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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Modular Arithmetic in RSA

Consider the following the following RSA public key $pk = (N, e) = (1457, 1307)$. (a) Knowing that $187^2 \equiv 1 \pmod {1457}$ find the factorization of $N$. (b) Given the factorization of $N$ ...
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130 views

Random Coin Flip

Quoting an old question: Consider the following protocol for two parties A and B to flip a fair coin (more complicated versions of this might be used for Internet gambling): A trusted ...
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131 views

Could Riemann hypothesis solve certainly RSA?

I don't have the background for dealing with Riemann hypothesis but is well known that covers the prime distribution below a specified number. In order to solve the RSA problem you have to factor the ...
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62 views

RSA Optimal Asymmetric Encryption Padding Beginner

I'm new to the OAEP scheme. I learn it from the Wikipedia page. Link The page does not explain a proper setup for of the system. So I'm not sure if the output of the padding scheme which contains ...
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54 views

help understanding part of Wiener's attack on RSA w/ small d

In this paper, the author writes: Now $k\phi(N) = ed - 1 < ed$. Since $e < \phi(N)$, we see that $k <d < \frac{1}{3}N^{\frac{1}{4}}$. Hence, we obtain: $\mid \frac{e}{N} - ...
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Does OEAP padding limit the size of my modulous to the size fo the hash function?

im looking at wiki at the moment as how to use oeap padding and it appears, help me out if im wrong as G(r) - expands r to the size of the padded message, I am then limited by the size of my hash ...
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153 views

Checking the integrity of RSA public key

Let's say I need to verify a digital signature and the public key is stored in untrusted storage which I need to fetch before I verify the digital signature. However, I can store the cryptographic ...
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87 views

Comparing messages given only the ciphertext

Under RSA protocol I was wondering how a message sent could be verified under the following scenario Alice has a private (encryption key) and public key (decryption key) If Bob sends Alice ...
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122 views

Are there comprehensive alternatives to RSA?

If we wished to, is there a comprehensive alternative to RSA? I say comprehensive as I wonder if there is one which does both encryption and digital signature like RSA? If not, simply what ...
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RSA & DH at risk due to math advances, will this eventually affect elliptic curves too?

I was looking into the predictions by some researchers that RSA and Diffie-Hellman may not be secure in the next few years due to advances in math and being able to calculate the discrete logarithm ...
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Why does the time complexity of RSA encryption and decryption depend on the size of the modulus?

I would think that the time complexity would depend on the exponent, not the number of bits in the modulus. For example, if the exponent were 5, using the "naive" method, we would perform 5 ...
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98 views

RSA: must $d$ be an integer?

I am only taking baby steps in RSA. If $p=11$, $q=7$ and $e=3$, $$\phi(n) = 10*6 = 60$$ Then: $$d = (2 (\phi(n)) + 1 ) / 3 = 121/3$$ Should $d$ be kept as a non-integer or is such a $d$ invalid? ...
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168 views

RSA: Most significant key bit always 1?

Is it possible to say that the most significant bit of an RSA private exponent is always 1? Wouldn't that weaken the key strength by exactly that one bit? I refer to the paper "Timing Attack: What ...
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1answer
75 views

Which hash function is usually used in RSA?

I know there are several available, however I can't seem to find whether there is one standard one or not. I think I understand the process of digital signatures, just wondering which has function is ...
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1answer
134 views

Help understanding basic Franklin-Reiter related message attack

I am trying to understand this attack at the most basic level. I set up the following basic scenario: Let the public encryption exponent, e = 3. Let p, be some arbitrary but known (to the ...
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82 views

Deletion in RSA Accumulator

I am studying RSA Dynamic Accumulator and I have a question: why is simpler to calculate the new accumulator value after a deletion if is known the secret ϕ(n)? Is possible to calculate the deletion ...
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79 views

Does the RSA algorithm use repeated squaring?

Simple question: in order to reduce such huge exponents in modular arithmetic, is repeated squaring used in RSA or is there a better way to implement it?
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Find plaintext of RSA by solving extended euclidean algorith for two encrptions with two different exponents for same plaintext

This is my homework question (but I am not asking the answer to it): Suppose two users Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eA and eB are ...
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46 views

how to calculate maximum data size of an RSA signature

I am reading a content, and am not sure if I follow how they come up with the maximum data size which can be signed by an RSA key. The author states: "...if you are trying to sign a message using a ...
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Why is PuTTYgen-created RSA public exponent(e) not in {3,17,65537}?

As far as I know, RSA public exponent(e) should be one of {3,17,65537}. However, I found PuTTYgen-created RSA public exponent(e) is 0x25(37) by default,as follows, (PuTTYgen version: 0.66) I am ...
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What followed findings of A. Lenstra et al. concerning shared factors of practical RSA moduli?

A. Lenstra et al. had a paper in 2012 "Ron was wrong, Whit is right", in which one reads: "What surprised us most is that many thousands of 1024-bit RSA moduli, including thousands that are contained ...
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89 views

Exactly how slow is asymmetric encryption?

I'm currently doing a project on RSA, and have just come across this website. https://www.namecheap.com/support/knowledgebase/article.aspx/798/67/what-is-an-rsa-key-used-for On here, it says that ...
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1answer
87 views

Why can you reverse a modulo function when knowing its primes

We are dealing with cryptography in school right now and superficially went over the Rabin cryptosystem with the (apparently usual) example of p=7 and q=11 etc (we didn't do RSA). I understand that ...
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164 views

How to generate a bilinear group of prime order p for key generation

I am trying to implement an IEEE Paper In Cryptography. I read many reference regarding an RSA key generation. But i am confused with above statement. Please someone explain me What it says with ...
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16 views

How to generate a bilinear group of prime order p [duplicate]

I am trying to implement an IEEE Paper In Cryptography. I read many reference regarding an RSA key generation. But i am confused with above statement. Please someone explain me What it says with ...
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240 views

Signing/verification between Java and the OpenSSL

I'm trying to sign/verify data between a C application and a Java application. In java for now I was using the built-in JCE provider with SHA256withRSA as ...
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207 views

How long does it take to decrypt an RSA/ECB encrypted message?

