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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Limit the number of private key uses for RSASSA-PKCS1-v1_5 with SHA-256 signature?

Assuming all messages and their signatures are available to the attacker, is it secure to use the same RSA private key to sign many messages (roughly $10^{6}$) via PKCS#11 ...
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119 views

Verify a RSA signature using only RSA encryption

I'm trying to verify a RSA signed message, however, the API that I have access to in that environment only has encrypt and decrypt. I think I understand that verification and encryption with public ...
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1answer
185 views

RSA - PKCS#1 padding - overall correction of algorithm

From PKCS#1, page 24: After we create the EM byte string and convert it to an integer, we then encrypt that integer with RSAEP (page 10) to get the ciphertext (as an integer). My question arrives ...
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25 views

Are there UFDs where the factorization problem is difficult but finding irreducibles is cheap?

Factorization of integers is hard, but finding irreducibles is expensive. Is there a ring where factorization is assumed hard but finding irreducibles is much cheaper than over $\Bbb Z$? It could ...
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104 views

RSA_DH vs ECDH implementation

In ECDH protocol is possible, naturally, to use the same algorithm for calculate a secret key for both communication parties (Alice and Bob for example). It is possible to design also a same algorithm ...
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324 views

ASN.1 encoding off RSASSA-PSS default parameters

I am not totally sure the question belongs to crypto and not stackoverflow but nevertheless... The problem is the encoding of the RSASSA-PSS default algorithm identifier parameters in an X509 ...
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2answers
368 views

RSA-KEM construction

"Create a random key for CCPA2 scheme, encrypt m, send it along with a PK encryption of the symmetric key. " Say in the process, the KDF is HMAC, then: get a random key (128-bit) C1 = encrypt ...
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178 views

RSA encryption and signature padding flaw

This is Oxford's computer security exam question: Suppose that Bob has published an RSA encryption key $ke$ (retaining in secret the corresponding decryption key $kd$), and Alice has published a ...
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110 views

RSA Key Blinding

I was looking the answer to the following question (Timing attack on modular exponentiation), discussing the Private Key Blinding as a countermeasure for timing attacks. Therefore I'm asking if ...
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223 views

Defending hybrid encryption schemes against padding oracle attacks

I intend to use a generic integrated/hybrid encryption scheme for transmitting information between a client and a server. Key encapsulation: a 128-bit symmetric key is generated and asymmetrically ...
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106 views

Timing attacks against RSA, DH and AES

I have been reading about “Timing Attacks on RSA: Revealing Your Secrets through the Fourth Dimension” by Wing H. Wong. I was wondering if this attack is feasible while signing with RSA and, if yes, ...
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102 views

Is MITM possible after key exchange phase done successfully in RSA?

Is MITM attack theoretically possible after public/private key pair exchange is done successfully. Say Alice and Bob have genuine public keys of each other. Is MITM possible further during ...
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153 views

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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427 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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670 views

RSA problem if i choose two specific small prime numbers?

I know that rsa normally is made to make it with big integers, but i trying to make the algorithm myself (with the help of wikipedia) and I´m making it with small numbers to track the problems easily. ...
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3answers
258 views

Maximum length in bits of the product n=pq

If p and q are two 1024-bit prime numbers, would the maximum length in bits of product $n=pq$ be ${1024}^2$ or $2^{1024}$? I think it is ${1048576}={1024}^2$? Also, would the least significant bit ...
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1answer
88 views

Is it secure to choose d in a RSA key pair?

An RSA key pair consists of the private key $(n,d)$ and a public key $(n,e)$ such that $de \equiv 1 \bmod{\lambda(n)} $. Usually one chooses a small $e$ and computes $d$ by inverting it modulo ...
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312 views

Message exchange with textbook RSA

I am working on this exercise but can't work out the answer to the question b. I have solved the question (a) by decrypting the ciphertext $C = 2$ using the formula: $$ M = C^d \bmod n = 2^{17} \bmod ...
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2answers
121 views

What is RSA key normalization?

How can I understand the term RSA key normalization? What exactly is done in the process?? Please explain.
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535 views

two public keys with same passphrase insecure? | can two hashes be compared?

Suppose someone had generated a 2.048-Bit RSA GPG/PGP key pair and published the public key on the usual key servers. Then he withdraws this key and generates a new one in 4.096-Bit RSA using the same ...
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1answer
248 views

Large primes p and q for RSA

I am writing a high-school paper on textbook RSA (the mathematical aspect only). Many definitions of the RSA method start off with saying that one should: Generate two large random (and distinct) ...
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129 views

Three different numbers with x³=x mod p

p is a prime greater than 2 and $a \in \mathbb{Z}_p$. Why are there exactly three solutions for a³ = a mod p? Obviously 0 and 1 are both in $\mathbb{Z}$ and valid solutions, but that still means, ...
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347 views

What is h in this RSA variant?

I am trying to implement a proposed improved algorithm of RSA . Here the author has increased the number of exponents. However I am unable to understand what $h$ is in the Key generation step. Can ...
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89 views

find solutions that solve the equations

I am implementing a timing attack on RSA for school and I need to generate two sets of messages $Y$ and $Z$ for which holds: $ (Y^d \mod N) \cdot Y < N $ and $ (Z^d \mod N) \cdot Z > N $ where ...
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1k views

Is it possible to use the RSA algorithm, or a variant, for software licensing?

