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 Decryption from samples

I am working on a project for a client which involves decryption of data which was encrypted using RSA. The system in question retains three independent copies of each data-set, but each copy is ...
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312 views

RSA key pair generation and FIPS 140-2, 186-4

I need to securely generate RSA key pair and I need to have access to private exponent in order to process it further. What's the difference in FIPS 140-2 and FIPS 186-4 in connection with RSA key ...
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124 views

Java RSA Padding: no libraries used

I'm trying to implement RSA without using any java libraries using the algorithm from wikipedia HERE So, anyone can clearly see that it is a raw RSA, and can directly be attacked. The question is ...
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123 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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57 views

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 ...
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82 views

Fault encryption attack on RSA [duplicate]

How to recover plaintext, if we know public key(RSA), correctly encrypted text and text encrypted with faulty public key, where one bit is changed?
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52 views

Is the half-homomorphic property of RSA a problem for blind RSA signatures?

For blind RSA signatures, is it problematic that RSA is half-homomorph? Take a scenario where blind RSA signatures are used for something like a voting procedure or this proposal: Lots of people, ...
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14k views

How does RSA signature verification work?

I understand how the RSA algorithm works for encryption and decryption purposes but I don't get how signing is done. Here's what I (think) I know and is common practice: If I have a message that I ...
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2answers
637 views

If we can find prime numbers larger than 17 milion digits, why can't we find all 1024bit primes? [duplicate]

"Largest Known Prime Number Discovered; Has 17,425,170 Digits" http://www.sciencedaily.com/releases/2013/02/130213225424.htm If we can find prime numbers larger than 17 milion digits, why can't we ...
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69 views

RSA Key composition

I'm trying to figure out how it is composed the RSA key. Follow what I know : For a RSA 2048, 2048 is the bit length of the module. The public key is composed by $(e,M)$ when $e$ is the public ...
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115 views

Convert numeric message from RSA ciphertext to alphabetic

I have a set of numeric values that are supposed to represent a message encoded via textbook RSA. For example: 60889 37946 13359 61629 35960 13747 I've decrypted ...
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56 views

Full Domain hash library

I need to know if any of the well-known crypto libraries (openssl, crypto++) supports full domain hash function. If not, what library I can use?
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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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67 views

Crack RSA with additional information [duplicate]

Suppose $N=3953$, Alice encryption key is $e_A = 337$ and bobs is $e_B=23$. Eve happens to know the corresponding decryption keys, $d_A=3385$ and $d_B=2663$. Can I use this information to find the ...
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1answer
76 views

Questions about updating the secret key of RSA?

I want to update the secret key of RSA. I understand there exists a common modular attack on RSA. Precisely, if adversary knows $(e_1, m^{e_1})$ and $(e_2, m^{e_2})$, where $e_1$ and $e_2$ are the ...
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1answer
83 views

Prime modulus for RSA and sharing a secret?

According to this paper entitled "Using Commutative Encryption to Share a Secret" they define their modulus to be a large prime p, which is public. Both exponents are private in this case. According ...
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1answer
285 views

Storing AES encrypted RSA private keys on a server

I'm thinking about creating an encrypted messaging web application where users create RSA key pairs, they store the public key on the server for others to see and also store an AES encrypted private ...
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0answers
43 views

RSA algorithm in this doesnt (ever) give right decryption [duplicate]

Lets consider p=47 q=57 msg=3 n=p*q=2679 ф(n)=2576 now e=11, and inverse of e is 1171 modulo ф(n) y=msg^e=333(mod n) ///Encryption y^d=1131(mod n) ///Decryption but this is not original message ...
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2answers
133 views

How fast would a polynomial time factoring algorithm compute?

I know factoring is the chief means of breaking RSA keys. I know an algorithm that runs in polynomial time would be able to break an RSA key pair "quickly". But how quickly is "quickly"? Note, I'm not ...
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489 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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2answers
78 views

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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2answers
727 views

Can RSA encryption produce collisions?

In RSA, a message is encrypted by $m^e \pmod N$. $N$ is the modulus, $m$ is the message and $e$ is the public exponent. (I know that $m$ should not be greater than $N$.) My question is, can $m^e$ be ...
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1answer
92 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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93 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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243 views

Can public key be recovered from ciphertext & encrypted private key?

I'd like to implement something like a write-once public/private encrypted shared secret (no better quick description for the lack of terminology knowledge). I guess, I'm trying to implement HSM. The ...
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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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2answers
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State of the art RSA key generation

I would like to know if there is an algorithm to generate a RSA key at the state of the art of the present cryptanalysis. Beside the key lenght I know there are some weakness in the choice of prime ...
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3answers
2k views

Why should the RSA private exponent have the same size as the modulus?

Consider the generation of an RSA key pair with a given modulus size $n$ and a known, small public exponent $e$ (typically $e = 3$ or $e = 65537$). A common method is to generate two random primes ...
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3answers
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In RSA, why does $p$ have to be bigger than $q$ where $n=p \times q$?

In openSSL – during RSA key generation – if $q$ is bigger than $p$, they exchange them. Why is that?
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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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81 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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Selection of cryptographic functions for OAEP

I can't understand how the "cryptographic functions" are to be selected RSA + OAEP which are used in OAEP. How to choose these "cryptographic functions"(G and H)?
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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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101 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
70 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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130 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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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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176 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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How big an RSA key is considered secure today?

I think 1024 bit RSA keys were considered secure ~5 years ago, but I assume that's not true anymore. Can 2048 or 4096 keys still be relied upon, or have we gained too much computing power in the ...
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120 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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106 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
164 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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290 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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174 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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27 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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150 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
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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
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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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P = NP and current cryptographic systems

I've recently heard some people claiming that if the fact that P = NP is proven, most (all?) the current cryptographic algorithm considered secure like RSA will be unusable in secure systems. My ...