In Memory of Stephen Pohlig

The foundation of our modern cyber security world was laid-down in the 1970s with the work of Ron Rivest, Adi Shamar, Whitfield Diffie and…

In Memory of Stephen Pohlig

The foundation of our modern cyber security world was laid-down in the 1970s with the work of Ron Rivest, Adi Shamar, Whitfield Diffie and Martin Hellman. One person who contributed greatly in the creation of the foundation was Stephen Pohlig. Unfortunately he died last year on 14 April 2017, but he left a great legacy.

In 1977, Stephen graduated with a PhD from Stanford University, and then became part of Martin Hellman’s amazing team at MIT. One of the labs core contributions was the Diffie-Hellman key exchange method. Stephen also contributed greatly to the foundation of cryptography with the creation of the Pohlig-Hellman exponential cipher, and also the Pohlig-Hellman method in solving discrete logarithms.

The exponential cipher cleared the ground for the RSA method. Here is an example:

https://asecuritysite.com/principles_pub/exp

Exponential ciphers uses a form of C=Mᵉ(mod p) to encrypt and decrypt a message (M) using a key of e and a prime number p. The following are some examples:

  • message = 5, e=5, p = 53. Try. This should give 5⁵ (mod 53) = 3125 (mod 53) = 51
  • message = 4, e=11, p = 79. Try. This should give 4¹¹ (mod 79) = 4194304 (mod 79) = 36

First we create a prime number, such as:

p = 5

The cipher is:

Cipher = Message^e mod p

For example if we have a Message of 2 and e of 3 we get:

Cipher = 2^3 mod 5 = 3

Outline code:

message = raw_input('Enter message: ')
e =  raw_input('Enter exponent: ') 
p = raw_input('Enter prime ')
cipher = (int(message) ** int(e)) % int(p)
print cipher

In many modern cryptography methods we use discrete logarithms, and which use the form:

h=gˣ(mod p)

and where p is a prime number, g is a generator value, and x is a secret value. The value is thus to find x for a given set of h, g and p values. Stephen’s inspiration shown through with the creation of the Pohlig-Hellman method:

https://asecuritysite.com/logs/log_poh

Here is some examples:

  • 8=5ˣ (mod43) Ans: 15 Try!
  • 22=5ˣ(mod53) Ans: 9 Try!
  • 15=7ˣ (mod131) Ans: 8 Try!
  • 50=11ˣ (mod997) Ans: 411 Try!

Conclusions

The roots of our modern cyber security world were created in the 1970s, and many of the core methods that we use now to secure data were developed then. The Diffie-Hellman method (with its discrete logarithms) lives on in the Elliptic Curve Diffie Hellman method. Stephen thus laid the ground for the RSA public key method, and also provided a way to solve discrete logs. The work of the 1970s led then led the way for the Cyber Punks in the 1990s to advanced their work in creating cryptocurrencies (Bitcoin) and blockchain. Though cryptography we move forward each day to a world which is more trusted and more secure.

So think about Stephen Pohlig when you see that little green padlock on your Web browser, as he helped make it trustworthy.