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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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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Does ssl_rsa_with_rc4_128_md5 have known weaknesses?

My bank's website uses HTTPS with the cipher suite ssl_rsa_with_rc4_128_md5. What are the known weaknesses of this suite? Do they have a practical impact for ...
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630 views

RSA Decryption with Private Key but no public exponent

I manually set the RSA private key, given the private exponent and modulus. When I use this key to decrypt a message encrypted using a public key (also set with public exponent and modulus) seems to ...
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961 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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581 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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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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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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414 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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170 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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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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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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172 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, ...
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175 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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489 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 < ...
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117 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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95 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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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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335 views

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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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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344 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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381 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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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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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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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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838 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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406 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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442 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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572 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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231 views

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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800 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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Is this a good communication scheme?

I'm writing a wrapper for a chat program to allow for end-to-end encryption. I'm using Python and PyCrypto to accomplish this. I'd like to use a well known library to do this, but to my knowledge, ...
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99 views

How “hard” it is to take an e'th root mod p?

I know it's hard to find the $e$th root of a number mod $n=p_1*p_2$, and if it would be possible we could break RSA. But how hard it is to take an $e$th root mod $p$ where $p$ is a prime and ...
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What part of an RSA key is referred to by the number of bits? [duplicate]

When we speak about 4096- or 2048-bit RSA keys, what part of the key is this number of bits? The public key comprises both the modulus and the public exponent, and the strength of the key can also be ...
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201 views

Why is the public/private key length used in libsodium so much shorter than needed for RSA [duplicate]

Reading the libsodium source I see that is uses a key length of 32 bytes (256 bit) for private/public key encryption. For RSA private/public key encryption a key length of 2048 (or 4095) bit is ...
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55 views

How to determine the exponent when using RSA

Can someone please explain to me how, when using RSA, to determine the exponent to be used in encryption and decryption? I have attempted a worked example on using RSA (shown below) but I can't ever ...
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351 views

Common Modulus Attack in RSA

Consider the following scenario: The Information Security Department (ISD) of an organization issues each of the organization's employees, domestic and abroad, with an individual RSA key. To simplify ...
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Is it a variant of Strong RSA assumption?

Informally, the hardness of RSA/Strong RSA assumption lies in the hardness of factoring a large composite number $N$ having two large primes as its factors. If RSA modulus $N$ is a prime number, then ...
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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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599 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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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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190 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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166 views

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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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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348 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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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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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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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 ...