That slides contains some explanation of the "All-or-Nothing Disclosure of Secrets" protocol introduced by Bruce Schneier in Applied Cryptography, Second Edition: Protocols, Algorithms, and Source Code in C
3. FBI
The fixed bit index of x and y are the bits
where the ith bit of x equals the ith bit of y.
x = 110101001011
y = 101010000110
FBI(x, y) = {1, 4, 5, 11}
4. (1)
Alice generates a public-key/private-key key pair and
tells Bob (but not Carol) the public key. She generates
another public-key/private-key key pair and tells Carol
(but not Bob) the public key.
Alice
Bob Carol
B C
5. (2)
Bob generates k n-bit random numbers, B1 , B2 , ..., Bk,
and tells them to Carol. Carol generates k n-bit random
numbers, C1 , C2 , ..., Ck, and tells them to Bob.
Bob Carol
B1 , B2 , ..., Bk
C1 , C2 , ..., Ck
6. (3)
Bob encrypts Cb (remember, Sb is the secret he wants
to buy) with the public key from Alice. He computes the
FBI of Cb and the result he just encrypted. He sends this
FBI to Carol.
Bob Carol
FBI(Cb, E(Cb)) =
FBI(Bc, E(Bc)) =
b
c
B
C
7. (4)
Alice
Bob Carol
CB
b
C
B
…, compl(FBIc,Bi), … …, compl(FBIb,Ci), …
Bob takes each of the n-bit numbers B1, B2 , ..., Bk, and
replaces every bit whose index is not in the FBI he
received from Carol with its complement. He sends this
new list of n-bit numbers, B'1, B'2, ..., B'k, to Alice
8. (5)
Alice decrypts all C'i with Bob’s private key, giving her k
n-bit numbers: C"1, C"2, ..., C"k. She computes
Si ⊕ C"i, for i = 1 to k, and sends the results to Bob
Alice
Bob Carol
CB
b
C
B
…, Si ⊕ D(C’i), … …, Si ⊕ D(B’i), …
9. (5)
Alice decrypts all C'i with Bob’s private key, giving her k
n-bit numbers: C"1, C"2, ..., C"k. She computes
Si ⊕ C"i, for i = 1 to k, and sends the results to Bob
Alice
Bob Carol
CB
b
C
B
…, Si ⊕ D(compl(FBIb,Ci)), … …, Si ⊕ D(compl(FBIc,Bi)), …
10. (6)
Bob computes Sb by XORing Cb and the bth number
he received from Alice.
Bob Carol
B
b
C
Sb
C’’i ⊕ Ci B’’i ⊕ Bi
Sc
Alice
11. REFERENCES
1. All-or-Nothing Disclosure of Secrets. Bruce Schneier.
Applied Cryptography, Second Edition: Protocols,
Algorithms, and Source Code in C. Wiley Computer
Publishing, John Wiley & Sons, Inc.
2. Python implementation:
https://gitlab.com/yalegko/secret-disclosure
