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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Key space vs Cardinality of 1024-bit RSA

I have been trying to figure out the encryption key space, and cardinality of 1024-bit RSA. From my understanding, the key generated from 1024-bit will be primes greater than $2^{1023}$ but less than ...
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264 views

Can all asymmetric key pairs be reversed?

After reading about public/private key cryptography, there are still a few points I don't really understand. Based on the way (I understand) challenges work, the public key is used to encrypt a ...
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What happens when a root CA has its private key compromised?

What happens when a root CA has its private key compromised? Then all children in the tree are compromised too? And then all certificates are compromised? What needs to happen then? Related: - How ...
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Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA. (Note: I do realize that in practice this is done through an intermediate symmetric key, but ...
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2k views

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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588 views

What's the main difference between Pohlig-Hellman and RSA?

Both Pohlig-Hellman and RSA perform encryption and decryption by exponentiation modulo some integer ($p$ prime for PH, $n$ composite for RSA). They both use a key $e$ as the exponent to encrypt a ...
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959 views

Is it possible to pick your Ed25519 public key?

Is it possible to generate an Ed25519 keypair that has a very similar public key as another keypair (fooling a casual visual comparison) or is this as hard as solving one of SHA-512 or the discrete ...
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413 views

Key space size when either of two public keys are valid for authentication?

If for authentication a user can own either A OR B public key instead of just one specific key is that equivalent to halving the key space. i.e. it it theoretically twice as easy to brute force and ...
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2k views

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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192 views

Protocol to generate Client Certificates at the start of a SSL session automatically?

A more secure form of 'cookie' could be created for SSL communications through the following method. The client generates and requests the server to sign a certificate. Then the client authenticates ...
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253 views

Public-key cryptosystems without poly-time quantum attacks

It's well-known that Shor's algorithm can solve integer factorization, discrete logarithm and discrete log over elliptic curves in cubic time. This implies that cryptosystems like RSA, ElGamal, and ...
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229 views

Crypto puzzle as proof of randomness?

I need an untrusted client to generate a random public/private keypair (in particular, an Ed25519 keypair, which can be generated really fast), but I'm only allowed to see the public key. The ...
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Difficulty of breaking RSA for a given key size

Is it true that breaking a 1024-bit RSA key is as difficult as breaking a 128 bit symmetric key (e.g. AES)? I know that breaking a RSA key is equivalent to factoring the modulus $N$. To factor it, you ...
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How to distribute session keys in public key cryptography?

In public key cryptography we can also use session keys which are symmetric. How do the sender (say a server) provides this session key information to its clients? If the sender (here server) ...
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82 views

Signing the hash of a key with the same key

Given a private signature key sk and a public signature key SK, does revealing sk(H(SK)) (in ...
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115 views

What's the alternative should PKI collapse?

Premises - please check it and critique if necessary: If factoring the products of large numbers suddenly becomes simple, PKI goes up in smoke. Is this correct? If it is correct, it seems to me ...
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631 views

Additive ElGamal cryptosystem using a finite field

I'm trying to implement a modified version of the ElGamal cryptosystem as specified by Cramer et al. in "A secure and optimally efficient multi-authority election scheme", which possesses additive ...
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415 views

What is the computational cost of a public key certificate signature verification?

What is the computational cost of a certificate signature verification in terms of exponentiation, multiplication and other computation operations?
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79 views

what is the public information in Elliptic curve cryptosystems [closed]

Currently my knowledge about Elliptic curve is quite limited to the textbook and I don't know how a practical Elliptic curve cryptosystem works. I read an example about key exchange using Elliptic ...
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193 views

Is it meaningful to consider the leakage of master key of KGC?

In the Identity-based cryptography, the user's private key in the systems is delivered by the key generation center(KGC). My question is : Is it meaningful to consider the leakage of master key of ...
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760 views

Why can't I break ElGamal encryption by brute-forcing the secret exponent?

I am doing a course on cryptography on coursera and one of the topics covered was the ElGamal Encryption system. I am using the terms as defined in Wikipedia. Alice publishes $g$ and $g^x$. ...
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759 views

How to generate a public key from a private ECDSA key?

Having some specific ECDSA curve and a private key, how does one calculate the public key? I am having a hard time finding the algorithm and equations for it.
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583 views

Public key cryptography - public key encrypts and cannot decrypt?

I understand the basics behind public key cryptography, in that each party has two keys - the public one encrypts, and the private one decrypts. What I cannot figure out is, How does the public key ...
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146 views

Correct method to encrypt data so that it can be decrypted only by Alice and Bob

I need to build a system that stores encrypted transactions. Transaction involves always two parties. Payer and payee. Both must be able to download encrypted transaction from server and decrypt it ...
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214 views

A set of key pairs and one hash to secure them

I have a simple problem: I have a set of users' ECDSA key pairs, and say I want to encrypt them with a simple algorithm. I have access to one variable that uniquely identifies the user, so I hash it ...
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230 views

Why have Nonce and why encrypt everything in step 2 for Needham-Schroeder?

