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 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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277 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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158 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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163 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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111 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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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 < ...
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75 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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99 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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How do RSA and ElGamal key sizes compare?

I have a rather silly question regarding the comparison of RSA with ElGamal over integers. If you want to compare their performance in the same level of security, does the modulus of both of them need ...
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176 views

Proof for exponentiation in modular arithemtic

If $e$ is a natural number, then this is true: $$m^e \bmod\ n = (m\bmod\ n)^e\bmod\ n$$ This is often used when encrypting, especially with RSA, since one can avoid directly calculating $m^e$, ...
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Why does plain RSA not work with big messages ($m>n$)?

From what I can remember, RSA is something like this: Generate 2 distinct prime numbers $p$ and $q$ that have similar bit length. Compute $n=pq$ and $\phi(n)=(p-1)(q-1)$ Compute $e$ such that ...
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502 views

What does an RSA signature look like?

I am using OpenSSL libs to generate signatures. Internally, I learn that a signature is a hash of the message with some padding added to it. I am trying to understand the structure of a signature. If ...
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Is javascript RSA signing safe?

I'm currently working on a secure open source messaging system (https://github.com/DSMNET/DSMNET). Currently I'm using the cryptico.js (https://github.com/wwwtyro/cryptico) library to encrypt all the ...
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437 views

RSA smaller number work-out-by-hand not working - I think I made a mistake

I tried out the paper/pencil explanation @ http://sergematovic.tripod.com/rsa1.html, and it seemed to make sense just fine until I came to decryption. Here is what I worked out: Key Creation: Choose ...
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201 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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728 views

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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512 views

why public key cryptography (RSA) is use in sites like Google, facebook (what is the need to ecode data in these sites)?

The RSA algorithm is used for encryption (plain text to cipher text) and decryption (cipher text to plain text) of data. What is the need for using public keys in these sites; why is data is encrypted ...
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479 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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306 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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329 views

Why is the following RSA PRNG cryptographically secure?

One requirement states that the generator has to withstand the next-bit test. Consider the following PRNG, where we calculate next output $x_i$ via the formula $x_i = x_{i-1}^ e\mod n$. I can see ...
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400 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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Breaking RSA, given a special kind of oracle that decrypts related ciphertexts for us

Let $c=E^{RSA}_{e}(w)$ be the ciphertext belonging to the plaintext $w$ if an $RSA$ system is used. Assume that the public exponent $e$ satisfies $e \le 10$. Furthermore, assume there is an oracle ...
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653 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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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 ...
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124 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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80 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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190 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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246 views

Use case of RSA CRT

I discovered the CRT version of RSA cryptosystem which is used in many crypto libraries (openSSL, Java...). The use of the Chinese Remainder Theorem improves the speed of decryption so why it's not ...
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193 views

Compare two approaches for cracking RSA key

I came across these questions while studying for a crypto course, does anyone have any ideas on how to answer these? (a) Random prime numbers of size 1536 bits are chosen to generate an RSA modulus ...
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177 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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Public and private key lengths

I am generating RSA Public and Private keys with node.js instead of reading them from pem/crt files as I can hide them inside a private object using this module https://www.npmjs.org/package/private ...
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84 views

How can a digital signature algorithm incorporate a random data if it is to be authenticated on a separate system

I am trying to understand how RSA digital signatures can incorporate any data from a PRNG into the final signature. Does this mean that separate implementations might fail to verify each others ...
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252 views

Prime factorization of RSA modulus

Consider RSA public-key encryption with public modulus $N=3953$. Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. ...
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130 views

Usage of Fermat primes in RSA

Why are Fermat primes ($2^{2^n}+1$) useful as $e$ (the public key) in RSA encryption? I understand why $2^n+1$ primes are useful, because they would simply be ...
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487 views

Forgery Attack Against RSA Digital Signature

I have been reading about attacks against RSA Digital Signature in a book The attacker chooses the signature first and then computes the message. As a consequence, he cannot control the ...
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99 views

Sample RSA-style signature confusion

I'm trying to study a simplified TLS-style protocol, including verifying RSA signatures. It's an attempt to verify using only a valid certificate. However, I can't manage to get anything to verify ...
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109 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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Would this program be useful in cryptography?

I know nothing of encrypting. I'm not even sure how to tag this. I wrote a program that can calculate this pretty quickly on my macbook pro 2.3GHz IntelCore i7. The two exponents are Mersenne primes, ...
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HMAC SHA256 vs RSA SHA256 - which one to use

Salesforce recently announced they are moving away from HMAC SHA256 to RSA SHA256. Why did they make that move?. Any technical factors? Is HMAC really easy to break? ...
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504 views

RSA decrypt long messages (javascript)

I am attempting to encrypty/decrypt a long message in RSA using javascript (with crypto-js and jsbn libraries). I posted this on stackoverflow too but I figured someone here on crypto might be able ...
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255 views

Understanding the “cube-root math” behind an RSA signature forgery

I'm trying to understand the math outlined in this paper on a RSA signature forgery attack. I understand it except for one aspect of how the cube root (that makes the forged signature) is computed. ...
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335 views

DSA, RSA, ECDSA etc - which one is cheapest for signing?

For a protocol where the server presents its signature to prove authenticity (e.g. IKE/SIGMA/STS with only one party authenticated), it's essential that the signing is extremely cheap, while ...
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chaining rsa with ecies

In an answer to a previous question it was suggested that one way to protect your asymmetrically encrypted AES-256 keys, from say a solution to prime factorization, would be to chain asymmetric ...
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How do I derive the time complexity of encryption and decryption based on modular arithmetic?

I want to calculate the time complexity of two encryption and decryption algorithms. The first one (RSA-like) has the encryption $$ C := M^e \bmod N $$ and decryption $$ M_P := C^d \bmod N. $$ ...
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Is there a big RSA Data Set

Is there a big dataset containing RSA public $(n,e)$ and private keys $d$ and primes $p,q$ where $n = p.q$ ?
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RSA 1024bit decryption performance

i want to know how many RSA 1024 bit long key decryption can a regular pentium4 computer do per second ? how to calculate RSA performance and determine its remaining time ?
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Can you distinguish encryption methods from the output?

Suppose that you see all IP communication packets between two computers for a day, as they pass through a connecting router, and this amounts to 10MB. You additionally know that all data transmission ...
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My custom handshake

I am a beginner in cryptography and I designed a custom handshake between 2 entities $\rm C$ (client) and $\rm S$ (server) which should meet the following requirements: Requirements: The handshake ...
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RSA padding confusion attacks

Server A produces signed messages on request. You can tell server A what type of RSA padding to use in the signature (either RSASSA-PKCS1v1_5 or RSASSA-PSS). Either way, the message will be signed ...