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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Sender and receiver having different moduli conflicts with encryption and signing in RSA

I should implement a security protocol as a part of which I need to: Encrypt the message with receiver public key. Sign it with my private key. Send it to receiver. Suppose that the system uses a ...
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3answers
14k views

RSA encryption with private key and decryption with a public key

When using the RSA cryptosystem, does it still work if you instead encrypt with the private key and decrypt with the public key? What about in the case of using RSA for sender authentication?
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112 views

RSA encryption and signature padding flaw

This is Oxford's computer security exam question: Suppose that Bob has published an RSA encryption key $ke$ (retaining in secret the corresponding decryption key $kd$), and Alice has published a ...
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1answer
191 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
346 views

Prove that textbook RSA is susceptible to a chosen ciphertext attack

Given a ciphertext $y$, describe how to choose a ciphertext $\hat{y} \neq y$, such that knowledge of the plaintext $\hat{x}=d_K(\hat{y})$ allows $x=d_k(y)$ to be computed. So I use the fact that the ...
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0answers
106 views

Rabin/RSA four possible messages?

Given this encryption method: $$f_{N,e} : Z^{*}_{N} \to QR(N)^{*};\quad f_{N,e}(x) = x ^{2e} \bmod N$$ I need to show that, for any $x_{0} \in Z^{*}_{N}$, there are four elements $x \in Z^{*}_{N}$ ...
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1answer
167 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 ...
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3answers
306 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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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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3answers
130 views

Question on RSA trapdoor permutation

You plan to use a public-key cryptosystem based on the RSA trapdoor permutation in three different real-life applications, in which the attacker has, respectively, only one of the following resources: ...
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0answers
93 views

m ∈ Zn \Z*n, RSA works but not secure

If you happen happen to have a message m ∈ Zn \ Z*n, RSA works but not secure. How likely is it going to happen? |n|=1024 bits |p| = 512 bits |q| = 512 bits.
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113 views

New modulus or new key pair?

I have this assignment question that I'm not sure how to answer. Any insight would be helpful. In the RSA public-key encryption scheme, each user has a public key, e, and a private key, d. Suppose ...
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1answer
146 views

Breaking RSA when some bits of one prime are known

RSA primes are 100 bit. You know first 80 bits of one of the primes. In this system, come up with an efficient way to decrypt the cipher-text. This was the question on my quiz. I'm not sure how ...
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1answer
74 views

Multiplication-homomorphic schemes

I'm looking into multiplication-homomorphic schemes now and basically I see that there are 3 options: RSA, Boneh-Goh-Nissim and ElGamal. RSA was proved to be insecure unless message is randomly ...
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0answers
97 views

Commutative Encryption with RSA scheme?

I wanted to know how I could manage to do what I'm going to tell you next, with the RSA encryption/decryption scheme. So Alice and Bob each have a public key $(n, e)$ and a private key $(p, q, d)$; ...
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1answer
89 views

Modulo properties of two prime numbers

I am supposed to prove that x = y mod (p*q) <=> x = y mod p and x = y mod q with p and q are prime numbers. It somewhat sounds reasonable to me, but unfortunately I don't have any clue how to prove ...
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2answers
117 views

Three different numbers with x³=x mod p

p is a prime greater than 2 and $a \in \mathbb{Z}_p$. Why are there exactly three solutions for a³ = a mod p? Obviously 0 and 1 are both in $\mathbb{Z}$ and valid solutions, but that still means, ...
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1answer
117 views

Pick faster private exponent

I recently tried to send 1536-bit modulus CSR to COMODO. They refused to sign the certificate. I later found out that it's because NIST mandated 2048-bit modulus on the SSL certificate. I think it's ...
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1answer
206 views

Montgomery Ladder vs Double-and-Add

I would like to know what (if any) are the advantages of using Montgomery Power ladder over the Double-and-Add-Always algorithm. I think that firstly, Monty would be slightly faster than DoubleAndAdd. ...
2
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1answer
328 views

Precomputation attacks on RSA

Are precomputation attacks - such as outlined in RFC 3610 chapter 5 - possible on RSA PKCS#1 v1.5 signature generation? If yes, are such attacks taken into account when calculating the cryptographic ...
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2answers
159 views

Creating a license system based on asymmetric encryption (RSA or ECDSA)

I’ve spent a couple of days researching the topic of creating a license system for my desktop software. While I fully understand that there’s no perfect copy protection, this approach seems to have ...
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1answer
94 views

RSA: Fermat's Little Theorem and the multiplicative inverse relationship between mod n and mod phi(n)

I'm learning about the proof of the RSA encryption algorithm, and I'm clearly fudging or missing something, because for me it doesn't add up. When generating keys for RSA encryption, we make sure ...
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Does RSA work for any message M?

I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but ...
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1answer
194 views

how to use common modulus attack?

