# 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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### RSA least significant bit oracle attack

I have been reading up on RSA attacks and came across one that could be called a least-significant-bit (LSB) oracle attack. For the sake of clarity lets define RSA primes $(p, q)$, private key $d$ ...
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### What kind of machine can generate 100-400 digits prime number? RSA

The 64 bit machine's biggest number can be 2^63 (9,223,372,036,854,775,807). So what kind of a monstrous machine can generate 100-400 digits prime number? I probably don't understand something, so ...
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### Key space: Dense and sparse

I'm taking a cryptography class and I come across these terms dense and sparse key space allt he time. What do they mean? As far as I can I understand, dense key space means that there are more ...
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### Are any Certificate Authorities using 4096 bit keys for their intermediate and root certificates? [closed]

Are any Certificate Authorities using 4096 bit keys for their intermediate and root certificates? I know you can, of course, use a 4096 bit key for your server certificate, but I usually see 2048 bit ...
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### What does an RSA signature look like?

I am using OpenSSL libs to generate signatures. Internally, I learn that a signature is a hash of the message with some padding added to it. I am trying to understand the structure of a signature. If ...
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### Openssl & RSA : how many public exponents are possible?

I would like to know if it is possible to set the public exponent we want with "OpenSSL RSA" or if it is really limited to 2 possible exponents: 3 65537 If yes, why ?
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### How does one deal with a negative “d” in RSA?

I'm trying to write my own RSA implementation using the textbook approach — which I know is not optimal — of picking primes $p$ and $q$, then computing Euler's totient $phi$, then randomly picking an '...
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### Which platforms are most vulnerable to Simple Power Analyse Attack

In a "Simple Power Analyse Attack", the difference in power consumption during multiply or square operation is used. In the RSA decryption process with the "Square and Multiply" algorithm, both ...
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### Decrypting a message without the private key using CRT

I am given 5 different encryption modulus, $N$, each ranging from 78 to 88 numbers long. Then for the encryption exponent, each has the same which is 5. Then I am given 5 different encrypted messages, ...
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### RSA encryption exponent

In RSA public-key material (e, N), why must the encryption exponent e be relatively prime to $\phi(N)$? Why must any public key encryption algorithm resist CPA?
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### Please punch holes in this authentication scheme

Folks, I am undertaking a crypto course in Uni. Our professor asked us to try and design some authentication schemes which are resistant to active attacks. This was just a in class exercise to get us ...
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### Generate key pair deterministically from a particular seed [duplicate]

I've been reading "SQRL Secure QR Login" at Gibson's website, and I'm wondering if there is a way to generate an RSA private/public key-pair based on some cryptographically secure input, so that if ...
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### Can an RSA private key have several public keys?

Ok, so my crpto lecturer in Uni posed this question at the end of the RSA key generation lecture as a brain teaser. I have been thinking about this and I think I have come up with a way ( I am aware ...
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### When NIST disallows the use of 1024-bit keys, what effect will that have on SHA-3 (with max. 512 bits)?

Quoting the article Gone in 60 Months or Less: The National Institute of Standards and Technology (NIST) has disallowed the use of 1024-bit keys after 31 December 2013 because they are insecure. ...
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### Would RSA make sense if we used no computers?

I was recently wondering - would RSA be useful if we brought it to, say, medieval times? Could you choose the keys so that you could encrypt/decrypt messages quite easily, but factoring the private ...
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### how to iteratively calculate a^emod n with modulus n sized 4096 bits

In most sites the exponent of the RSA public key is 24 bits. But the modulus can get to 4096 bits size. I have an accelerator that can get max. 2112 bit size modulus. It calculates ...
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### Hybrid encryption with RSA and AES versus spliting into multiple RSA messages?

I've done research about this subject, but I can't find the answer I'm looking for. The problem is that the string I want to send doesn't fit into the RSA key that the client have, and during ...
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### How can I determine the GPG/PGP key ID from the RSA modulus?

According to http://www.pgp.net/pgpnet/pgp-faq/pgp-faq-keys.html#key-public-key-forgery, key ID is some lower bits sequence from the modulus (i.e. the $n$ variable): A PGP key ID is just the ...
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I am a first year math PhD student with work experience and an MS in math. Do you have any advice regarding internships involved with cryptography and other mathematics other than the NSA? Thanks.
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### What makes RSA secure by using prime numbers?

I am just learning about the RSA algorithm. Looking at the first two steps: Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$. I have some probably stupid questions: Why do $p$ ...
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### RSA Decryption with Private Key but no public exponent

I manually set the RSA private key, given the private exponent and modulus. When I use this key to decrypt a message encrypted using a public key (also set with public exponent and modulus) seems to ...
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### 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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### Can someone explain how this unpadded RSA formula works?

Taken from http://en.wikipedia.org/wiki/Homomorphic_encryption, $\mathcal{E}(x_1) \cdot \mathcal{E}(x_2) = x_1^e x_2^e$ $\bmod\; m = (x_1x_2)^e \;$ $\bmod\; m = \mathcal{E}(x_1 \cdot x_2)$ What is ...
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### PKCS1 and blind RSA signatures

Wikipedia's article on RSA blind signatures says that you need to raise the message $m$ to the secret exponent $d$ modulo the public modulus $N$. Implicit within that, it seems to me, is that m needs ...
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### Is SSH public key authentication weakened by 'none' cipher?

