Tagged Questions

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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1answer
47 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
498 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
172 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
416 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 $\varphi(n)$?
2
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1answer
82 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
519 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 ...
7
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2answers
460 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
129 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 ...
2
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1answer
170 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
684 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 ...
-2
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1answer
109 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?
1
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1answer
269 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 ...
4
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1answer
176 views

Solve a Modular Exponentiation

It might be common, but if we had to solve an equation like this $m=s^{e}$ mod $n$ where $m,e,n$ are known. How can we find $s$. What optimisations could be applied? And what would the complexity of ...
9
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3answers
526 views

Can we ensure the security of a crypto-algorithm and -implementaton against acoustic cryptanalysis?

Like people always say: “Attacks only get worse…” — which is why I'm asking early. I have been reading the paper “RSA Key Extraction via Low-Bandwidth Acoustic Cryptanalysis” published December 18, ...
4
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3answers
502 views

How to perform authentication without central server in P2P?

How can one be sure that the man who you're talking with is the one who you think he is? i.e. How can one perform authentication in P2P network without a central trust server or Certificate Authority? ...
4
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1answer
374 views

RSA Encryption and Signature - Weak Padding

Assume that I have an plaintext $m$ and it is padded with $randompad||00||m$ and then it is encrypted with RSA and a public encryption key so we get the encrypted $Sm$. Then to assure its integrity ...
6
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2answers
330 views

RSA Signature Weak Padding Attack

Assume that we have a message $m$ of size $n$, and it is padded with two 01 bytes in front. Then the signature $s$ is computed using a private key $ks$. Can we ...
5
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1answer
241 views

RSA exhibits symmetrical properties — is it possible to form a cryptanalytic attack?

This question is broken into two sections really: Symmetry in RSA I have been analyzing raw RSA and I have noticed some interesting symmetrical properties of the algorithm. Assume that $M$ is a ...
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2answers
195 views

Attacks against El Gamal private key

El Gamal encryption involves picking $(p,g,b)$ which is our public key. We compute $b=a^x$ $mod$ $p$. Here, $x$ is the private key which we don't know. What are some efficient and strong algorithms ...
1
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1answer
211 views

What exactly is inside a private key?

May sound stupid to many, but I would like to have some pointers on what exactly is contained inside a private key. I have decent understanding of public/private keys/certificates (have created them ...
2
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1answer
204 views

Hierarchical Encryption

Is there a way to setup a hierarchical encryption using public key encryption? Let's say a higher level user can decrypt messages encrypted by lower level users. Is that possible? I guess it is only ...
1
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2answers
221 views

Encrypt and decrypt data accessible by multiple users within a team

I'm currently working on web services which allows to send and retrieve data. The data belong to a team. A team is composed of users. Each authenticated user can send and retrieve data to/from their ...
1
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1answer
87 views

Sample RSA-style signature confusion

I'm trying to study a simplified TLS-style protocol, including verifying RSA signatures. It's an attempt to verify using only a valid certificate. However, I can't manage to get anything to verify ...
4
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2answers
1k views

In RSA, why is it important choosing e so that it is coprime to φ(n)?

When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$. I know that a common choice is to have $e = 3$ (which requires a good padding ...
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0answers
90 views

Is it possible to modify SSL handshakes to enable PFS while still using RSA during the handshake?

I know we could possibly be using DH key exchange, that would enable PFS. However, what if we make modifications on our SSL 3.0 handshake such that the only cipher we use is RSA for the achieving PFS? ...
2
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2answers
226 views

How does this happen in RSA malleability?

I don't understand how the $E(m)$ turns into $E(mt)$. I mean, I don't know how does that transformation happen and how does the equation occur. $$E(m) \cdot t^e \bmod n = (mt)^e \bmod n = E(mt)$$ ...
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1answer
82 views

Assuming that we had a way of finding primes, could RSA be used without computers?

I once asked a question "Would RSA make sense if we used no computers?". The answer was negative, because finding primes that would make secure keys would prove too hard. Assuming that we had found ...
2
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0answers
114 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
413 views

why RSA uses Semiprime numbers? [duplicate]

Why does RSA use semiprime numbers? Why not just use any big number ?? What is the advantage of the two original numbers being prime? Because factoring any big number will be difficult
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1answer
91 views

How do we arrive to the equation for solving D in RSA?

We have been shown that DE is congruent to 1 mod phi(n). How do we arrive to the real equation for figuring out d that is d = e^-1 mod phi(n). I want to know the entire process. I am just curious, ...
0
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2answers
224 views

Why are these techniques not feasible to crack RSA?

For $d = e^{-1} \mod \phi(n)$ $$d\cdot e \operatorname{mod} \phi(n)=1$$ $$d = (e^{-1} \operatorname{mod} \phi(n))$$ With having $e$ and $n$, we can calculate the value of $d$ , the private key for ...
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2answers
394 views

How do I calculate the private key in RSA?

