An asymmetric cipher is an encryption scheme using a pair of keys, one to encrypt and a second to decrypt a message. A special class of asymmetric ciphers are public-key ciphers, in which the encrypting key need not be kept secret to ensure a private communication.

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RSA: how does it work and how is it more secure than symmetric systems

Before starting the question, I know that RSA is naturally a key exchange cryptosystem rather than an antilogarithm fully implemented for encrypting and decrypting data since the length of the secret ...
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75 views

Converting a number to a member of a multiplicative cyclic group

I am currently trying to make an implementation of the ElGamal encryption for educational purposes. As I understand it, when using the encryption with multiplicative cyclic groups, one generates a ...
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3answers
862 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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4answers
304 views

Comparison among algorithm based on key length

Some months ago I found in some paper that we cannot compare symmetric algorithm with asymmetric algorithm based on the key length and more important we cannot compare asymmetric algorithm using only ...
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1answer
85 views

PKI Infrastructure

I've got a very simple but for me a difficult question. I analyzed the public key cryptography and understand the process. But I didn't understand why is only the receiver able to decrypt to message. ...
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2answers
289 views

Factors of RSA modulus

In the article A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...
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29 views

How to find the factors of the modulus? [duplicate]

In the article "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...
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5answers
12k views

What is the SSL private key file format?

I was researching about how to encrypt with RSA. I understood everything but not the format of the private keys. In the phpseclib (RSA in PHP), you can import your private key (private.key format) ...
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5answers
2k views

Why is the private key generated first in public key crypto?

I'm still new to public key crypto. I'm trying to understand how it is that the private key is generated first in public key crypto? I would have expected the private and public key to be generated at ...
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108 views

Public key encryption [duplicate]

I am not getting whole idea behind Public Key Encryption technique. As according to fact, public key encryption method uses two keys a public key known to everyone private key known only to recipient ...
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0answers
149 views

Relations between RSA and DLOG, factoring and DLOG

Definition: (The generalized Diffie-Hellman problem) Let $n=pq$ for two large primes $p,q$. Given $x, x^a, x^b,n$, find $x^{ab}\pmod{n}$. (1) Is there a known reduction from the GDH problem to ...
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2answers
252 views

Smart Card - Entropy during on-board public key generation

I know that some (advanced) smart cards or tokens allow generating key pair directly on the device, but I wonder how the card can gather entropy during the process. Any idea ?
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2answers
885 views

How much extra information is in an RSA public key?

I'm trying to calculate the size of an RSA public key in Ruby. I've retrieved the key in PEM format, and once I've decoded the base64 part from the PEM format, I get the size in bytes. What I find is ...
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2answers
434 views

Sharing an encrypted file between a group of people

Is there any way to share an encrypted file with a group? In the other words, can I encrypt a file with a public key so that each person in a group decrypt it with his/her private key? Is there any ...
3
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1answer
170 views

Multi-key decryption

Let's assume I want to send a secret message to $N$ recipients in an asymmetric way. My message could be encrypted with $N$ different public keys $p_i$ one after another and send to each user ...
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2answers
157 views

Do I have to transfer the private key to digitally sign a remote document?

I'm trying to digitally sign a document which is uploaded by a user. I want the user to sign that document using his digital signing certificate (DSC). Should I: transfer the file to the user, and ...
2
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2answers
151 views

how to let other people respond to emails only decrypt-able with my private key

First of all I have to say it's a homework question but since I have no one to consult with, I ended up here :) Suppose a case in which you are the manager of a company and all employees encrypt ...
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2answers
686 views

Implement deniable encryption with AES/RSA

I'm on a crypto app using OpenSSL (I'm more an implementer/cryptographer than a cryptologist), mainly as a hobby, for now. My app will be able to encrypt a file (not a container) with symmetric or ...
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0answers
64 views

Obliviously computing the Least common multiple of two poylnomials

Consider I have two polynomials $f_1$ and $f_2$ of the same degree. I want to secure them (using any kind of encryption except FHE) and outsource them to an untrusted server. I want him to compute the ...
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1answer
90 views

For which RSA moduli, precisely, is $e=d$ for all $e$?

This question shows that there are at least two valid RSA moduli $n$, namely $35$ and $91$, such that for any $e$ coprime to $\lambda(n)$, $$e^2\equiv1\mod\lambda(n)\text.$$ Reading the linked ...
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1answer
241 views

Can keys from Bitcoin's Hierarchical Deterministic Wallets be correlated (reducing privacy)?

I'm trying to understand if the feature "Hierarchical Deterministic Wallets" in Bitcoin allows for complete privacy of all derived keys, and if any of those keys can be associated with each other ...
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2answers
120 views

Group description in pairing based cryptography

Suppose we have a public key encryption scheme, in which public parameter contains $(p, G, G_t, e, g)$, where $p$ is prime number, $G$ is a (cyclic) group of prime order, $e:G \times G \mapsto G_t$. ...
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1answer
107 views

What are the potential (major) flaws in this security scheme?

It’s been a few years since I read anything involving crypto. I’ve come across this scheme and I wonder how secure it is: Alice generates an RSA keypair (we assume Alice is using proper random ...
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3answers
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Difference between Symmetric and Asymmetric. Is this answer correct, based on a written test?

