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.

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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 ...
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RSA enc/decryption with multiple prime modulus using CRT

Every information I found on internet about RSA-CRT encryption/decryption uses only two primes. I'm interested in my project in doing that using multiple (up to 8) primes. The general idea is to ...
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ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
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What does “Inverting the RSA function is as hard as factoring” mean (a rigorous explanation or intuitive will do)?

I was reading that a current open problem is if inverting the RSA function is as hard as factoring. Does this mean that, its an open problem whether, if given a subroutine that computes in ...
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RSA-based authentication and key-agreement protocol

An authentication and key-agreement protocol between devices shall mutually demonstrate their identity, and establish a shared random secret $R$ suitable for securing later communications. To that ...
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why did oaep change from pkcs1 v2.0 and v2.1?

In PKCS1 v2.1 the OAEP output is prepending with a null byte. Quoting RFC3447, ...
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State of the art RSA key generation

I would like to know if there is an algorithm to generate a RSA key at the state of the art of the present cryptanalysis. Beside the key lenght I know there are some weakness in the choice of prime ...
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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 bottom ...
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In textbook RSA with low public exponent, how big does a random message needs to be?

Assume RSA with a public modulus $N$ of $n$ bits, a small odd public exponent $e$, plaintext $M$ a random non-negative integer less than $2^m$ for some integer parameter $m$, with $M\mapsto C=M^e\bmod ...
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RSA factorization with special primes

Suppose that primes for RSA modulus are generated using formula: $P_i(x,y) = \operatorname{next\_prime}(x^{z_i}+y^{z_i}) = x^{z_i}+y^{z_i}+d_i$ where $x,y$ are unknown random numbers with size 128 ...
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Are there attacks against broken RSA signature pad checking with $e = 65537$?

Let's say that an RSA implementation of PKCS #1 signatures fails to validate that the 00 01 FF FF FF ... FF 00 portion of the decrypted signature is exactly as long ...
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RSA: What would happen if you chose n to be a prime? [duplicate]

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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Can RSA encryption produce collisions?

In RSA, a message is encrypted by $m^e \pmod N$. $N$ is the modulus, $m$ is the message and $e$ is the public exponent. (I know that $m$ should not be greater than $N$.) My question is, can $m^e$ be ...
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RSA4096 vs AES256 for secure Chat application?

Which of these two methods suits better the implementation of a secure chat application? In this context, chat will be limited up to 150 letters for one message. I would prefer RSA because what I ...
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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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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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Can an ephemeral RSA key give forward secrecy?

Suppose party A generates an ephemeral RSA key and sends the public key to B. Party B then generates a symmetric key, encrypts it with Party A's public key and sends the Ciphertext to Party A. Party ...
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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 ...
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In RSA, do I calculate d from e or e from d?

In the original paper introducing RSA, it is implied that one should first choose $d$ and then calulate $e$ from $p$, $q$, and $d$. However, I have found in other places (such as the wikipedia article ...
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Why should the RSA private exponent have the same size as the modulus?

Consider the generation of an RSA key pair with a given modulus size $n$ and a known, small public exponent $e$ (typically $e = 3$ or $e = 65537$). A common method is to generate two random primes ...
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Why is RSA encryption significantly faster than decryption?

I am designing an implementation of RSA . I recorded computation times in Java by using System.currentTimeMillis(). It returned an encryption time of 0.05 ms and ...
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Reverse engineering secret key in RSA encryption with the help of signature

Consider the following: $i$th message, $m_i$, in its original state. $i$th message, $M_i$, encrypted message $m_i$ using public key. Public key, $p$, in a $b$-bit RSA encryption setup. We can ...
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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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How to argue to a paranoid that RSA is safe?

From today's standpoint, most people would claim RSA to be secure. However, to my knowledge, this is purely based on the speculation that no one knows a computational feasible way to find a $d$ for ...
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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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How do other, non-RSA algorithms, compare to the PKCS #1 standard?

Arguably the PKCS suite of standards have a profit-oriented bias as they are promoted by RSA and promote their algorithms over others in the form of RFCs and other means. I'm considering the ...
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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 ...
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RSA blind signatures in practice

Hi I have a problem with moving my blind signature implementation from educational (textbook RSA) to more practical (padded RSA) side. David Chaums paper gives a following figure: $r$ - blinding ...
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What does “a 15360-bit RSA key is the equivalent to a 256-bit symmetric key” mean?

NIST key management guidelines suggest that 15360-bit RSA keys are equivalent in strength to 256-bit symmetric keys. If a 15360-bit RSA key is the equivalent to a 256-bit symmetric key, does that mean ...
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Why isn't Rabin-Williams cryptosystem widely used?

