Gambling with Secrets: Part 6/8 (Perfect Secrecy & Pseudorandomness)

Bob hides a selected card from Eve by returning it to the deck and shuffling rather than locking it separately, achieving perfect secrecy through randomization instead of physical security mechanisms.

Shannon demonstrated that perfect secrecy requires the message space, key space, and ciphertext space to have equal size, with each possible message mapping uniquely to one ciphertext through each possible key.

Computer scientists distinguish between what adversaries can theoretically accomplish versus what they can achieve within reasonable time bounds, exemplified by bike locks that anyone could crack given sufficient time.

Pseudorandom generators expand short random seeds into long random-appearing sequences, with a 4-digit seed producing one of 10,000 possible 20-digit sequences rather than the 26-to-the-20th-power truly random possibilities.

Mathematicians visualize random sequences by drawing paths that change direction according to each generated number, creating random walks that demonstrate pattern absence across all observation scales.

Cryptographers must continuously increase pseudorandom seed sizes as computers become faster, maintaining the requirement that exhaustive seed search remains computationally infeasible for contemporary hardware.

Claude Shannon published the mathematical definition of perfect secrecy on September 1, 1945, in a classified paper that formalized when encryption systems provide absolute security regardless of adversary computational power.

Pseudorandomness frees Alice and Bob from sharing message-length random keys in advance, requiring only short random seed exchange that both parties independently expand into identical random-looking sequences when needed.

Physical systems generate truly random numbers through measuring random fluctuations called noise, with processes like TV static electrical current providing non-deterministic number sequences when sampled over time.