The Pohlig-Hellman exponentiation cipher as a
bridge between classical and modern cryptography

                          ...
The Pohlig-Hellman Exponentiation Cipher:
Background




   Originally proposed in 1976 (about same time as Diffie-Hellman)...
A Classical (Block) Additive Cipher



   m letters → 2m-digit number
   Example: m = 2, blocks are 4 digit numbers
      ...
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography
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The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography

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The Pohlig-Hellman exponentiation cipher is a symmetric-key cipher that uses some of the same mathematical operations as the better-known RSA and Diffie-Hellman public-key cryptosystems. First published in 1978, the Pohlig-Hellman cipher was never of practical importance due to its slow speed compared to ciphers such as DES and AES. The theoretical importance of the Pohlig-Hellman cipher comes from the fact that it relies on the Discrete Logarithm Problem for its resistance against known plain text attacks, as does RSA and several other modern cryptosystems. For this reason, the Pohlig-Hellman systemcan play a very important role pedagogically, since it also shares many features in common with classical ciphers such as shift ciphers and Hill ciphers. Thus, it allows the instructor to introduce the important concepts of the discrete logarithm and known plain text attacks separately from the more conceptually difficult idea of public-key cryptography.

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The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Modern Cryptography

  1. 1. The Pohlig-Hellman exponentiation cipher as a bridge between classical and modern cryptography Joshua Holden Rose-Hulman Institute of Technology http://www.rose-hulman.edu/~holden Joshua Holden (RHIT) The Pohlig-Hellman exponentiation cipher 1 / 17
  2. 2. The Pohlig-Hellman Exponentiation Cipher: Background Originally proposed in 1976 (about same time as Diffie-Hellman) Not published until after RSA and Diffie-Hellman Private key cipher In some ways, logical successor to classical ciphers But also uses ideas from RSA and Diffie-Hellman Joshua Holden (RHIT) The Pohlig-Hellman exponentiation cipher 2 / 17
  3. 3. A Classical (Block) Additive Cipher m letters → 2m-digit number Example: m = 2, blocks are 4 digit numbers ca → 0200 ts → 1918 an  

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