Cryptography207610 marksNumerical: ElGamal cryptosystem encryptionElgamal Cryptographic System
State Fermat’s theorem with an example. Given the prime number p=29 and its primitive root g=8, private key sender with X=9 and random integer K=11, encrypt the message m=13 using ElGamal cryptosystem.
State Fermat’s theorem with an example. Given the prime number p=29 and its primitive root g=8, private key sender with X=9 and random integer K=11, encrypt the message m=13 using ElGamal cryptosystem.[10]
If $p$ is a prime number and $a$ is an integer with $\gcd(a, p) = 1$, then: $$a^{p-1} \equiv 1 \pmod{p}$$ Let $p = 7$, $a = 3$: $$3^{6} \bmod 7$$ - $3^2 = 9 \equiv 2 \pmod 7$ - $3^3 = 27 \equiv 6 \pmod 7$ - $3^6 = (3^3)^2 = 6^2 = 36 \equiv 1 \pmod 7$ Thus $3^6 \equiv 1 \pmod 7$, confirming the th...