

I wish to send some small data that RSA alone can encrypt, and I send a shared secret along with it. ...
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131 views

Encrypt letters separately?

I am trying to encrypt the word Hello using RSA. When encrypting Hello’s integer representation, is each letter encrypted ...
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199 views

Why doesn't this defeat RSA?

Apologies for the obviously ridiculous question but I need to know where I'm going wrong here. For RSA, we compute $n=pq$ for primes $p$ and $q$. We then choose an $e$ such that $gcd(e, \varphi(n))=1$...
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206 views

Why is this a fix to Bleichenbacher's attack?

Looking at the excellent explaination of the attack here: Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5? I have one additional question: It says that: ""To prevent this attack, SSL ...
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856 views

RSA Key generation: How is multiplicative inverse computed?

As per Wikipedia, RSA keygen goes like this: Choose two distinct prime numbers p and q. Compute $n = pq$. Compute $\varphi(n) = (p − 1)(q − 1)$. Choose an integer e such that $1 < e < \varphi(...
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135 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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107 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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448 views

File format of an $2048$ bits RSA public key

From here, there are $14$ bytes specifying the file format of the key. I am still quite confused about the format bytes. For example, the following public key 30 82 01 0a 02 82 01 01 00 8e a3 d1 c7 ...
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424 views

Why would an RSA library tell me that the public key must be at least 512 bits in size?

I'm trying to interoperate with a web service by reverse-engineering it. Currently, when sending a POST request, it encrypts the form data one-by-one with a 'RSA' function. But it's rather weird as ...
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248 views

How do we arrive to the equation for solving D in RSA?

We have been shown that DE is congruent to 1 mod phi(n). How do we arrive to the real equation for figuring out d that is d = e^-1 mod phi(n). I want to know the entire process. I am just curious, ...
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266 views

Brute force attack on RSA - success criteria?

In a hypothetical discussion we ended up with a concrete question I'd like to find the answer to: If you try to brute force an RSA encryption, but the original vale which was encrypted was just ...
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1k views

Help with example RSA problem

While learning about RSA, I found this example problem. The answer is supposed to be "a 4-digit number that is a pattern of digits." I have computed it to be 16657 twice. OK, now to see if you ...
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457 views

Amateur question: two-way RSA?

Is this a sensible scheme for 2-way client/server communication? A client connects to a server. The server and client both generate RSA keys, and send over the public ones to each other. If the client ...
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653 views

Why are RSA keys encoded with ASN.1 for TLS?

Browser vendors use ASN.1 encoding for RSA certificates in the TLS protocol. RSA public keys are just a number, so why do we need encode them to something else? That increases the risk of security ...
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920 views

How to jusify {e,n} is a valid RSA public key?

I have a two set of key {36,77} and {50,117}, How can validate if it is a valid RSA public keys? Is there any simple method?
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What is the correct value for “certainty” in RSA key pair generation?

I'm creating an RSA key pair in Bouncy Castle and need to specify an int value for certainty. This Stack Overflow answer says it is a relative test for how prime the values are. There is another ...
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349 views

One-way function and factoring

I am confused about the hardness of the one-way function behind cryptography -- if someone could factor the large number produced back into two primes quickly then the one-way function would be broken?...
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73 views

SHA256(RsaPrivateKey) == AES key?

I have an RSA private key (more specifically, an SSH key in Putty format, 4096bit) and want to use its SHA256 hash as an AES256 key, instead of using an independent newly generated AES key. Are ...
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87 views

Can RSA with padding detect all errors in ciphertext?

I'm new in cryptography and there are a couple of things that i'm not sure if i understand correctly. First, when using padding (PKCS or OAEP), if the chiphertext has errors in transmission we'll we ...
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67 views

RSA numerical questions

Let $n$ be the modular arithmetic, $p$ and $q$ the two large primes such that $n=p*q$ and $e$ the public exponent. Here they are two "simple" numerical questions: If $p = 13$ and $q = 17$, what is ...