Label: toy hand arithmetic. Historical 2026-10-12 QA separately recorded toy-rsa.py printing worked n 33, activity n 15 and round trip 4.
Public pair on the worked card: n=33, e=3. Private exponent on that card: d=7.
Message m=4. Cipher c = 4^3 mod 33 = 64 mod 33 = 31.
Return: 31^7 mod 33.
31^2 = 961 = 29*33 + 4
31^4 = 16 mod 33.
31^5 = 1 mod 33.
31^7 = (31^5)*(31^2) = 4 mod 33.
31^7 = 4 mod 33.
Predicted return: 4.

Activity primes: p=3, q=5.
Predicted modulus: 15.