Q12Information System Security

Diffie-Hellman (DH) is NOT an encryption algorithm. It is a brilliant mathematical architecture that allows two parties (Alice and Bob) to violently generate an identical, highly secure shared symmetric key while communicating over a completely public, hacker-infested internet. Its absolute security relies on the catastrophic computational difficulty of solving the Discrete Logarithm Problem.

Alice and Bob publicly agree on two mathematical constants: a massive prime number $p$, and a base generator $g$. These are sent in absolute plaintext; hackers can see them.

• Step 1 (Private Secrets): - Alice violently generates a secret integer $a$. She keeps this absolutely hidden. - Bob violently generates a secret integer $b$. He keeps this absolutely hidden.
• Step 2 (Public Calculation): - Alice mathematically calculates her Public component: $A=g^a(\mathrm{mod}p)$. She sends $A$ to Bob over the public internet. - Bob mathematically calculates his Public component: $B=g^b(\mathrm{mod}p)$. He sends $B$ to Alice.
• Step 3 (The Genius Shared Secret): - Alice receives $B$. She mathematically calculates the Shared Secret $S=B^a(\mathrm{mod}p)$. - Bob receives $A$. He mathematically calculates the Shared Secret $S=A^b(\mathrm{mod}p)$.

Both Alice and Bob arrive at the EXACT same mathematical number because: $B^a=(g^b{)}^a=g^{ab}(\mathrm{mod}p)$ $A^b=(g^a{)}^b=g^{ab}(\mathrm{mod}p)$

A hacker sniffing the network sees $p,g,A,$ and $B$. To find the secret key $S$, the hacker MUST find Alice's secret $a$ or Bob's secret $b$. To find $a$, the hacker must mathematically solve $A=g^a(\mathrm{mod}p)$. This is the Discrete Logarithm Problem, and for a 2048-bit prime $p$, it is mathematically impossible to solve before the universe ends.