Алгоритм эль гамаля python

The ElGamal ciphertext is twice as big as p.

Domain parameters¶

For both signature and encryption schemes, the values (p,g) are called domain parameters. They are not sensitive but must be distributed to all parties (senders and receivers). Different signers can share the same domain parameters, as can different recipients of encrypted messages.

Security¶

Both DLP and CDH problem are believed to be difficult, and they have been proved such (and therefore secure) for more than 30 years.

The cryptographic strength is linked to the magnitude of p. In 2017, a sufficient size for p is deemed to be 2048 bits. For more information, see the most recent ECRYPT report.

The signature is four times larger than the equivalent DSA, and the ciphertext is two times larger than the equivalent RSA.

Functionality¶

This module provides facilities for generating new ElGamal keys and constructing them from known components.

Crypto.PublicKey.ElGamal. generate ( bits, randfunc ) ¶

Randomly generate a fresh, new ElGamal key.

The key will be safe for use for both encryption and signature (although it should be used for only one purpose).

• bits (int) – Key length, or size (in bits) of the modulus p. The recommended value is 2048.
• randfunc (callable) – Random number generation function; it should accept a single integer N and return a string of random N random bytes.

Construct an ElGamal key from a tuple of valid ElGamal components.

The modulus p must be a prime. The following conditions must apply:

\[\begin\begin &1 < g < p-1 \\ &g^= 1 \text < mod >1 \\ &1 < x < p-1 \\ &g^x = y \text< mod >p \end\end\]

A tuple with either 3 or 4 integers, in the following order:

Class defining an ElGamal key. Do not instantiate directly. Use generate() or construct() instead.

Whether this is an ElGamal private key

A matching ElGamal public key.

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ElGamal Encryption Algorithm in Python

Elgamal Encryption is a type of asymmetric key algorithm used for encryption. It is used for public-key cryptography and is based on the Diffie-Hellman key exchange.

Here, I will include the introduction, uses, algorithm, and code in Python for Elgamal Encryption Algorithm.

This asymmetric-key encryption cryptography is on the basis of the difficulty of finding discrete logarithm in a cyclic group that means we know g^a and g^k, computes g^ak.

USE: Hybrid cryptosystem uses this algorithm.

Elgamal Encryption Algorithm has three parts

Public Parameter: A trusted third party publishes a large prime number p and a generator g.

1.Key Generation:

2. Encryption:

3. Decryption:

• Alice computes x=c1^a mod p and its inverse x^-1 with the extended Euclidean algorithm.
• Computes the plaintext m’=Dsk(c1,c2)= x^-1.c2 mod p where m’=m.

import random from math import pow a=random.randint(2,10) #To fing gcd of two numbers def gcd(a,b): if a0: if b%2==0: x=(x*y)%c; y=(y*y)%c b=int(b/2) return x%c #For asymetric encryption def encryption(msg,q,h,g): ct=[] k=gen_key(q) s=power(h,k,q) p=power(g,k,q) for i in range(0,len(msg)): ct.append(msg[i]) print(«g^k used= «,p) print(«g^ak used= «,s) for i in range(0,len(ct)): ct[i]=s*ord(ct[i]) return ct,p #For decryption def decryption(ct,p,key,q): pt=[] h=power(p,key,q) for i in range(0,len(ct)): pt.append(chr(int(ct[i]/h))) return pt msg=input(«Enter message.») q=random.randint(pow(10,20),pow(10,50)) g=random.randint(2,q) key=gen_key(q) h=power(g,key,q) print(«g used=»,g) print(«g^a used=»,h) ct,p=encryption(msg,q,h,g) print(«Original Message=»,msg) print(«Encrypted Maessage=»,ct) pt=decryption(ct,p,key,q) d_msg=».join(pt) print(«Decryted Message 94365a85b89752c4e3cfeb40-text/javascript» data-no-defer=»1″>const post_content = document.getElementById(‘post-content’); const paragraph_for_ad = post_content.getElementsByTagName(«p»); // console.log(«FRK»); //console.log(«frk tag»+paragraph_for_ad.length); if (window.innerWidth 5) < let adparagraph = paragraph_for_ad[2]; adparagraph.insertAdjacentHTML('afterEnd', '

‘); > if (paragraph_for_ad.length > 15) < let adparagraph = paragraph_for_ad[10]; adparagraph.insertAdjacentHTML('afterEnd', '

‘); > if (paragraph_for_ad.length > 30) < let adparagraph = paragraph_for_ad[25]; adparagraph.insertAdjacentHTML('afterEnd', '

