RSA Modular Math

Extended Euclidean + successive squaring

Mission tie-in: Your RSA lecture builds the private key by hand. This lesson matches the professor's 5-column table (A, B, Q, X, Y) and binary exponentiation for encryption.

Step 1 — Find d (multiplicative inverse of e mod φ)

Given e = 19, φ(n) = 160. Find d such that e·d ≡ 1 (mod 160).

Step 2 — Encrypt M = 21 with successive squaring

Compute C = 2119 mod 187.

Check: 9859 mod 187 = 21 (decryption works)

Retrieval practice

What is d when e=19 and φ=160?

Retrieval practice

Encrypt M = 21 with e = 19 mod n = 187 (successive squaring). What is C?

Stuck? Ask: "Walk me through the Extended Euclidean table for e=7, φ=40."