I think we all know RSA. And of course we also know DJB (a.k.a. Daniel J. Bernstein). Now some already have noticed that he has an opinion towards cryptographic questions. In his 2008 paper ("RSA ...
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In RSA, rationale for prime $p$ with $p-1$ having prime factor $u$ with $u-1$ having large prime factor?

In the 1978 RSA paper, it is recommended, among other things, to choose primes $p$ such that $(p-1)$ has a large prime factor $u$. This was motivated by Pollard's p-1 algorithm. Further, the authors ...
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Is it possible to have multiple RSA private keys?

I just did some math: Pick $p$ and $q$ distinct primes; Calculate $N=p\cdot q$; Calculate Euler`s totient => $\phi=(p-1)\cdot(q-1)$; Pick an $e$ (public key), coprime with $\phi$; Calculate $d$ (...
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When/why is RSA (hybrid) encryption used rather than alternatives?

I've read that RSA is not meant for encrypting large plaintext because: (Are these also true for other public-key encryptions like ElGamal?) It is slow. Padding makes the ciphertext blocks much ...
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What is the harm if I publish an encrypted RSA private key publicly?

What is the harm if I publish an encrypted RSA private key publicly? Or in this case, what is the harm if I publish many thousands or millions of them? Assuming that the private key is encrypted ...
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Deterministic RSA blinding

I have an implementation of the RSA private key operation in a context where I don't have access to an entropy source. I'd like to add blinding to it (both message and exponent), to make it resist ...
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Can RSA be securely used for “blind decryption”?

Assume we have the following setup: A client with trusted storage and computing capabilities (e.g. a smartcard) A server with trusted computing and short-term storage capabilities (e.g. RAM + CPU, ...
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Bleichenbacher RSA1024 signature forgery, closed-form solution

Hal Finney's writeup (Bleichenbacher's RSA signature forgery based on implementation error) shows a formula for RSA3072. I tried to replicate the attack for RSA1024 and failed, since the first term of ...
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Why can’t the public key exponent in RSA be negative?

I am looking at why certain public keys in RSA can't be used, such as: 2 and all other even numbers (since $\gcd(\phi,e)$ must equal 1) 1 (since the cipher text would equal the message) 0 (since the ...
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Initialize a PRNG with a password

Let's assume that we have a secure PRNG. Is it "safe" to initialize it with password, or seed based on a password like SHA256(password)? If yes, is it "safe" to generate an RSA or DSA key from it? ...
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Why are RSA ciphertexts different for the same plaintext?

I am using SpongyCastle for a project in android. I have used RSA to encrypt the data and then decrypt it in another activity, the keys are stored in the shared preferences. I discovered a thing I ...
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RSA: Letting $p$ and $q$ have different bit-size

I am aware that there are concerns if $p$ and $q$ are close i.e. $\Delta=|p-q|$ can't be too small. But I would like to know if there are any known attacks for cases where $p$ and $q$ take on ...
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Is RSA of a random nonce with no padding safe?

Consider the following protocol: Bob has a private RSA key $B_{priv}$, and Alice knows the public key $B_{pub}$. Alice wants to send confidential messages to Bob (no integrity intended). To send a ...
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The 9 lives of Bleichenbacher's CAT, it puts another scratch again

Bleichenbacher demonstrated a padding oracle attack against RSA implementations that follow the PKCS #1 v1.5. Through the years, there are various mitigation techniques developed as OAEP and limiting ...
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Is unusual (non power-of-two) RSA key size more secure?

On this blog https://blog.josefsson.org/2014/06/23/offline-gnupg-master-key-and-subkeys-on-yubikey-neo-smartcard/ there is a following sentence Generate master key Below I will use a 3744 bit ...
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Is knowing the private key of RSA equivalent to the factorization of $N$?

Given the RSA modulus $N$ the fastest method to factor it is of sub-exponent order. But, now if I know the private key $d$ of RSA, does that mean I can factor $N$ efficiently?. It intuitively seems ...
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Anonymous trust/reputation system

Suppose there are 3 persons, Alice, Bob and Peter. They are identified by their pseudonyms (public RSA keys). Alice has a key Alice, Bob has ...
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RSA: If n=35, show that e will equal d

Show that if $n = 35$ is used as an RSA modulus then the encryption exponent $e$ always equals the decryption exponent $d$? What I have so far: $n = 35$ Therefore $p = 5$ and $q = 7$ or vice versa, ...
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RSA with 3 primes

I was trying to understand how does RSA with 3 primes work. I have checked Wikipedia but yet I didn’t fully understand their solution. I would like to know how do you encrypt for $n=p*q*r$ How do you ...
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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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Is a known plaintext, ciphertext, and public-key a viable attack on RSA?

Assume Alice and Bob are using RSA to create a common session key and Cindy is listening, attempting to obtain the session key. Alice and Bob each have their public- and private-key pairs ($\left[...