1. Merkle-Hellman

2. Merkle-Hellman
= 30 =
(Encrypted)

3. Merkle-Hellman 3 5 9 18 40 1 0 1 1 0 = 30 = 0 1 1 1 1 (Encrypted)
= 30 =
(Encrypted)
30 < so first bit is (Decrypt)

4. Merkle-Hellman 3 5 9 18 40 1 0 1 1 0 = 30 = 0 1 1 1 1 (Encrypted)
= 30 =
(Encrypted)
30 < so first bit is (Decrypt)
30 > 18 so second bit is 1 remainder is 12

5. Merkle-Hellman 3 5 9 18 40 1 0 1 1 0 = 30 = 0 1 1 1 1 (Encrypted)
= 30 =
(Encrypted)
30 < so first bit is (Decrypt)
30 > 18 so second bit is 1 remainder is 12
12 > 9 so third bit is 1 remainder is 3

6. Merkle-Hellman 3 5 9 18 40 1 0 1 1 0 = 30 = 0 1 1 1 1 (Encrypted)
= 30 =
(Encrypted)
30 < so first bit is (Decrypt)
30 > 18 so second bit is 1 remainder is 12
12 > 9 so third bit is 1 remainder is 3
3 < 5 so fourth bit is 0

7. Merkle-Hellman 3 5 9 18 40 1 0 1 1 0 = 30 = 0 1 1 1 1 (Encrypted)
= 30 =
(Encrypted)
30 < so first bit is (Decrypt)
30 > 18 so second bit is 1 remainder is 12
12 > 9 so third bit is 1 remainder is 3
3 < 5 so fourth bit is 0
3 == 3 so fifth bit is 1 and we are done

8. Merkle-Hellman 3 5 9 18 40 Public key 1 0 1 1 0 = 30 = 0 1 1 1 1
Public key
= 30 =
(Encrypted)
30 < so first bit is (Decrypt)
30 > 18 so second bit is 1 remainder is 12
12 > 9 so third bit is 1 remainder is 3
3 < 5 so fourth bit is 0
3 == 3 so fifth bit is 1 and we are done

9. Merkle-Hellman
Problem: Anyone can decrypt the message

10. Merkle-Hellman Problem: Anyone can decrypt the message
So, choose multiplier m and modulus p
and for every number ki in the key set pki = ki*m mod p
for example, if m=4571 and p=7187 then

11. Merkle-Hellman Problem: Anyone can decrypt the message
So, choose multiplier m and modulus p
and for every number ki in the key set pki = ki*m mod p
for example, if m=4571 and p=7187 then ⇒

12. Merkle-Hellman Problem: Anyone can decrypt the message
So, choose multiplier m and modulus p
and for every number ki in the key set pki = ki*m mod p
for example, if m=4571 and p=7187 then
The bottom part and p are sent as the public key, the inverse
of m and p are the private key. The inverse m-1 of m is 1283
(See ⇒

13. Merkle-Hellman Problem: Anyone can decrypt the message
So, choose multiplier m and modulus p
and for every number ki in the key set pki = ki*m mod p
for example, if m=4571 and p=7187 then
The bottom part and p are sent as the public key, the inverse
of m and p are the private key. The inverse m-1 of m is 1283
(See
What is an inverse?
Start with msg = ∑ici*ki
Encrypt: ∑ici*ki*m mod p
Decrypt: ∑ici*ki*m*m-1 mod p = ∑ici*ki*1 mod p = ∑ici*ki ⇒

14. Merkle-Hellman Problem: Anyone can decrypt the message
So, choose multiplier m and modulus p
and for every number ki in the key set pki = ki*m mod p
for example, if m=4571 and p=7187 then
The bottom part and p are sent as the public key, the inverse
of m and p are the private key. The inverse m-1 of m is 1283
(See
Encrypt: as = 18329 ⇒

15. Merkle-Hellman Problem: Anyone can decrypt the message
So, choose multiplier m and modulus p
and for every number ki in the key set pki = ki*m mod p
for example, if m=4571 and p=7187 then
The bottom part and p are sent as the public key, the inverse
of m and p are the private key. The inverse m-1 of m is 1283
(See
Encrypt: as = 18329
Decrypt: *1283 mod 7187 = mod 7187 =
use = 243 to receive
(See ⇒