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The concepts of digital envelopes, zero knowledge, and the role of computational complexity in enabling digital security and privacy in modern cryptography. It covers the history of cryptography, the challenges of secure online elections, and the concepts of one-way functions and digital envelopes. The document also introduces the El Gamal encryption scheme and the power of digital envelopes, as well as the concepts of simultaneity and symmetry breaking in cryptography.
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Axiom 1: Agents are computationally
limited.
p,q pq
Fact: Axioms -- > “Digital Envelope”
x E(x)
Public Lottery (on the phone)
Identification / Passwords
alice Palice =E (…)
grant Pgrant=E (haha)
bob Pbob =E (…)
Computer: 1 checks if E (pswd)= Pgrant
login: grant password: haha
Zero-Knowledge Proof
with high probability
Goldwasser-Micali -Rackoff 1984