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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Why is this a fix to Bleichenbacher's attack?

Looking at the excellent explaination of the attack here: Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5? I have one additional question: It says that: ""To prevent this attack, SSL ...
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909 views

RSA Key generation: How is multiplicative inverse computed?

As per Wikipedia, RSA keygen goes like this: Choose two distinct prime numbers p and q. Compute $n = pq$. Compute $\varphi(n) = (p − 1)(q − 1)$. Choose an integer e such that $1 < e < \varphi(...
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137 views

Why are cryptographically secure hashes required for digital signing (RSA or DSA)?

I know that a cryptographically secure hashing algorithm is required for proper message signing (SHA-1, or I think SHA-2 is the current suggested algorithm). However, why does the hashing algorithm ...
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109 views

Does it necessary the public key is prime number in RSA algorithm?

I read some books talk about RSA cryptography but I did not understand something when choosing a public key $e$ Sometimes the condition is $1<e<$$\phi(n)$ Where $\phi(n) = p-1 * q-1$ also ...
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480 views

File format of an $2048$ bits RSA public key

From here, there are $14$ bytes specifying the file format of the key. I am still quite confused about the format bytes. For example, the following public key 30 82 01 0a 02 82 01 01 00 8e a3 d1 c7 ...
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439 views

Why would an RSA library tell me that the public key must be at least 512 bits in size?

I'm trying to interoperate with a web service by reverse-engineering it. Currently, when sending a POST request, it encrypts the form data one-by-one with a 'RSA' function. But it's rather weird as ...
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271 views

How to calculate bit strength of Integer Factorization Cryptography (IFC) such as RSA using Python

I would like to know how to calculate the bit-strength of Integer Factorization Cryptography (IFC) such as RSA by using Python. I gathered it is based off the complexity of factorizing the modulus (...
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248 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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272 views

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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1k views

Help with example RSA problem

While learning about RSA, I found this example problem. The answer is supposed to be "a 4-digit number that is a pattern of digits." I have computed it to be 16657 twice. OK, now to see if you ...
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466 views

Amateur question: two-way RSA?

Is this a sensible scheme for 2-way client/server communication? A client connects to a server. The server and client both generate RSA keys, and send over the public ones to each other. If the client ...
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666 views

Why are RSA keys encoded with ASN.1 for TLS?

Browser vendors use ASN.1 encoding for RSA certificates in the TLS protocol. RSA public keys are just a number, so why do we need encode them to something else? That increases the risk of security ...
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931 views

How to jusify {e,n} is a valid RSA public key?

I have a two set of key {36,77} and {50,117}, How can validate if it is a valid RSA public keys? Is there any simple method?
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1k views

What is the correct value for “certainty” in RSA key pair generation?

I'm creating an RSA key pair in Bouncy Castle and need to specify an int value for certainty. This Stack Overflow answer says it is a relative test for how prime the values are. There is another ...
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355 views

One-way function and factoring

I am confused about the hardness of the one-way function behind cryptography -- if someone could factor the large number produced back into two primes quickly then the one-way function would be broken?...
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42 views

Clarification on Key exchange approaches in TLS/SSL

When RSA is used for key exchange in SSL, the client basically encrypts some random data using the server's public key and and sends it to the server. This data is then used to compute the shared key ...
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77 views

SHA256(RsaPrivateKey) == AES key?

I have an RSA private key (more specifically, an SSH key in Putty format, 4096bit) and want to use its SHA256 hash as an AES256 key, instead of using an independent newly generated AES key. Are ...
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91 views

Can RSA with padding detect all errors in ciphertext?

I'm new in cryptography and there are a couple of things that i'm not sure if i understand correctly. First, when using padding (PKCS or OAEP), if the chiphertext has errors in transmission we'll we ...
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68 views

RSA numerical questions

Let $n$ be the modular arithmetic, $p$ and $q$ the two large primes such that $n=p*q$ and $e$ the public exponent. Here they are two "simple" numerical questions: If $p = 13$ and $q = 17$, what is ...
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126 views

How “hard” it is to take an e'th root mod p?

I know it's hard to find the $e$th root of a number mod $n=p_1*p_2$, and if it would be possible we could break RSA. But how hard it is to take an $e$th root mod $p$ where $p$ is a prime and $\gcd(e,p-...
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352 views

Signing/verification between Java and the OpenSSL

I'm trying to sign/verify data between a C application and a Java application. In java for now I was using the built-in JCE provider with SHA256withRSA as ...
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45 views

What part of an RSA key is referred to by the number of bits? [duplicate]

When we speak about 4096- or 2048-bit RSA keys, what part of the key is this number of bits? The public key comprises both the modulus and the public exponent, and the strength of the key can also be ...
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103 views

How is RSA able to prevent brute forcing using the public key?

Bob calculates a private and public key. Bob sends his public key to John. Jeff is a third party unwanted member and manages to snatch the public key mid-transfer. John encrypts his message ...
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148 views

How many bits to flip in an RSA public key to do signature forgery?