I am struck with the following problem: Let Alice, Bob, Chris and Eve communicate over a public network. They encrypt all messages they send using RSA system. Bob and Chris have the RSA modulus ...
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1answer
52 views

How small are we talking about when defining the small public/private key exponent [duplicate]

I've been wondering about the 'small' part of the attacks on RSA, like the small public key exponent and the small private key exponent and what's not really clear is how small are we talking about? ...
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1answer
45 views

The improvement of the private key exponent in the M.Weiner Attack

I am working on attacks on RSA and came across the M. Weiner attack. The limit for $d$ in order for the attack to apply is $d <= (\frac{1}{3})N^{0.25}$. The paper states that Boneh and Durfee ...
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3answers
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Why is elliptic curve cryptography not widely used, compared to RSA?

I recently ran across elliptic curve crypto-systems: An Introduction to the Theory of Elliptic Curves (Brown University) Elliptic Curve Cryptography (Wikipedia) Performance analysis of identity ...
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2answers
161 views

Is RSA key size the size of private key exponent in public key encryption?

I have implemented a key pair generation scheme for RSA algorithm. I have taken the length of private key exponent as RSA key size, but then I've got to know that RSA key size is the size of the ...
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1answer
124 views

RSA and ECDSA performances

Signature algorithms with elliptic curves have small output sizes compared to RSA for the same level of security. What about the processing time to generate a signature ? I've seen figures giving ...
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4answers
589 views

Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key?

I have just learned about using PGP/GPG for email encryption and one thing has always bugged me: How is it possible that a message encrypted with somebody's public key can be decrypted only with that ...
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3answers
666 views

Is sharing the modulus for multiple RSA key pairs secure?

In the public-key system RSA scheme, each user holds beyond a public modulus $m$ a public exponent, $e$, and a private exponent, $d$. Suppose that Bob's private exponent is learned by other users. ...
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1answer
48 views

How to write the encrypted message after using RSA

I have created a RSA encryption/decryption program but how do i write out the results after doing a encryption? Right now I have it so that it will just print out the decimal value of one character ...
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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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2answers
102 views

Understanding math behind RSA key derivation [duplicate]

I was reading through the key derivation for RSA. Here are the steps per wiki - Select strong primes $p$ and $q$ such that $pq = n$ $\phi(n)$ = $(p-1)(q-1)$ select $e$ such that $e$ and $\phi(n)$ ...
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2answers
150 views

How can one encrypt with RSA (or ElGamal) without revealing whom the ciphertext is intended for?

Imagine Alice wants to encrypt for Bob and post this encryption publicly, so that only Bob can decrypt but no one can other than Alice or Bob tell that the message was encrypted for Bob. The naive ...
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0answers
1k views

encryption and decryption time for RSA-crt in java? [duplicate]

I try compute execution time for encrypt and decrypt data has 1024 bit = 128 byte in RSA-crt algorithm. I need this results. But I believe this result wrong. because big diffrent between execution ...
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1answer
2k views

Security strength of RSA in relation with the modulus size

NIST SP 800-57 §5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength $s$ in bits: ...
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1answer
104 views

Sequence of Encrypting RSA like Chaum Blinding scheme

I'd be a noob in cryptography but reading up a little on RSA, I do get some understanding and I want to specifically resolve this issue. UPDATED Lets say we have the following values in place: ...
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1answer
88 views

RSA private exponent primality

I know that the public exponent is always a prime, but what about the private exponent? Is it always a prime too?
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1answer
81 views

Low level explanation of how a message is sent via RSA

I understand that RSA encryption uses this formula: C = M^e (mod N) public key is e and N N is pq - p and q are private key. mod N makes above function one-way ...
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1answer
217 views

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 = ...
3
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1answer
310 views

ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
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1answer
139 views

Why should a signature use PSS padding in RSA?

Suppose I send a message using AES (private keys already negotiated securely) and I send a hash of this message using RSA (encrypted with private key) with OAEP to verify the authenticity and ...
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46 views

RSA Key Blinding

I was looking the answer to the following question (Timing attack on modular exponentiation), discussing the Private Key Blinding as a countermeasure for timing attacks. Therefore I'm asking if ...
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1answer
58 views

Symmetry between a public and a private key

I know that the private and public key in assymetric cryptography are different and the public is used for encryption while the private for decryption. My question is if they are symmetrical to each ...
2
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2answers
825 views

Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA. (Note: I do realize that in practice this is done through an intermediate symmetric key, but ...
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71 views

Cryptodefense ransom use RSA-2048. Any chance with known plaintext attack? [duplicate]

The "new" kind of ransomware invade your computer and crypt all your files using the RSA-2048. Personally, I have been victim of cryptodefense: 40000 files encrypted... I'm not going to pay anything ...
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1answer
238 views

Decrypting a small Message using RSA with a Private Key [closed]

If I have a private key of (43, 341). What would be the steps I need to take to decrypt a small message using RSA? I have looked ...
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1answer
276 views

Is knowing the private key of RSA equivalent to the factorization of $N$?

Given the RSA modulus $N$ the fastest method to factor it is of sub-exponent order. But, now if I know the private key $d$ of RSA, does that mean I can factor $N$ efficiently?. It intuitively seems ...
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1answer
77 views

RSA Proof - Is Z(n) closed under multiplication

In RSA proof it can be proved that $\mathbb{Z}^*_n$ is closed under multiplication. Can it be also proved that $\mathbb{Z}_n$ is closed under multiplication? If yes, then how?