I asked the following question on a final exam: Symmetric Ciphers (e.g. AES, DES, Blowfish) use up to 256 bit on the best case, which are considered strong against brute-force attacks. On ...
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1answer
110 views

what is the benefit of lcm in cryptography? [closed]

what is the benefit of lcm in cryptography? and what is the effect of lcm on public key? note * lcm = Least common multiple thanks
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1answer
479 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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Asymmetric encryptions' computational complexity [duplicate]

I need to know the computational complexity of the public key encryption (e.g. Paillier), please. (i.e.Paillier in his paper mentions that the computational complexity of most of public key ...
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1answer
314 views

Secure double encryption using CPA and CCA

Do you mind if you give me any hints, links or ideas about how to improve the security of double regular encryption and decryption, by using CPA game and CCA game, it sounds interesting question, and ...
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0answers
85 views

Corporate PKI - SHA1 deprecation [closed]

Here is the context. Suppose you have a corporate PKI with : AC_Root (offline in safe store - SHA1 signature) SubRootA ans SubrootB (offline in safe store - SHA1 signature) SubSubRootC, SubSubRootD,...
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179 views

Generation of strong primes

It seems that this is pretty difficult to find large (above 1024 bits) strong primes, or at least such primes p where (p-1) has a very large prime factor. Is there any information regarding the ...
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3answers
281 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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118 views

RSA OAEP: prevention of partial decryption of ciphertexts

I'm trying to understand RSA encryption (as a beginner in cryptography). go on this wiki page http://en.wikipedia.org/wiki/Optimal_asymmetric_encryption_padding scroll down to the 2 numbered points: ...
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1answer
137 views

what are multi-primes and how are they different from semiprimes?

I came to know of semiprimes recently. The simplest explanation of semiprimes is you take any two prime numbers and you multiply them, say 3*11 = 33 in which case 33 would be a semiprime. The numbers ...
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3answers
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How can one sign with NTRU?

I am looking at implementing NTRU, but I noticed that while the encryption/decryption algorithm seems to be mature and well-documented, there is comparatively little information about how to sign ...
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2answers
215 views

DHE key exchange. Is it really secure?

Context I recently came across a video on the net showing the process of key exchange in Diffie Hellmann. Alice and Bob want to communicate. Eve is the (wo)man in the middle. This video is the ...
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6answers
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Types of Cryptography for a 4-8 bit microcontroller

This is more of a research question. I was wondering what types of crypto algorithms would work best on a small 4-8 bit micro controller. I recently read a paper called Security Considerations for ...
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187 views

Verbatim of early work on public-key cryptography?

In late 1997, the history of public-key cryptography was turned around with the announcement by the CESG (April 2000 archive) that public-key cryptography was theorized in a 1970 note [1] by James ...
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1answer
68 views

special public keys and modulo n

I just picked up cryptography and have some questions on RSA cryptosystem: Say there are two public keys (n, e1), (n, e2), e1 is coprime to e2. They share the same n. Is it possible to find the ...
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1answer
2k views

Is it possible to determine a PGP public key from encrypted data?

Is it possible to find out which public key was used to generate the message? Scenario is like this : I got data which is encrypted with a public key. Now a "bad guy" hast the encrypted data, and ...
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2answers
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Impacts of not using RSA exponent of 65537

This RFC says the RSA Exponent should be 65537. Why is that number recommended and what are the theoretical and practical impacts & risks of making that number higher or lower? What are the ...
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Opinion on my idea for storing credit cards securely

I've been thinking of ways to store credit cards securely, I thought of this: Take the users credit card info Put the card info in a standard format "Full Name/Card Num/Security Num/Expiry Date"...
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0answers
151 views

How can I prove CPA secure by using a new scheme gen,enc,dec from GEN,ENC,DEC?

Given public key encryption scheme $(gen; enc; dec)$, we now construct a new scheme $(Gen; Enc; Dec)$ as follows: The key generation algorithm $Gen$ is the same as $gen$. Each ciphertext for a ...
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1answer
190 views

Determining message given cipher-text and public key [duplicate]

Consider the following scenario: Suppose A and B have set up their RSA public keys, namely $(e_a, n)$ and $(e_b, n)$, where the n-value is the same. Also, it happens that the $\gcd (e_a, e_b) =...
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3answers
2k views

How do public key rings work in cryptographic applications?

I am wondering if there are any links to articles or resources available online, or explanations that you can give, that would help me to understand the concept of a public key ring, and why I might (...
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2answers
844 views

Is RSA encryption of a cryptographic hash with a private key the same as signature generation?

It is often said that RSA encryption with a private key is the same as signing (signature generation). Will RSA encryption with a private key over a cryptographic hash give the same result as ...
4
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1answer
216 views

Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$

The Congress of ThéOùÇa enacted that civilian use of any public-key encryption system is authorized on the territory of ThéOùÇa, subject to meeting certain security requirements published by the ...
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2answers
101 views

what is contained in a public key certificate

Public key certificate is a digitally signed document which verifies the sender is indeed the person. May I know how can the receiver tell the sender is indeed the person solely based on information ...
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449 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 ...