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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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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226 views

Blum-Blum-Shub Cryptosystem

I am given $N$, which is Bob's encryption key. I was able to successfully factor $N$ into $N=p*q$. Alice encrypts a messages for bob and sends $a = [1,1,1,0,0,0,1,0,1,1,0,...]$ $b = 1545164156...$ ...
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1answer
124 views

Digital signatures under plain RSA

Show that digital signatures under plain RSA are insecure (Plain RSA means that signing is done by calculating $m^d\bmod n$, with $0\le m<n$, and no padding or hashing of $m$). Write an algorithm ...
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3answers
162 views

Question on RSA trapdoor permutation

You plan to use a public-key cryptosystem based on the RSA trapdoor permutation in three different real-life applications, in which the attacker has, respectively, only one of the following resources: ...
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2answers
107 views

Do we need symmetric cryptosystems?

One question I had to answer in my crypto exam today was: Do we need symmetric cryptosystems? As it stands, that's probably a debatable question, so I'd like to reformulate this as: Are ...
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2answers
148 views

weaknesses in ElGamal with public key of small order

Suppose $p=29$, $\alpha = 2 \in F_p^*$ is a generator of $F_p^*$. Bob picks $d \in \{2,...,27\}$ such that $\beta = \alpha ^d=28 \pmod{29}$. He then sends his $(p,\alpha ,\beta)$ to Alice who herself ...
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1answer
91 views

Question about dual system encryption

Recently, I have been reading some dual system encryption papers. In these systems, is the adversary able to generate “semi-functional ciphertexts”?
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1answer
123 views

Measure ECC key size

I have implemented a ECC key generation scheme successfully. Now I need to find ECC key sizes of each generating key pairs. I assumed that ECC key size is the size of the ECC private Key. So I would ...
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0answers
84 views

How can I make a message into a blocks for NTRU?

I have more bits than the degree of the NTRU polynomial. For example: $x^{11}-1$ message: Hello (I am using ascii, 8 bits for 1 symbol) got: ...
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5answers
2k views

Does RSA work for any message M?

I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but ...
4
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1answer
258 views

how to use common modulus attack?

I am struck with the following problem: Let Alice, Bob, Chris and Eve communicate over a public network. They encrypt all messages they send using RSA system. Bob and Chris have the RSA modulus ...
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1answer
354 views

Smart Card Basics

I want to implement some of the basic encryption algorithms on smart card, could any body guide me how to program a smart card, which tools (hardware and software) I should have, and if these tools ...
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3answers
40k views

Why is elliptic curve cryptography not widely used, compared to RSA?

I recently ran across elliptic curve crypto-systems: An Introduction to the Theory of Elliptic Curves (Brown University) Elliptic Curve Cryptography (Wikipedia) Performance analysis of identity ...
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4answers
694 views

Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key?

I have just learned about using PGP/GPG for email encryption and one thing has always bugged me: How is it possible that a message encrypted with somebody's public key can be decrypted only with that ...
6
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3answers
965 views

Is sharing the modulus for multiple RSA key pairs secure?

In the public-key system RSA scheme, each user holds beyond a public modulus $m$ a public exponent, $e$, and a private exponent, $d$. Suppose that Bob's private exponent is learned by other users. ...
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2answers
293 views

Is there a public-key cryptography method that enables public keys to be much smaller than private keys?

Does a public key cryptography method that enables the public key to be orders of magnitude smaller than the private key exist?
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0answers
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encryption and decryption time for RSA-crt in java? [duplicate]

I try compute execution time for encrypt and decrypt data has 1024 bit = 128 byte in RSA-crt algorithm. I need this results. But I believe this result wrong. because big diffrent between execution ...
0
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1answer
36 views

Is the private key static or variable key in the elgamal algorithm?

I read about elgamal algorithm it work like the follow steps Bashir chooses a large random prime p and a primitive root α modulo p. Bashir then chooses a random integer a with 2 ≤ a < p - 1 and ...
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1answer
75 views

Key exchange if forward secrecy is not an issue

Let's say that we have a cryptosystem where Forward Secrecy and Man-In-The-Middle attacks are not an issue, purely hypothetically. Would it be correct for a key exchange with any given public-key ...
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2answers
132 views

Is it necessary to generate a private key for each encryption process?

I read about Asymmetric key cryptography like EG-ECC , RSA, ECDH. I understand the concept of mathematics to these algorithms. But I have wondered about the public key for sender and private key for ...
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0answers
58 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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2answers
160 views

Why is ElGamalEngine in bouncy castle restricting input data to be less than the length of the group parameter p?

I am currently using the ElGamalEngine of bouncy castle to implement exponential ElGamal for the purpose of making ElGamal additively homomorphic. To do this i raise the message to be encrypted to the ...
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2answers
176 views

Asymmetric key derivation – Who derives the new pub key can't know the new private key

I'm looking for a peer reviewed protocol or algorithm that can do this, preferentially I need something based on elliptic-curves cryptography. Alice know the main public key of Bob (B-PUB-1). Alice ...
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1answer
63 views

Symmetry between a public and a private key

I know that the private and public key in assymetric cryptography are different and the public is used for encryption while the private for decryption. My question is if they are symmetrical to each ...
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0answers
94 views

Decrypt a public encrypted message and Sign a signature, how the math is different?