I'm almost a newbie about RSA encryption, so my question could it be banal. I'm beginning to create a licensing system for my software. I need to distribute a crypted license file to many customers. I ...
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1answer
83 views

Really simple RSA style public private key generator

I am giving a talk to high school students and would love to do a real life encryption/decryption demonstration. I am not too familiar with the maths but is it possible to create like a 5-10 bit ...
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1answer
104 views

Why is RSA encryption version 1.0 not specified in an RFC?

I saw that there are three RSA encryption versions, as follows: RSA encryption version 1.5 (RFC 2313) RSA cryptography specification version 2.0 (RFC 2347) RSA cryptography specification version 2.1 ...
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2answers
2k views

Is ECB mode safe to use with RSA encryption? [duplicate]

Firstly, bear with me, I'm relatively new to cryptography. In a recent static analysis scan of our application, one of the findings complained that we are using ECB: A mode of operation of a block ...
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722 views

Use cases and implementations of RSA CRT

I discovered the chinese remainder theorem (CRT) version of RSA cryptosystem which is used in many crypto libraries (OpenSSL, Java...). The use of this theorem improves the speed of decryption so, ...
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1answer
168 views

Brute force RSA cracking

Suppose one had a complete list of primes up to $2^{n+1}-1$. Then wouldn't one be able to crack an $n$-bit RSA public key in time $O(\pi(2^{n+1}-1))$, making RSA insecure? Thanks, René
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363 views

modulo operations in crypto algorithms

Am not a mathematician. Every crypto specification I see uses the modulo operation. For example RSA - If $e$ is the public key and $m$ is the plaintext with a modulus $n$ - the cipher text is $c = ...
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1answer
673 views

RSA Decryption with Private Key but no public exponent

I manually set the RSA private key, given the private exponent and modulus. When I use this key to decrypt a message encrypted using a public key (also set with public exponent and modulus) seems to ...
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1answer
1k views

Why is it a security problem that two RSA moduli are not co-prime?

I found this security problem, for example: Alice has an RSA public key: $e = 37$ and $\phi$ (totient, $N_A = (pa-1)(qa-1)$) is $55$, so the key is $(37, 55)$. Bob has an RSA public key: $e = 37$ ...
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608 views

Possibility of factorisation of rsa modulus due to vulnerability in java implementation code

Below is my implementation of the RSA algorithm. Actually I'm choosing the private key (d) instead of public key (e) and computing the public key.It is working fine but I want to know if this is a ...
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1answer
99 views

Tweaking textbook RSA to make the encryption a Pseudorandom function

Lets say I want to tweak/alter the textbook RSA encryption function to create a pseudorandom function by pre-processing the input. Suppose I do something simple like add 2 to the input before ...
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1answer
5k views

RSA 4096 bit key benchmark

How can I benchmark RSA operations on my computer? I want to know about 4096-bit long keys on general computers. How many encryptions and decryptions are possible per second? All benchmarks I found ...
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1answer
451 views

Does RSA-OEAP have integrity and authenticity properties?

RSA-OAEP is IND-CCA2 secure (indistinguishable under an adaptive chosen ciphertext attack). Does it also have the INT-CTXT (integrity of ciphertext) and INT-PTXT (integrity of plaintext) properties? ...
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1answer
185 views

RSA encryption input range - plaintexts that map to ciphertexts?

According to the wiki article on the RSA encryption function, the valid range of input $m$ is $0 \leq m \lt n$. However I have found that the following values of $m$ always return themselves when ...
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2answers
167 views

Idea for secure password hash-likes, is this feasible/usable/workable?

(Hand moved from stackoverflow.com,due to suggestion) Since breaking password hashes has become a new passtime for scriptkiddies, I thought of the problem and came up with a novel(?) idea. store ...
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3answers
83 views

RSA message integrity

I wish to send some small data that RSA alone can encrypt, and I send a shared secret along with it. ...
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2answers
102 views

Encrypt letters separately?

I am trying to encrypt the word Hello using RSA. When encrypting Hello’s integer representation, is each letter encrypted ...
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1answer
192 views

Why doesn't this defeat RSA?

Apologies for the obviously ridiculous question but I need to know where I'm going wrong here. For RSA, we compute $n=pq$ for primes $p$ and $q$. We then choose an $e$ such that $gcd(e, ...
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2answers
199 views

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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3answers
736 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 < ...
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1answer
127 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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1answer
101 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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408 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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468 views

How do RSA and ElGamal key sizes compare?

I have a rather silly question regarding the comparison of RSA with ElGamal over integers. If you want to compare their performance in the same level of security, does the modulus of both of them need ...
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400 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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513 views

Proof for exponentiation in modular arithemtic

If $e$ is a natural number, then this is true: $$m^e \bmod\ n = (m\bmod\ n)^e\bmod\ n$$ This is often used when encrypting, especially with RSA, since one can avoid directly calculating $m^e$, ...