I am working on assignment where I have specific scenarios and I am little bit struggling with this one. Alice sends and email to Bob.For this e-mail, she uses the following method of encryption: ...
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92 views

How to compare the efficiency of public key cryptosystems, i.e., RSA vs El Gamal?

As part of my Mathematics degree I'm taking a Discrete Mathematics module which partially covers Public Key Cryptography but does not at all enter it in depth. I'm currently working on a project that ...
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43 views

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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88 views

Securely generating auth tokens

(Disclaimer: I'm an experienced server-side Java programmer, but with little crypto experience.) Objective: I've got a login server which, given a login+password pair, should issue a unique auth ...
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137 views

Cracking simple RSA when just the ciphertext and one public key is known

Can someone explain to me (Or better yet, point me to a tool that does the brute forcing) how to crack a standard, simple RSA cipher (So don't bother with padding) if I know just one public key, the ...
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141 views

Symmetric encryption using RSA for random generated password

I'm fairly new to encryption, so I wanted to check the logic for a .net solution I'm working on that encrypts data between two parties. the receiving (decrypting) party will have an RSA key pair ...
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Leading 00 in RSA public/private key file

I found these following values ALWAYS have the leading 00 in public/private key, public key: modulus private key: modulus, p,q, d mod (p-1), d mod (q-1), coefficient e.g., modulus ...
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17 views

Strength of a cryptography algorithm [duplicate]

I'm just read this article from Atmel corporation in comparing RSA with ECC cryptography algorithms. First of all please read these two paragraphs quoted from the article: P1: Strength of an ...
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1answer
133 views

Consequence of a change on the Guillou-Quisquater Protocol

In the Guillou-Quisquater Protocol, the prover convinces the verifier that he knows an $e$-th root of an element $y \in \mathbb{Z}^*_n$ ($p, q, e$ are primes, $n = pq$ and $e$ is coprime with ...
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Factorizing N to derive D [duplicate]

So I have the value of N. I have to use this value of N to find the value of D. N = 265291078722948385089717069136983657793 Now I read about RSA algos and found out that ...
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118 views

Relationship between exponent and modulus in RSA (as RSA properties as listed in X.509)

In one of my assignments, I had the following question (Please read on. Not a homework assignment :) ): X.509 (1998 version) lists properties that RSA keys must satisfy to be secure. One such ...
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60 views

Calculating Phi(M) and D for RSA decryption given p,q,e

I've been given a message in 4 digit numbers but it doesn't seem to work when I use my calculated values for phi(m) and d. If I'm correct phi(m) = (p-1)(q-1) correct? And d is given by ed = ...
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165 views

RSA vs ECDSA/ECDH

So we've been using RSA for a while now. I wonder, is it still secure? I'm wondering whether surveillance agencies can at this point read traffic encrypted with say, TLS_ECDH_RSA_WITH_AES_128_GCM? ...
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102 views

Why is RSA encryption version 1.0 not specified in an RFC?

I saw that there are three RSA encryption versions, as follows: RSA encryption version 1.5 (RFC 2313) RSA cryptography specification version 2.0 (RFC 2347) RSA cryptography specification version 2.1 ...
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72 views

Find a constant $C$ in $O(Cn^2)$?

I am writing a paper on RSA, and I am calculating some encryption running times. I have been told that the encryption running time is $O(n^2)$ where $n$ is the modulus. I have also been told that ...
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1answer
77 views

Diffie-Hellman using a different modulus on both sides

For Diffie-Hellman Key Exchange, the used modulus is the same throughout the process. Is it possible to use 2 different for both sides? For example, $A \gets M^{d_1} \pmod{n_1} $ $B\gets M^{d_2} ...
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Is using same key pair for both encryption and signing secure in RSA [duplicate]

In GPG, we can use same key pair for encryption and signing. Can't/Shouldn't we do this in RSA. I am using RSAES-OAEP and RSASSA-PSS, not raw RSA btw.
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76 views

How to decrypt RSA cipher text? [closed]

How can I decrypt an RSA cipher text in which I am only provided with a public key and the cipher text. The person who encrypted it made a mistake in taking the exponent.
4
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1answer
200 views

RSA time function

I am doing a paper on textbook RSA (highschool-level). I am explaining and proving the significance of the public key exponent in time and security. So far, I have encrypted a constant message with a ...
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51 views

PublicKey Unknown Encoding

I have a public key: ...
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121 views

Is it possible to correct the exponent of an RSA public key if it has been altered?

Is it possible to change the exponent of an RSA public key?
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Usefulness of ability to calculate $m^{p+q}$ with RSA

I noticed that with only an RSA public key, it is possible/tractable to calculate $m^{p+q} \pmod n$ for any $m$ without knowing $p$ or $q$. Namely, $m^{p+q} \equiv m^{n+1} \pmod n$. (This follows ...
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Is it possible to recover an RSA modulus from its signatures?

Let's say that you have some small number of RSA signatures of known data: you know some pairs $(m_k, c_k)$ such that ${c_k}^e \equiv m_k \pmod n$. If you know $e$, because probably it's one of $\{3, ...
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2answers
111 views

Possible to guess RSA public key $e$ using $n$ and $\phi$

We know that if $n$ and $\phi$ is known, then it is possible to find $p$ and $q$ (initial prime numbers). I have following the questions: Assume the public key $e$ is not known, how difficult would ...