As far as I know, SSH2 first does a key exchange based on the server host key and brings up transport authentication and encryption derived from this kex. The real authentication (password or public ...
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### Should new applications still use RSA? Is it worth going down the ECDH route for protocols?

I am currently designing an application for communication between two and more users. At the moment I am trying to figure out what methods to use for the asymmetric cryptology. With the recent "...
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### RSA key pair generation using PRNG with same seed

I see a lot of Q/A where persons are trying to generate a specific key pair using static data such as a password. Now say we use a known PRNG (dangerous assumption), seeded with a the data as a static ...
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### Is javascript RSA signing safe?

I'm currently working on a secure open source messaging system (https://github.com/DSMNET/DSMNET). I'm currently using the cryptico.js (https://github.com/wwwtyro/cryptico) library to encrypt all the ...
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### Proof of elliptic curve difficulty

Are there any proofs that cryptographic functions on an elliptic curve are any more difficult than the analogues over modulo arithmetic? While at present, ECC appears to be more difficult, as it is ...
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### Key exchange and man in the middle issue. Secure solution

I am trying to design MiTM protected key exchange algorithm. For instance I am using RSA asymmetric keys. Alice and Bob respectively have each their own pair of keys. And they should be able to ...
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### RSA PCKS1 v2.1 RSAES-OAEP algorithm

Using RSA public key (n,e) the encryption of a message is c= (m^e) mod n and the corresponding message is decrypted as ...
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### RSA smaller number work-out-by-hand not working - I think I made a mistake

I tried out the paper/pencil explanation @ http://sergematovic.tripod.com/rsa1.html, and it seemed to make sense just fine until I came to decryption. Here is what I worked out: Key Creation: Choose ...
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### What is the meaning of “trapdoor” in cryptography?

I do not really understand the meaning of a "trapdoor" in cryptography, so here are my questions: What is the meaning of trapdoor and how can I convert a word or string using a trapdoor in ...
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### Why is the complexity of RSA-1024 80 bit and not 86 bit?

Why is the complexity of RSA-1024 80 bit and not 86.76611925028119 bit? Here is the complexity for the GNFS (pulled from the linked Wikipedia article): \exp\left( \left(\sqrt[3]{\frac{64}{...
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### RSA Attack with some known values

There is an RSA implementation which I need to attack to get the encrypted messages. Some of the values are known. Plain text value for input. So if I enter a message, say it "A", the plain text is ...
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### How can I take advantage of repeated patterns in non random RSA prime factors?

I am researching vulnerable RSA moduli which are composed of primes generated with poor entropy. Having a list of these primes I searched for variable sized repeated patterns among them and I noticed ...
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### Is it possible that two distinct RSA moduli share both of their prime factors?

I am using an algorithm (can be found here1) that can compute efficiently the GCD of multiple RSA keys. It intended for RSA keys that were generated with low entropy and may have one of their primes ...
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### What signature schemes allow recovering the public key from a signature?

It seems to be possible to retrieve the (public) key used for creating an ECDSA signature just from the signature alone. This seems like an interesting property; as far as I know, RSA doesn't share ...
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### Can anyone explain most popular RSA attacks like I'm 5?

Suppose I implement RSA myself in C and I use just the formulas from number theory. What attacks would my implementation be vulnerable to? Can anyone explain this to me like I'm 5?
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### 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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### Understanding the “cube-root math” behind an RSA signature forgery

I'm trying to understand the math outlined in this paper on a RSA signature forgery attack. I understand it except for one aspect of how the cube root (that makes the forged signature) is computed. ...
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### Brute force attack on RSA - success criteria?

In a hypothetical discussion we ended up with a concrete question I'd like to find the answer to: If you try to brute force an RSA encryption, but the original vale which was encrypted was just ...
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### Textbook-RSA meet-in-the-middle attack against other RSA based schemes?

A “meet-in-the-middle” (not “man-in-the-middle”!) attack on textbook-RSA was presented to me. The only requirements for it was that the attacker gets the output of RSA and the public key, and that the ...
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### What are the security effects of reusing a public RSA key to encrypt large data by blocks? [duplicate]

I'm trying to figure out a way to do public key encryption on a very large piece of data. For this, I of course want one side to do the encrypting but is unable to decrypt the data, and the other ...
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### CKM_RSA_PKCS vs CKM_RSA_X_509 mechanisms in PKCS#11

What is the exact difference between the CKM_RSA_PKCS and CKM_RSA_X_509 mechanisms in the PKCS#11 v2.20 specification (Please ...
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### Does it necessarily mean that an RSA moduli generated with poor randomness is not random?

In 2012 a group of researchers collected a large amount of RSA moduli and calculated their greatest common divisor in order to find common factors between them. By finding a common factor they could ...
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### Why Elliptic curve cryptography are not popular in practice

RSA and ElGamal can be implemented using the technique of Elliptic curves. I am confused on why the it seems that Elliptic curves are not so popular in cryptographic applications since they provide ...
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### Recent attacks on RSA

At Blackhat 2013 this week, there was a talk saying RSA is (essentially) doomed in the near future. networkworld.com ~ “Black Hat: Elliptic curve cryptography coming as smarter algorithms threaten ...