‘); > > else if(window.innerWidth > 1360) < if (paragraph_for_ad.length >15) < let adparagraph = paragraph_for_ad[10]; // 71161633/article_incontent_1/article_incontent_1 adparagraph.insertAdjacentHTML('afterEnd', '

‘); > if (paragraph_for_ad.length > 22) < let adparagraph = paragraph_for_ad[18]; // 71161633/article_incontent_2/article_incontent_2 adparagraph.insertAdjacentHTML('afterEnd', '

‘); > if (paragraph_for_ad.length > 30) < let adparagraph = paragraph_for_ad[29]; // 71161633/article_incontent_1/article_incontent_1 adparagraph.insertAdjacentHTML('afterEnd', '

3 responses to “ElGamal Encryption Algorithm in Python”

How do I implement and verify the homomorphic property of ElGamal algorithm? I mean how do I allow users to input m1 and m2 from keyboard and verify that E(m1m2)=E(m1)E(m2) by adding some codes to above program? Thank you!

If you don’t use a primitive root of p as g you could end up with g being subgroup of much reduced order which then would only generate numbers within the subgroup. This could lead to keystream reuse and therefore seriously weaken the encryption. Finding a primitive root g mod p with p >> 1024 Bit is not trivial, as one ends up with the same problem as with finding a huge prime. But simply using a random g could lead to serious security issues if this code would ever be used in a production environment with high security requirements. Its good enough to show the function, not good enough to be used as either teaching nor production material. The original paper by Taher Elgamal even states that g must be a primitive root mod p.

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A Python implementation of Elgamal algorithm: encryption, decryption and signature generation and verification

ricardojoserf/elgamal-python

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README.md

Implementation of Elgamal algorithm in Python, based on these series of videos (the parameter nomenclature is based on them).

Public and private keys are composed of 3 elements each:

• p (parameter -m): A random integer
• alfa (parameter -a): A generator of Zp
• b (parameter -b): A secret integer between 2 and (p-2)
• B (parameter -B): A public modular exponentiation calculated as B = (alfa^(b))mod(p)

For the encryption process, it is necessary to add —encrypt, the parameters of the public key (-p, -a and -B) and the plaintext message (parameter -m). The verbose parameter (-vv) is optional:

python3 main.py --encrypt -p 79 -a 30 -B 59 -m 44 -vv 

For the decryption process, it is necessary to add —decrypt, the parameters of the private key (-p, -a and -b), the encrypted message (parameter -m) and the ephemeral key received with the message (-ke). The verbose parameter (-vv) is optional:

python3 main.py --decrypt -p 79 -a 30 -b 61 -m 73 -ke 13 -vv 

For the signing process, it is necessary to add —sign, the parameters of the private key (-p, -a and -b) and the plaintext message (parameter -m). The verbose parameter (-vv) is optional:

python3 main.py --sign -p 541 -a 128 -b 105 -m 95 -vv 

For the signature verification process, it is necessary to add —verify, the parameters of the public key (-p, -a and -B), the plaintext message (parameter -m) and the signature parameters (-r and -s):

python3 main.py --verify -p 541 -a 128 -B 239 -m 95 -r 280 -s 65 -vv 

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A Python implementation of Elgamal algorithm: encryption, decryption and signature generation and verification

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Python implementation of the elgamal crypto system

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RyanRiddle/elgamal

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README.md

Overview: elgamal is a python module that lets you encrypt and decrypt text using the ElGamal Cryptosystem.

Intended Use: This program was created as an exercise in cryptography in one of my classes at the University of Kentucky. I later turned it into a module. I do not recommend you use it to protect any sensitive information.

Using elgamal: Install elgamal by downloading elgamal.py and placing it in your module search path.

If you don’t know your module search path, fire up a python console and run

To generate a public/private key pair do

elgamal.generate_keys() #returns a dictionary

By default generate_keys() generates a key of 256 bits with probability 0.9999999997671694 (1-(2^-32)) that your key is prime. You can alter the bitness of your keys and the certainty that your key is prime by passing arguments n and t like this.

where n is the number of bits you want your key to have and t means the probability that the key is prime is 1-(2^-t).

cipher = elgamal.encrypt(publicKey, "This is the message I want to encrypt") #returns a string 

To decrypt the cipher text do

plaintext = elgamal.decrypt(privateKey, cipher) #returns the message passed to elgamal.encrypt() 

Compatibility: Python 3.4. Does not work in python 2.7!

Like this module? Tell me what you like about it here https://goo.gl/forms/nA8gBcjPiwAoWzg32

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Python implementation of the elgamal crypto system

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