Scenario: Alice wants to verify a signature from Bob. Alice knows Bob's RSA public key (e, n). However, Alice is getting the data, the signature of the data and the public key from an attacker Eve. ...
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401 views

Why is the public/private key length used in libsodium so much shorter than needed for RSA [duplicate]

Reading the libsodium source I see that is uses a key length of 32 bytes (256 bit) for private/public key encryption. For RSA private/public key encryption a key length of 2048 (or 4095) bit is ...
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58 views

How to determine the exponent when using RSA

Can someone please explain to me how, when using RSA, to determine the exponent to be used in encryption and decryption? I have attempted a worked example on using RSA (shown below) but I can't ever ...
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109 views

with RSA encryption, how do I find the md5sum of the private key from the public key?

This is a purely mathematical question on RSA encryption. Having $e$ as the public key exponent and $n$ the modulus of a public key. Can I recover the md5sum of the private key $d$ (inverse of $d$ ...
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858 views

Common Modulus Attack in RSA

Consider the following scenario: The Information Security Department (ISD) of an organization issues each of the organization's employees, domestic and abroad, with an individual RSA key. To simplify ...
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174 views

Is it a variant of Strong RSA assumption?

Informally, the hardness of RSA/Strong RSA assumption lies in the hardness of factoring a large composite number $N$ having two large primes as its factors. If RSA modulus $N$ is a prime number, then ...
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484 views

rsa public and private keys

I have a question about RSA key generation. This is a simple RSA algorithm: Choose p = 3 and q = 11 Compute n = p * q = 3 * 11 = 33 Compute ?(n) = (p - 1) * (q - 1) = 2 * 10 = 20 Choose e such that ...
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299 views

Compare two approaches for cracking RSA key

I came across these questions while studying for a crypto course, does anyone have any ideas on how to answer these? (a) Random prime numbers of size 1536 bits are chosen to generate an RSA modulus ...
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185 views

Public and private key lengths

I am generating RSA Public and Private keys with node.js instead of reading them from pem/crt files as I can hide them inside a private object using this module https://www.npmjs.org/package/private ...
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110 views

How can a digital signature algorithm incorporate a random data if it is to be authenticated on a separate system

I am trying to understand how RSA digital signatures can incorporate any data from a PRNG into the final signature. Does this mean that separate implementations might fail to verify each others ...
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425 views

Prime factorization of RSA modulus

Consider RSA public-key encryption with public modulus $N=3953$. Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. ...
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273 views

Usage of Fermat primes in RSA

Why are Fermat primes ($2^{2^n}+1$) useful as $e$ (the public key) in RSA encryption? I understand why $2^n+1$ primes are useful, because they would simply be ...
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2k views

Forgery Attack Against RSA Digital Signature

I have been reading about attacks against RSA Digital Signature in a book The attacker chooses the signature first and then computes the message. As a consequence, he cannot control the ...
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Sample RSA-style signature confusion

I'm trying to study a simplified TLS-style protocol, including verifying RSA signatures. It's an attempt to verify using only a valid certificate. However, I can't manage to get anything to verify ...
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170 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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532 views

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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443 views

DSA, RSA, ECDSA etc - which one is cheapest for signing?

For a protocol where the server presents its signature to prove authenticity (e.g. IKE/SIGMA/STS with only one party authenticated), it's essential that the signing is extremely cheap, while ...
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312 views

chaining rsa with ecies

In an answer to a previous question it was suggested that one way to protect your asymmetrically encrypted AES-256 keys, from say a solution to prime factorization, would be to chain asymmetric ...
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152 views

Certificate == signed public key

For primes p and q used to create a keypair, I understand that the following operation is used to create a signature: $M^d (\bmod\ N)$ where d and N have their usual meanings and M is the message. ...
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6k views

How do I derive the time complexity of encryption and decryption based on modular arithmetic?

I want to calculate the time complexity of two encryption and decryption algorithms. The first one (RSA-like) has the encryption $$ C := M^e \bmod N $$ and decryption $$ M_P := C^d \bmod N. $$ ...
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102 views

Is there a big RSA Data Set

Is there a big dataset containing RSA public $(n,e)$ and private keys $d$ and primes $p,q$ where $n = p.q$ ?
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909 views

RSA 1024bit decryption performance

i want to know how many RSA 1024 bit long key decryption can a regular pentium4 computer do per second ? how to calculate RSA performance and determine its remaining time ?
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170 views

Can you distinguish encryption methods from the output?

Suppose that you see all IP communication packets between two computers for a day, as they pass through a connecting router, and this amounts to 10MB. You additionally know that all data transmission ...
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My custom handshake

I am a beginner in cryptography and I designed a custom handshake between 2 entities $\rm C$ (client) and $\rm S$ (server) which should meet the following requirements: Requirements: The handshake ...
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Factorization of RSA modulus using a qubic residue

Suppose that someone uses RSA with $n = pq$, exponent $3$, also $3$ divides $\varphi(n) = (p-1)(q-1)$ and $2$ different roots $y$ and $z$ of the equation: $$x \equiv c \ (mod \ n)$$ are known (for ...
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Where is the mistake in my RSA by-hand calculation?

Like several previous askers, I seem to have made a mistake in my RSA calculation, but despite going back over it three times, I cannot spot it. I picked 1000003 and 6000011 as my primes, ...
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52 views

Can I get successful signature verification with just altering message and signature?

Assuming I can modify a message and also modify the verification signature, and I also have the public-key but not the private-key. Can I create a message that can be verified with a signature that I ...