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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248 views

Does it make sense to have a 4000 bit long key?

My question is about the key length of a asymetric algorithm. How is it possible to memorize or remember a key that is about 4000 bits long?
3
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1answer
167 views

Questions about OAEP for RSA

I have two questions about OAEP for RSA. How are the number of bits to pad with 0 chosen? For example, if I'm sending a 255 byte message with RSA-2048 I have 8 unused bits (1 byte). Should I split ...
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1answer
111 views

RSA public key security issue

The public key for RSA is $[e,n]$. Since $n = p * q$, are $p$ and $q$ already exposed because it takes no effort to figure out $p$ and $q$ from $n$?
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1answer
195 views

Timing Attack on RSA

So far I have researched on timing attack on RSA, We all know the ransomware named Cryptolocker it uses RSA 2048 bit encryption. Now is it possible to break the encryption using timing attack. I have ...
3
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0answers
101 views

How much plainext could be known without reducting security of RSA?

It is known, for example, that exposing 50% of most significant bits of RSA private exponent does not provide security risk (when a small public exponent it used). So how to qualify security ...
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1answer
70 views

Necessity of changing $p$ and $q$ when your private key is exposed?

Suppose your private key $d_1$ has been exposed. Instead of changing $p$ and $q$, instead you just choose a new public and private key (say $e_2$ and $d_2$) and use these instead. What kinds of ...
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1answer
93 views

Secrete message sharing using N private keys

I'm looking for an encryption scheme that could possibly meet the following requirements. Let, $X = plaintext$ $M = (pub, priv)$, where $priv == (Ky + Kz)$ Given ...
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1answer
124 views

Non-interactive Zero-knowledge proof signature validation without public key

I'm looking for a method for a scenario with following requirements: At least 3 people (A,B,C,...) are in a Network where they can broadcast messages to everyone but not communicate with a specific ...
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1answer
119 views

Digital signatures under plain RSA

Show that digital signatures under plain RSA are insecure (Plain RSA means that signing is done by calculating $m^d\bmod n$, with $0\le m<n$, and no padding or hashing of $m$). Write an algorithm ...
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0answers
282 views

Who first published the interest of more than two prime factors in RSA?

Multi-prime RSA is now a well known technique: it uses $k>2$ distinct secret prime factors in the public RSA modulus, with the advantage that, using the CRT, we can gain a speed boost in ...
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0answers
55 views

Plaintext patterns leaked based on single bit

Assuming that Elgamal is used as an encryption cipher, where lets say $p$ is 2048bit prime. Is it possible for an attacker to figure out $x$, a secret key, if any part of 2048 bits ciphertext and ...
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2answers
151 views

RSA: What happens to restrictions of plaintext n, dependent on p and q?

Ok - i will try to ask my question as clear as possible. Im getting a little deeper into the RSA-cryptosystem. At one point i'm a little confused. We have a plaintext $x$ and ciphertext $y$, with $x ...
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1answer
186 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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1answer
165 views

Certificate signature with SHA-1 and RSA: where do 1888 bits come from?

Plenty of X.509 Certificates use "PKCS#1 SHA1 with RSA encryption" as the Certificate Signature Algorithm for generating a 2048-bit signature. The SHA-1 hash function generates a hash value of 160 ...
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0answers
78 views

how to calculate power $n$ over Gaussian integers?

In the paper Extended RSA cryptosystem and digital signature schemes in the domain of Gaussian integers the authors calculate $(4007621+145835\cdot i)^{7848211742013} \mod (x)$, please explain to me ...
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3answers
305 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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2answers
196 views

How can I simulate and measure brute force hacking using RSA?

I want to implement brute force hacking using RSA. How can I simulate and measure time duration? What software (or software-based simulator) would be needed?
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2answers
284 views

Securely send public key from client to server in RSA?

I have a client and a server communicating with messages encrypted using RSA. Initially, the client knows server's public key, but the server does not know the client's public key. Is it possible to ...
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2answers
92 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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2answers
141 views

Encryption of a number with RSA bigger than $n$

I'm having trouble understanding why encrypting a number $m$, which is larger than $n=p\cdot q$. I've looked into the following threads: Why RSA can't handle numbers above 76? Why does plain RSA ...
5
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5answers
460 views

Is there a technique to confirm that a given large integer value is a product of two primes?

Given a list of 2048 bit integer values in which one or few 2048 bit integer values may be product of two prime numbers and other values may be just 2048 bit odd integers numbers. My question is - ...
2
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1answer
283 views

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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2answers
377 views

How do institutions like banks do RSA with big primes?

When encrypting with RSA it is often infeasible to decrypt by just doing c^d mod n, because for example when using the primes $(p,q)=(12553,1233)$, which are small ...
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1answer
102 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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2answers
204 views

Avoiding overflow when encrypting with RSA

When encrypting with RSA one calculates $ m^e \pmod n $ by doing the following: m^e % n Where $m$ is what we encrypt. Often $e$ is a very big number to make it ...
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1answer
83 views

Method to calculating e in RSA

For simplicity I choose two small primes for p and q. p=3 q=11 n=33 Φ(n)=20 Now we need ...
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3answers
711 views

How can I find the prime numbers used in RSA?

