# 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.

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### Possible to encrypt message without knowing recipient public key?

Assume Bob is sender and Alice is future recipient. In ideal situation Bob know Alice public key, and encrypt message with it. But what if Bob don't know Alice public key (he only will know Alice ...
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### Factoring RSA $N = pq$ knowing that $(p+q) >> 200$ [closed]

We have $N = pq$, with $p$ and $q$ are prime numbers, and $hint = (p + q) >> 200$. How to find $p$ and $q$?
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### Are Safe and Sophie Germain primes evenly distributed?

Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value? This is important in one area of triangular ...
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### Textbook RSA on random numbers mod a smaller prime

I have a protocol where I have a random one-time number message $m \in \mathbb{Z}_p$, where $p$ is a 256 bit prime from an Elliptic Curve (EDIT: The order of an elliptic curve prime order group). I ...
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### Is there an algebra group (or ring) in which computing the inverse element is hard without some trapdoor information?

Specifically, I want an algebra group $G$ (or ring $R$) features: Given elements $g,h\in G$ (or $R$ ), computing $g\cdot h \in G$ (or $R$ ) is easy. Given an element $g \in G$ (or $R$ ), finding the ...
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### How to create RSASSA-PSS keys using openssl?

I am trying to understand the RSASSA-PSS and process of generating keys with rsassaPss. I am using below ...
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### How to find modulus and decrypt a message with a CPA on textbook RSA. The encryption oracle only allows two queries

The encryption oracle only allows you to encrypt a custom message $m$ or the secret message $m_s$. In both cases it asks you to choose a public exponent $e>16$. Of course, $n$, is not available. If ...
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### Decrypt RSA knowing N, invp, and invq

im having a problem while solving a RSA problem, so i have python script to create a RSA key and cipher, from that i have n, invp, and invq. so my question is possible to decrypt the message only with ...
1 vote
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### Is gcd(e,p−1)=1=gcd(e,q−1) similar to gcd(e,phi(n))=1?

I wonder, is $\gcd(e,p−1)=1=\gcd(e,q−1)$ similar to $\gcd(e,\phi(n))=1$ ??
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### RSA/ ECC keygen HW vs SW

i have a pretty straightforward question but i can’t seem to find an answer : Regardless of the physical protection provided by an HSM or TPM or any hardware cryptographic key storage system, are keys ...
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### In RSA Encryption, Can I choose the public exponent e > m (modulus) ? or e > φ(n)? [duplicate]

In RSA ,the encryption, Can we choose the public exponent (e) greater than m (modulus) or e > φ(n) ? I wonder about choosing public key exponents (e) because the most information on the internet or ...
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### How much can we compress RSA public keys with two equal size factors?

Can we define an RSA variant in which the public key with $n$-bit public modulus $N$ has a compact representation of $\kappa\ll n/2$ bits, with a security argument that it is as safe as regular RSA ...
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### Is this new bound for Wiener Attack well accepted?

I found this recent paper The Wiener Attack on RSA Revisited: A Quest for the Exact Bound, which reported a new bound $d\le \frac 1 {\sqrt{18}} N^\frac 1 4$. Is this well accepted in the ...
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### In RSA Encryption, Can the public exponent e > m (modulus) ? and can we choose any public key without paying attention to the conditions? [duplicate]

In RSA ,the encryption, Can we choose the public exponent (e) greater than m (modulus) or e > φ(n) ? I wonder about choosing public key exponents (e) because the most information on the internet or ...
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### Best cryptographic algo with asymmetric cost: expensive to sign, cheap to validate

I'm looking to prevent a DDoS attack on a web service, by making the cost of performing an attack prohibitive. Typical users will only need to call out it once a day, and can afford to spend a few CPU ...
1 vote
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### Cryptography to tackle deepfake, proving the photo is original

Deepfake technology has become very difficult to tackle due to sophisticated machine learning algorithms. Now, even when a journalist or bystander provides photo or video evidence, the culprit denies ...
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### RSA derivation of ed=1 mod(ϕ(n)) [duplicate]

I know that $m =m^{ed} \bmod n$, and there is Euler's $a^{\varphi(n)} = 1 \bmod n$, but how do we derive that $ed=1 \bmod(\varphi(n))$ holds for all m. Where does that equality come from? Couldn't ...
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### Best cryptographic method to distribute license files

I will describe my problem high-level, and not ask a very specific cryptographic question, since I am open for general suggestions as well. So in my question I will only speak about "security ...
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### Is signature same as hash value encrypted with the private key in openssl?

Computing the signature of hello.txt file which has the text hello in it, here is done in two steps: ...
1 vote
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### Is there any harm using a pseudo-prime endorsed by a probablistic test like Miller-Rabin in RSA?

In RSA, the decryption exponent $d$ is typically calculated as $$d= e^{-1} \bmod{(p-1)(q-1)}$$ or $$d = e^{-1} \bmod \operatorname{lcm}{(p-1, q-1)}$$ where $p$ and $q$ are often randomly selected ...
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### Operands size in RSA Cryptography (C language)

I am trying to implement the RSA cryptography algorithm using C language. I am not sure of the size that each operand should have. Let me explain: RSA requires to generate two huge prime numbers p and ...
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### Curious behavior of EVP_DigestSign for DKIM

Difficulties porting code to OpenSSL 3 may raise some doubts on digest signing. Before version 3 came, digest signing was the only way to use ED25519. On version 3, RSA_sign() being deprecated, I ...