Cryptography Stack Exchange
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Questions tagged [rsa]

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 with proper paddings.

RSA is named after its inventors Ronald L. Rivest, Adi Shamir, and Leonard Adleman.

The security of RSA depends on the hardness to factor big numbers (e.g. the public key) into its prime factors (to derive the private key) and RSA problem.

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What data is saved in RSA private key?

What data is saved in RSA private key in openssl? How to view it? Wikpedia says these variables are saved.
Smit Johnth
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How do ciphers change plaintext into numeric digits for computing?

For example, in RSA, we use this for encryption: $ciphertext = (m^e \mod n)$ and for decryption. If our message is "hello world", then what number do we have to put as $m$ in the RSA formula?
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Is there a specification for the "BEGIN RSA PRIVATE KEY" format?

Until now I didn't find a specification (RFC or similar) for the file format that uses the BEGIN RSA PRIVATE KEY prefix and END RSA PRIVATE KEY suffix. Where is it defined? Is there an official name for it? It seems to be at least related to the…
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RSA Proof of Correctness

Can anyone provide an extended (and well explained) proof of correctness of the RSA Algorithm? And why is it needed? I can't say that this or this helped me much, I'd like a more detailed and newbie like explanation, if you don't mind too much... ;)
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RSA cracking: The same message is sent to two different people problem

Suppose we have two people: Smith and Jones. Smith public key is e=9, n=179 and Jones public key is e=13, n=179. Bob sends to them a message $M$. The encrypted message $C_s$ to Smith is 32. The encrypted message $C_j$ to Jones is 127 I tried to…
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RSA encryption using multiplication

Generally in RSA we encrypt as $m^e \pmod n$. Will RSA work if we replace the power by normal multiplication? $E = (m \times e) \mod n$ and decryption as $c \times d \mod n$. What will be $d$ disadvantage if it works ?
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How much stronger is RSA-2048 compared to RSA-1024?

How much stronger is RSA-2048 compared to RSA-1024? It is hard to imagine very big numbers. So what would be your way to explain the difference to someone who doesn't know much about cryptography?
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Can RSA be used to encrypt p?

In RSA you choose $n=pq$ where $p$ and $q$ are large primes with similar length. Then you choose $e$ that is coprime with $\phi(n)$ and find $d$ that is modular multiplicative inverse of $e$ modulo $\phi(n)$, so $ed \equiv 1 \mod \phi(n)$. Then…
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Encrypting small values with RSA private key

I'm looking for best practices when it comes to encrypting small (< 128 bytes) amounts of data with the RSA private key. Signing it would make the resulting payload too large.
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Is this definition of an RSA modulus safe?

Suggested definition A positive integer is a safe RSA modulus if, after removing all its prime factors less than 512 bits, it is composite and has size at least 2048 bits. Discussion I want to build the smallest-possible safe RSA modulus without a…
Randomblue
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Is an RSA variant with public exponent $e=f+(p-1)\cdot(q-1)$ safe (for $f$ random in some small interval)?

Alice is going to use some existing RSA scheme (employing industry-standard signature or/and encryption with proper padding), which she can't change, or influence beyond her choice of key. In this scheme, all public modulus $n$ are exactly $b$ bits…
fgrieu
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33c3ctf beeblebrox RSA Sign challenge: any tipps?

I recently participated in the 33c3 ctf competition and tried to solve the beeblebrox challenge but could not crack it and nobody posted a writeup/exploit of it so far so I want to get help solving it (the competition is long over). You can get the…
arturh
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Is it possible to apply RSA on complex numbers?

RSA is a popular public-key cryptography algorithm. It has some mathematical assumptions. I mean, one cannot apply RSA on elements of any algebraic structure. Elements from certain algebraic structures are only eligible for utilization in RSA. I…
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If we can find prime numbers larger than 17 milion digits, why can't we find all 1024bit primes?

"Largest Known Prime Number Discovered; Has 17,425,170 Digits" http://www.sciencedaily.com/releases/2013/02/130213225424.htm If we can find prime numbers larger than 17 milion digits, why can't we find all 1024bit (just 309 decimal digits) primes?
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RSA: What would happen if you chose n to be a prime?

If Alice were to choose n to be a prime, instead of the product of two primes, what exactly would go wrong in the RSA cryptosystem? How would Bob decrypt her message?
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