Here is the protocol outline I am looking at (source: Foundations of Computer Security, Lecture 60: The Needham-Schroeder Protocol) $$ \begin{array}{ccl} 1.& A \to S \colon& A,B,N_a \\ ...
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658 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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381 views

Can I save space for short messages by using encryption with private key instead of a signature?

Let's say I have a message, a Private Key and a Public Key. Normally if you want to see if the message is unaltered and is from the sender you would have the message part + signature part, which you ...
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396 views

Is truncating a hashed private key with SHA-1 safe to use as the symmetric key for AES for data at rest?

I realize this is mixing the purposes between asymmetric and symmetric crypto, but I was wondering if it is safe to use a hashed, truncated private key (asymmetric) as the symmetric key for encrypting ...
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129 views

When to prefer exchanging cryptographic certificates over exchanging only public keys?

Let's think of the following case: A group of peers want to exchange messages with each other. They use public-key cryptography to sign and encrypt messages. Anyone with any name can join the ...
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8k views

Calculating private keys in the RSA cryptosystem

The number $43733$ was chosen as base for an implementation of the RSA system. $M=19985$ is the message, that was encrypted with help of a public key $K=53$. What is the plaintext text? What is the ...
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185 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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123 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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102 views

Is email an example of public-key cryptography?

It seems like email is at least analogous to public-key cryptography, the public portion of the key being your email address, and the private portion of the key being the password to the email ...
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What are good combinations of public key algorithms or primitives for long term security?

There has been talk in literature about doing multiple encryption with different block ciphers or stream ciphers several times before, and the benefits and risks of such efforts. There may be hidden ...
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263 views

What differences between Menezes–Vanstone ECC and ElGamal ECC?

After researching ECC encryption, I found that we can use ElGamal cryptosystem with elliptic curve and can we use Menezes-Vanstone cryptosystem with elliptic curve. What is the essential difference ...
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514 views

ECC public key encryption and authentication - ECIES with ECDSA vs ECDH with AES

I'm currently working on a project where I want to establish a secure and authenticated communication channel between to entities, using Elliptic Curve Cryptography. Now I'm not really sure how to ...
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416 views

Are there any elliptic curve asymmetric encryption algorithms?

RSA offers the functionality of encrypting (short messages, or symmetric keys) with a public key, and decrypting with a private key. However, RSA key generation is extremely expensive, especially for ...
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Using ECDSA keys for encryption

I know that ECDSA is used for signature only, but I wonder if I can use the public/private Elliptic Curve keys for encryption too. I have ECDSA SSH public keys and I wonder if I can use them to ...
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97 views

Asymmetric Cryptography Confusion - 'Sign' a file to guarantee its source

What I want to do is use asymmetric crypto to guarantee that a file comes from a source. I have software that runs on lots of wireless devices, and each of those has a license file with an encrypted ...
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128 views

Why is $-1$ an illegal message in the Goldwasser-Micali Encryption Scheme

I'm not sure why in the Goldwasser-Micali encryption scheme with a Blum integer $N$, the message $-1$ is always a illegal message. Can you give me some direction for starting? What is illegal ...
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456 views

How difficult is it to brute force d in RSA: d = (1/e) mod φ in a CPT attack?

Given that RSA key generation works by computing: n = pq φ = (p-1)(q-1) d = (1/e) mod φ If I was an attacker who wanted to brute force d, could I brute force d given just the public key, the ...
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465 views

Can you identify the public key used to encrypt something?

If I encrypt a string with a public key, does the encrypted ciphertext reveal the public key I used to encrypt it? Basically, I don't want anyone to know who the ciphertext is addressed to. I'm ...
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1k views

Secure encrypt-then-sign with RSA

I understand that when you want to encrypt and sign data with RSA the generally recommended approach is sign-then-encrypt. However, I have encrypted data that I need to sign, to prove the author of ...
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239 views

Algorithm to securely exchange identities

Say four people each have a public/private key pair that they can use to encrypt or sign messages. They have an anonymous way to post messages such that the others can see them. Malicious entities can ...
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854 views

Digital Signature Algorithm signature creation

I was studying DSS from "Cryptography and Network Security" by William Stallings. What puzzled me was the DSS approach figure described in the text. It says it uses Public and Private Keys for ...
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351 views

Why does FIPS 186-4 require specific sizes for keys?

In FIPS 186-4, page 32, about FFC crypto it is required that the length of $p$ will be exactly 1024 bit and the length of $q$ will be exactly 160 bit. Why is the requirement not stated in terms of ...
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Which public key encryption scheme is re-randomizable? How can I re-randomize an encryption scheme?

Which public key encryption scheme is re-randomizable? Is there any library for re-randomizable encryption scheme? If not, how can I re-randomize a given public key encryption scheme? I cannot find ...
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Diffie-Hellman Key Exchange with Authentication: Man-in-the-Middle query

I have been reading up on MiTM attacks, and the prevention of them using public key certificates. Recently I learnt about Diffie-Hellman Key Exchange with Authentication, and how it uses signed ...
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168 views

How to protect against ephemeral key reuse in some signature schemes?

Given that some signature schemes (for instance Elgamal) use an ephemeral key that cannot be reused ever. How do people usually protect against this? I'll elaborate more: if you reuse the ephemeral ...