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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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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357 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
88 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, ...
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2answers
219 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
362 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 ...
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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 ...
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267 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 ...
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712 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 ...
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1answer
201 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 ...
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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 ...
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3answers
285 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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96 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 ...
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1answer
391 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 ...
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1answer
118 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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139 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 ...
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1answer
235 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 $d$: ...
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1answer
661 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, ...
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1answer
176 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 ...
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329 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
161 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, ...
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2answers
282 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 ...
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1answer
247 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 ...
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4answers
426 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 $p'$ ...
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183 views

Factoring large numbers

I am trying to factor few integers that are each between 115 and 135 digits long. I have just, little over a month ago, began my study of Cryptography. I was wondering if anyone knew of any efficient ...
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1answer
277 views

RSA 896 vs 1024 vs 2048 in Javascript?

I am currently working on a secure messaging website and I had been using RSA 2048 for encryption, decryption and signing of messages but I found it to be EXTREMELY LAGGY so i've moved to 1024. I did ...
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1answer
86 views

What is the difference between exhaustive search and factorization in relationship to determining a key?

It seems to me an exhaustive search would simply try to use all the possible bit combinations of a key, while factorization is some mathematical formula for determining the key? When discussing the ...
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1answer
931 views

Does ssl_rsa_with_rc4_128_md5 have known weaknesses?

My bank's website uses HTTPS with the cipher suite ssl_rsa_with_rc4_128_md5. What are the known weaknesses of this suite? Do they have a practical impact for ...
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1answer
474 views

How are IVs used in association with RSA Encryption?

How are IVs used in association with RSA Encryption? Can someone explain why we use them in this RSA context?
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2k views

HMAC SHA256 vs RSA SHA256 - which one to use

Salesforce recently announced they are moving away from HMAC SHA256 to RSA SHA256. Why did they make that move?. Any technical factors? Is HMAC really easy to break? ...
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1answer
389 views

RSA with modulus product of many primes

I would like to ask what happens if we build an RSA system with modulus a product of more than 2 primes, for example let $n=p_{1}p_{2}...p_{L}$. I know only the classical RSA system with $n=pq$ with ...
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1answer
138 views

Good Encryption Exponent

I have placed a bet that I can create a public key such that my adversary will not be able to crack (decrypt) it for at least one week. For my primes $p$ and $q$, I chose very large numbers that are ...
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326 views

RSA decrypt long messages (javascript)

I am attempting to encrypty/decrypt a long message in RSA using javascript (with crypto-js and jsbn libraries). I posted this on stackoverflow too but I figured someone here on crypto might be able ...
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169 views

Isn't the deterministic property of (EC)DSA a security problem?

From what I read in Wikipedia's article "Elliptic Curve DSA ~ Security", the "deterministic" generation of $k$ can help prevent certain type of attacks (such as the one happened to Sony). However, ...
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1answer
191 views

In RSA, what is faster attacking “d” when plaintext is known, or factoring when M is unknown?

I'm aware of two methods to attack RSA: Brute force factoring, where no plain text is available Brute force (1/e) mod φ where the plain text is available as described here Question Given an ...
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1answer
299 views

How difficult is it to brute force d in RSA: d = (1/e) mod φ in a CPT attack?

Given that RSA key generation works by computing: n = pq φ = (p-1)(q-1) d = (1/e) mod φ If I was an attacker who wanted to brute force d, could I brute force d given just the public key, the ...
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162 views

Diffie-Hellman exchange

So for a Diffie-Hellman problem, I am given the prime $p$ for the Diffie-Hellman exchange. I am also given $g$, secret number for machine as $A$, secret number for station as $B$, a Diffie-Hellman ...
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1answer
195 views

How vulnerable is RSA when using it to encode ~1000s of datasets with 500bytes each? How easy can the private key passphrase be hacked?

I know that this is not the best use case for RSA, but for a customer of mine I have to encode user data on the server in a way so that it can be decoded/downloaded by the customer through a "secure" ...
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134 views

How can one calculate the estimated RSA key life based on Moore's law?

How can someone estimate the number of years needed to factor an RSA key based on the advancement of technology if followed Moore's law?
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607 views

Bleichenbacher 1998 “Million message attack” on RSA

I have been reading Bleichenbacher's 1998 paper on a forged message attack on RSA. The paper assumes access to an Oracle that takes a ciphertext $c$ and will check the decrypted text for valid PKCS #1 ...
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1answer
96 views

Verifying a Signature

Alice publishes $(n,e)$ where $n$ is exponential modulus and $e$ is the public key. We have $n=80$ digit number and $e=3$. Bob, in correspondence with Alice, asked Alice to prove she is really Alice, ...
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1answer
327 views

Prime number theorem - RSA

I am having trouble understanding the prime number theorem. As part of some revision for an exam, I am trying to answer the following questions (but seeing as I don't understand the concept of the ...
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1answer
56 views

RSA Proof - di-mgt - modulo properties

I´m trying to follow one of the very detailed RSA Proofs given by di-mgt: "RSA theory", but unfortunately I stuck at the beginning of solution (chapter 3). I don´t understand where the second part ...
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1answer
844 views

RSA square and multiply

If an RSA encryption uses a modulus $n$ of 15000 bits and $e = 3$ or $e = 2^{16} + 1$, how many squarings and multiplications will we need for encryption, and for decryption? Could you please explain ...
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435 views

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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266 views

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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192 views

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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198 views

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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1answer
345 views

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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2answers
248 views

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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399 views

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 ...