International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: A General Correlation Theorem

Kishan Chand Gupta
Palash Sarkar
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Abstract: In 2001, Nyberg proved three important correlation theorems and applied them to several cryptanalytic contexts. We continue the work of Nyberg in a more theoretical direction. We consider a general functional form and obtain its Walsh transform. Two of Nyberg's correlation theorems are seen to be special cases of our general functional form. S-box look-up, addition modulo $2^{2k}$ and X-OR are three frequently occuring operations in the design of symmetric ciphers. We consider two methods of combining these operations and in each apply our main result to obtain the Walsh transform.
  title={A General Correlation Theorem},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography /  Boolean function, cryptanalysis, AES, DES.},
  note={not published 12223 received 19 Jun 2003, last revised 19 Jun 2003},
  author={Kishan Chand Gupta and Palash Sarkar},