I got this question in a local hacking event, but I couldn't solve it. Problem Statement ---- Continuing their snooping habit, NSA kept bugging Alice's communication. Resorting to the age old ...
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4answers
468 views

RSA with composite numbers

It has been said that RSA uses a modulus product of two prime numbers for security reasons. But does RSA even work correctly if we allow composite integers instead? I think that the answer is "NO". ...
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1answer
201 views

What does “Inverting the RSA function is as hard as factoring” mean (a rigorous explanation or intuitive will do)?

I was reading that a current open problem is if inverting the RSA function is as hard as factoring. Does this mean that, its an open problem whether, if given a subroutine that computes in ...
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2answers
181 views

RSA cipher wrong use

Why is it foolish if you decide to use an RSA cipher to encode some message by first converting each letter of the message to an integer? So for exmaple Space=0, a=1, b=2,... After the conversion I ...
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1answer
553 views

What is the difference between SHA256WITHRSA and SHA256WITHRSAENCRYPTION digest algorithms?

I installed djigzo on my android phone and I want to use it for smime mail. I don't know the difference between choosing SHA256WITHRSA and ...
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0answers
87 views

Distributed integer factorization?

I'm looking around for publicly published work on factorization of large numbers using distributed systems of any kind. So far I've come across the PDF "Mapreduce for integer factorization" by Javier ...
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1answer
165 views

how do you calculate the private exponent in asymmetric key encryption [duplicate]

Here is an excellent paper on the math of asymmetric key encryption: http://www.mathaware.org/mam/06/Kaliski.pdf‎ See the example on Page 6. The public key = $55$ Primes used to calculate public ...
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0answers
98 views

Can you show how that RSA does/doesn't provide anonymity?

Considering a CPA-secure version of RSA where the ciphertext is just a rundom element from $Z^*_N$. Does that meet the anonymity requirement in which an cpa adversary cannot distinguish between a ...
2
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1answer
148 views

RSA key length choice for TLS when confidentiality not important?

I've a couple of questions about this, the scenario is embedding a key pair in a hardware device which will speak with other hardware devices over tls. computing resources are an issue so i want to ...
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1answer
162 views

Short length asymmetric encryption?

I want to send out short messages to the world which listeners could verify to be send from me. The way this is usually done is to encrypt the message with a private key where the readers decrypt it ...
2
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1answer
160 views

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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2answers
1k views

Why hash the message before signing it? Digital signature with RSA

Here's a method to sign the message with RSA: Why hash the data before signing it? Why not sign the whole message? It'll save time if you sign the hash value, but I've heard there are also security ...
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1answer
46 views

Digital Signature with Encryption

Hope it will be clear. I need to digitally sign pieces of information. What I'm currently doing is the following (for each piece of information): Run SHA1 on the information Encrypt the result with ...
2
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2answers
227 views

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 ...
3
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1answer
165 views

Is differential calculus related to RSA?

I'm writing a high school math paper on RSA and I'm wondering if it's possible to relate calculus to RSA. Is calculus used for any part of RSA? It can be for proving equations/theorems, for generating ...
4
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4answers
408 views

Where does the $\varphi(n)$ part of RSA come from?

$e d \equiv 1 \pmod{\varphi(n)}$ Where does the $\varphi(n)$ part come from? How did the inventors of RSA arrive at $\varphi(n)$?
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1answer
76 views

Usability of padding scheme in blinded RSA signature?

In Wikipedia's article on Blind signature, in the section Dangers of blind signing which describes RSA blinding attack one reads the following This attack works because in this blind signature ...
4
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1answer
298 views

Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5?

I've studied that the Bleichenbacher's CCA attack on PKCS#1 v1.5. is a base to many versions of attacks in the area. I'm trying to understand that attack, but every explanation I saw starts with the ...
6
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2answers
379 views

How does Clifford Cocks 'Non-Secret Encryption' work?

I have read Clifford Cocks "A Note on 'Non-secret Encryption'" and thought I would try to implement this, but I don't seem to be able to get it to work. I'm obviously missing something. From the ...
3
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1answer
124 views

Security Level Estimate when Cascading/Compositing Ciphers?

Way back when, DES had a theoretical security level 56-bits. 2-key TDEA provides about 80-bits of security, and 3-key TDEA provides about 112-bits of security. Obviously, those security levels are not ...
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1answer
168 views

Off-the-record communication

Is my protocol correct? For fun, I tried to design a protocol that would allow off-the-record communication. I'm not sure it works, I have a feeling there might be a problem with it that I'm not ...
3
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1answer
510 views

Good entropy source for generating openssl keys

I need to generate a CA (4096-bit RSA) and server keys for openvpn and I want them to be "top quality". Here is my plan: gather entropy from multiple sources (saving individual files): FreeBSD ...
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1answer
104 views

What parts of number theory does the RSA algorithm use?

It is said that the RSA algorithm uses number theory. What parts of number theory does it use? I know it uses modular arithmetic and Euler's totient theorem and function. Is that all?
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1answer
128 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 ...