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 generation of private key using public key

In RSA private key generation e*d ≡ 1 mod φ e is public, also n is public. How to prove mathematically, generation of ...
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1answer
96 views

Proof that $gcd(e, \lambda(N)) = 1 \hspace{1mm} \Longleftrightarrow \hspace{1mm} gcd(e, \varphi(N)) = 1$

What is the proof for the fact that $gcd(e, \lambda(N)) = 1 \hspace{1mm} \Longleftrightarrow \hspace{1mm} gcd(e, \varphi(N)) = 1$ Where: $N = P * Q$ where $P$ and $Q$ are both primes. $\varphi(N)$ ...
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25 views

Reducing key shares in Damgård-Dupont threshold RSA

I'm working on understanding and implementing Damgård, I., & Dupont, K. (2005). Efficient Threshold RSA Signatures with General Moduli and No Extra Assumptions. Public Key Cryptography-PKC ...
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1answer
85 views

RSA: How effective is this keypair-trash attack [duplicate]

A question that could very well be part of xkcd's "what if?": Let's say Monica made a piece of software that sends all RSA keypairs to a central database after they're not used anymore. Something ...
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1answer
89 views

x509 Certificate Signature

I've got a question about the signature of a CA. As I understand, the CA takes the public key of the client and signs it with his own private key by using "md5WithRSAEncryption" (like explained here: ...
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1answer
93 views

Negative exponents in Shoup's threshold RSA?

I'm trying to implement threshold RSA operations, starting with decryption based on Peeters, R., Nikova, S., & Preneel, B. (2008). Practical RSA Threshold Decryption for Things That Think. ...
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44 views

Is signing a message just encrypting it with private key? [duplicate]

I have a simple question, When I sign a message (in RSA) does the program encrypt the text with my private key? Because I can decrypt it with my public key. Yes or no. Is signing a message just ...
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1answer
105 views

RSA: how does it work and how is it more secure than symmetric systems

Before starting the question, I know that RSA is naturally a key exchange cryptosystem rather than an antilogarithm fully implemented for encrypting and decrypting data since the length of the secret ...
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1answer
76 views

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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1answer
56 views

What is contained in a RSA key file? [duplicate]

Consider a RSA key file like this: ...
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2answers
141 views

How does RSA padding work exactly?

I've read everywhere online and people say plain text RSA is very unsafe. To make it safe you pad it but no examples are shown anywhere on how to do it. It's explained that random data is added to the ...
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2answers
321 views

Practical Attack on RSA

Currently I am designing an RSA based application, and I am thinking of how long should the key be in order to be secure against attacks. I know that RSA 4096 bit key can be recovered using Sound ...
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1answer
88 views

Montgomery and Galois fields

I'm a little bit confused about the design of a RSA module in VHDL. My question isn't directly related to hardware design. I've read a lot of publications and I bought also a book. In one publications ...
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0answers
121 views

Two questions on EMSA-PKCS1-v1_5

If I implement EMSA-PKCS1-v1_5 in the following two non-standard ways, what kind of things could go wrong? The padding structure will be referred as (00|01|PS|00|DER(Digest Algo)|Digest), where | is ...
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3answers
218 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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2answers
107 views

RSA signing security

I'm curious about the security of RSA signing with the same public private key pair when the same message is sent multiple times. It's my understanding that once you generate the hash of the message ...
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1answer
113 views

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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1answer
205 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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2answers
176 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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28 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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1answer
161 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
78 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
136 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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1answer
92 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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0answers
134 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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0answers
97 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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1answer
86 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
78 views

Asymmetric sign in public enviroment

I have RTS game, where all players run game and server just relays messages. Game can generate and store text file on player pc. I want to allow some players to be moderators, so I need to sign or ...
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5answers
1k 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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0answers
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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1answer
111 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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4answers
586 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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2answers
131 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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1answer
71 views

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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1answer
198 views

Find private exponent in RSA

The other answers for this confuse me, I know the principle of d in terms of the equation it has to satisfy. However I'm not sure how I would go about finding the private exponent without trial and ...
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2answers
301 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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1answer
93 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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1answer
98 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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0answers
70 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
221 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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1answer
105 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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1answer
83 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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0answers
130 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 ...
2
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1answer
235 views

2048-bit RSA Decryption

If a message is encoded with 2048 bit RSA. The ciphertext is $M^e mod N$. In some cases, the message is short, $ M \approx 10^{20} $. With a high probability, $M$ can be written as $M = ab$ with $a, b ...
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90 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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1answer
87 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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269 views

Timelock puzzle improvment

I came across this question with this answer about a cryptographic timelock-puzzle that needs approximately 30 years to be solved. There is also an explanation with source code for that puzzle ...
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151 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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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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1answer
70 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