Given $n=pq$ for $p,q$ known, I can calculate $\phi(n)$. $e$ is selected such that $\gcd (e,\phi(n)) = 1$. Using this, how do I calculate the RSA private key? Example: I have $n = 35$, with ...
4
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3answers
185 views

Why can an RSA signature be authenticated ONLY with the signer's public key?

I'm an undergraduate Math student currently taking a cryptology course. I have a question about the RSA signature authentication mechanism. An RSA signature can be authenticated with the public key ...
1
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2answers
282 views

RSA performance

I was wondering what is the performance bottleneck in RSA algorithm? Is it the size of message, calculating the modular inverse, exponentiation? Say I have a fixed value of n to encrypt and decrypt ...
6
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2answers
825 views

Using the same RSA keypair to sign and encrypt

The RSA signature operation is basically the same as encrypting with the private key. In particular, both operations use the same kind of keys. Is it safe to use the same RSA keypair both for ...
3
votes
1answer
208 views

Purpose of leading zero in PKCS1-v1_5 padding

According to this document the padded message has the following structure: $EM \;= \; 0x00 \; || \; 0x02 \; || \; PS \; || \; 0x00 \; || \; M$ What is the purpose of this null byte at the beginning ...
2
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2answers
145 views

Publicly exposed hash of private key

Would exposing a cryptographic hash function's digest (e.g. SHA-3) of RSA private key data compromise the key? If so, what are the possible (cryptanalysis-) vectors for attacking the key if an ...
2
votes
3answers
286 views

Is it possible to attack RSA with a WalkSat derivative?

We consider a large $n$-bit number $N$. We want to find a factor, if it admits any. For $m$ taking values from $1$ to $n$, perform the following three steps (actually, for each $m$, perform many ...
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0answers
97 views

Unblind a RSA blinded signature

I have blinded $m = 16$ with $r= 13$, $e = 7$ and $n = 209$. This resulted in $m' = 464$, which led to a $s' = 8$. Now, I want to unblind this $s'$ by using $s = s' \times r^{-1}$ but im stuck at ...
1
vote
1answer
441 views

Why does plain RSA not work with big messages ($m>n$)?

From what I can remember, RSA is something like this: Generate 2 distinct prime numbers $p$ and $q$ that have similar bit length. Compute $n=pq$ and $\phi(n)=(p-1)(q-1)$ Compute $e$ such that ...
0
votes
1answer
120 views

Is it possible to decrypt an RSA ciphertext with only $N$ and $e$?

Is it possible to perform RSA decryption if one only knows $N$ and $e$? Failing that, what is the maximum key length where brute-force is still practically feasible?
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2answers
149 views

Any real world implementation using message recovery?

During my master thesis I came across RSA-PSS-R which is in my opinion a quite elegant way of saving bandwidth and space using digital signature. But I didn't find any information about any real world ...
6
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1answer
241 views

Blinding twice in RSA

I understand that if you have a message $m$, you can blind it by selecting a random $r$ and then multiplying $r^e\times m \pmod{n}$ Someone else then signs it with $d$, raising to the power of $d$: ...
2
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1answer
788 views

Is it true for Java that the transformation mode and padding is ignored when using RSA?

Consider GregS's comment to this question (more specific to bouncycastle's provider implementation): http://stackoverflow.com/questions/11717646/bouncycastle-rsa-key-size-and-padding The mode, ...
1
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1answer
178 views

How do I sign data that's been encrypted using public key? (RSA)

I've received a public key to encrypt my data for the other end to decrypt using their private key. Now, they want us to sign the data as well to ensure non-repudiation. I thought that I should only ...
6
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2answers
335 views

Is encrypting credit card numbers one by one with rsautl secure?

I wish to encrypt credit card numbers one by one using asymmetric encryption on the command line. My current approach is this… Encrypt: ...
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2answers
162 views

Would this program be useful in cryptography?

I know nothing of encrypting. I'm not even sure how to tag this. I wrote a program that can calculate this pretty quickly on my macbook pro 2.3GHz IntelCore i7. The two exponents are Mersenne primes, ...
2
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2answers
328 views

Computing p and q from private key

We are given n (public modulus) where n=pq and e (encryption exponent). Then I was able to crack the private key d, using Wieners attack. So now, I have (n,e,d). My question is, is there a way to ...
1
vote
1answer
259 views

Appropriate AES key length for short term protection

Currently I'm doing some initial research for a fully connected distributed network communication model. The context here is a peer-to-peer multiplayer protocol, using a majority-voting system. More ...
4
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4answers
438 views

Why $n=pq$ with $p=2p'+1$ and $q=2q'+1$ instead of just $n=p'q'$ for RSA crypto?

For RSA cryptography, we know that the modulo $n$ is a product of two big prime numbers(say $p$ and $q$). However, in some documents I see an extension of $p=2p'+1$ and $q=2q'+1$ with $q'$ and $p'$ ...