Trap-Door Cryptosystems

What is a trap-door cryptosystem?

• Asymmetric, public-key system

• Four sets:
  • $\mathcal {P}$ = the set of all possible plaintexts
  • $\mathcal {C}$ = the set of all possible ciphertexts
  • $\mathcal {U}$ = the set of all possible public keys
  • $\mathcal {R}$ = the set of all possible private keys

• ``One-way'' function f : $\mathcal {R}$$\to$$\mathcal {U}$, bijective

• Encryption and decryption functions:
  • For each u in $\mathcal {U}$, E_u : $\mathcal {P}$$\to$$\mathcal {C}$
  • For each r in $\mathcal {R}$, D_r : $\mathcal {C}$$\to$$\mathcal {P}$
  • D_r(E_f(r)(P)) = P for all P in $\mathcal {P}$
  • E_u is also called a ``trap-door one-way function''

Computational Requirements

1. ``Easy'' to find r in $\mathcal {R}$ and compute u = f (r) given r

2. ``Easy'' to compute C = E_u(P) given P and u

3. ``Easy'' to compute P = D_r(C) given C and r

4. ``Hard'' to compute r = f^-1(u) given only u

5. ``Hard'' to compute P = D_f^-1(u)(C) given only u and C

About this document ...

Trap-Door Cryptosystems

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