As I understand, when you want to send a confidential message to someone, you encrypt the message with his public key. And he use his private key to decrypt the message. At the same time, one can use ...
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2answers
1k views

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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1answer
116 views

Does AES 256 really make sense in hybrid crypto systems when the PKI is the bottleneck?

AES 256 is used widely in hybrid crypto systems (e.g. SSL/TLS). According to keylength.com a 2048 bit public key corresponds to 112 bits of security. Does it make sense to use AES 256 in this ...
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1answer
68 views

Generating the keys for the RSA cryptosystem in probabilistic polynomial time

In general every public key cryptosystem ``has'' a probabilistic polynomial time algorithm $G$ such that $G(1^k)=(\textrm{public key}, \textrm{private key=trapdoor})$; $G$ is called the key generator. ...
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1answer
303 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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1answer
56 views

What cryptographic paradigm is appropriate for this use case?

This is a very newbie question... I have to quickly implement a solution for our application that works like this... We have a binary executable that is given a configuration file. I need to encrypt ...
3
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1answer
1k views

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 ...
3
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2answers
191 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 \\ ...
3
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1answer
156 views

Are RSA or ECC vulnerable to an attack where the same (unknown) plaintext is encrypted with multiple public keys?

I'm not sure what this attack model is called - it's not known-plaintext and also not quite cipher-text-only. It is similar to this question except the general case (not just two keys) and using keys ...
0
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1answer
52 views

Is the product of two primes only factorisable by those two primes? [closed]

The question is as per the subject line. Does the fundamental theorem of arithmetic imply (prove?) that if I multiply two primes, then those two primes are the only factors of the product? I.e. 17 x ...
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268 views

Security of RSA for paranoids with padding?

RSA for Paranoids (RSAP) (in cryptobytes v3n1), also known as Unbalanced RSA, is a variant of RSA proposed in 1995 by Adi Shamir, as a mean to increase the RSA public modulus size while keeping ...
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1answer
99 views

Key construction in the Full Cramer-Shoup cryptosystem

The Full Cramer-Shoup Encryption scheme needs to choose six random numbers from $\mathbb{Z}_q$, which we denote them by $ x_1,x_2,y_1,y_2,z_1,z_2 $. Then the scheme hides these random numbers in the ...
3
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2answers
247 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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1answer
324 views

How to select $g$ in Paillier Cryptosystem

For my cryptography class project in university I have selected Paillier Cryptosystem as a course project ...
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1answer
80 views

How to keep phi(n) secret in RSA?

As we know, RSA cryptosystem have both private key(a,p,q) and public key(b,n), by chinese remainder theorem and fermat's little theorem, we know that the importance of keep p and q secret, and from ...
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83 views

Threshold signatures vs. certificate authority+voting verification

Perhaps a silly question, but I am wondering what the advantages are of threshold signatures. Let's consider the following two signature schemes: $(t,n)$-threshold signature with a trusted dealer, ...
3
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1answer
144 views

Why do we encrypt-then mac but sign-then-encrypt?

This question was asked in comments on my answer to should we sign then encrypt or encrypt then sign. I think posing the question as a separate entity is best, so: The general advice for applying ...
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2answers
1k views

Cycle attack on RSA

I originally posted this question in the mathematics section, you can see it here. Let $p$ and $q$ be large primes, $n=pq$ and $e : 0<e<\phi(n), \space gcd(e, \phi(n))=1$ the public encyption ...
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1answer
169 views

Security Consideration on The Use of Random Number in Digital Signature

key-exchange protocol allows two parties to establish a shared key over public network. Lacking of authentication the original Diffie–Hellman key exchange is insecure under man-in- -the-middle ...
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1answer
240 views

Is symmetric key encrypted with server's public key secure

I'm trying to implement lightweight yet secure protocol for communicating two trusted parties with each other. Consider following scheme: Alice wants to establish secure two-sided channel with ...
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1answer
69 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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1answer
372 views

Verify Signature Failed [closed]

I am writing a small module which will verify signed message. Message will be signed using private key in Smart Card. The inputs are: Signed Message Original Message Public Key / Certificate with ...
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1answer
2k views

Generating Random Primes

Although this has been extensively discussed around here, I'm curious whether my approach makes sense, or I should just stick to "the standard version". I'm implementing some homomorphic encryption ...
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1answer
308 views

How are trapdoor functions developed/found and where can I find existing ones?

Trapdoor functions are a fundamental part of public key cryptography. An example of the most common trapdoor is Prime Factorization, used in cryptosystems such as RSA How are these trapdoor ...
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51 views

1-1 trapdoor function mapping the set of $n$-bit numbers to themselves

I am looking for a trapdoor one-to-one function $f : \{0,1\}^n \rightarrow \{0,1\}^n$ (that is, mapping the set of $n$ bit numbers 1-1 onto itself [any $n$ is OK]). I was considering the use of ...
2
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1answer
148 views

Do any one-key-of-many cryptographic schemes exist?

I'm pretty sure I understand how public/private key cryptography works. Anybody can encrypt a message using a well-known public key, but only the person who holds the private key can decrypt it. My ...