Redundancy in XOR encryption
-----BEGIN PGP SIGNED MESSAGE----- I have a question I hope someone here might be able to answer: As the method of cryptanalysis of XOR (Ie. index of coincidence) relies on redundancy in the plaintext, would the following be strong: Compress P to get perfect compression (ie. 0 redundancy) Encrypt F (the compressed text) using a repeated key XOR of course this is all rather theoretical as there is no such thing as perfect compression, but I just thought it might be interesting to see if this is indeed strong, superficially it appears so to me... -----BEGIN PGP SIGNATURE----- Version: 2.6.3ia Charset: cp850 iQCVAwUBMj2TvL5OPIRbv66xAQGRpgP+LU0Y8sxzO6rObCYAQdrD8/R/iDJN3m0Z 4ZetS7jcbz7wT6bj2l7Usb0F4h/YMhxtl0y9EQ91ozg35jfRKdy2IwUoMDvqsVSZ wKmaM/DpEt2LDyRQnzIvlNYQp6/eXQoBUb7r9SH/dZbjM7culpjzJLhd07Nx5okE jUmPNBLm9m0= =RHie -----END PGP SIGNATURE----- Datacomms Technologies web authoring and data security Paul Bradley, Paul@fatmans.demon.co.uk Http://www.fatmans.demon.co.uk/crypt/ "Don`t forget to mount a scratch monkey" -----BEGIN PGP PUBLIC KEY BLOCK----- Version: 2.6.3ia mQCNAjH9j+cAAAEEAMBvREiQR0ot9dFCO0TiSCSunAYLv2g1Bc6I3bz8FzKXNH53 6mieJf/W4rD+CxJpT0q9RQaaoRtkHJLwbjfK2il3D7mEahMAyqvF/xRJNqkXfhM3 sRJM0Jh43l+W0M5vwokbEbk25/bxWWGspTsLD3YHbzKnG6pOcL5OPIRbv66xAAUR tCdQYXVsIEJyYWRsZXkgPHBhdWxAZmF0bWFucy5kZW1vbi5jby51az6JAJUDBRAy NwfvNkCBjDT0xHEBATQPA/9TORmN/UjNecj03q4anpvdyCLiez5sKuNbnYK50RiP Jj4QpWWvST3smyQ0A86DrZY/re056MXwQmARESx0rFZxdnD0oORICl5r8dJLIy3b j8rbA5olXwZwKz73/X5s13v/pvHYX4cIsbVK8NHXqh5llSKt6TBAuGgkIGF29z5k C4kAlQMFEDI3B9mdtf/umVkv7QEBcRYD/1FBteLqsUmr81euxqqnnrpLlyHb58B/ 9sdATuua4uSjX46hXDZ264YozspNrzSB4NEdrmXOWVX3fiE0ga6XkSSkIeF23V90 En37Z0BdbFzgF00FRYTFyTq8eezQrdg/+rBPUsZUmG5wpq3e12FKHQsX01i+1mB2 YmqqwCV5e95eiQCVAgUQMh8uSb5OPIRbv66xAQEqJwP/fxQyiCasjFcbDpsFfsYp put5cCC/9pOx6X3DlbKShPMpUOS+A9HsTEmJQN8Iawv1nSwPdtc2cR/GhW6ilVjW LSloGdMVLabm9pGpZZMkRaZlXFUkOv7VhfgsUiL+vIDryBCAwUZCzQiWycjt/cPi mUqFH41Z7NkyO8ZFdi5GGX0= =CMZA -----END PGP PUBLIC KEY BLOCK-----
paul@fatmans.demon.co.uk wrote:
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I have a question I hope someone here might be able to answer:
As the method of cryptanalysis of XOR (Ie. index of coincidence) relies on redundancy in the plaintext, would the following be strong:
Compress P to get perfect compression (ie. 0 redundancy) Encrypt F (the compressed text) using a repeated key XOR
of course this is all rather theoretical as there is no such thing as perfect compression, but I just thought it might be interesting to see if this is indeed strong, superficially it appears so to me...
Paul: I think that if the cryptanalyst knows that F has zero redundancy that he can run searches from 0 to n bits for the key and have the computer flag solutions that have zero redundancy. I also think that a perfectly compressed file would have a relative entropy value close to one also, hence the computer could flag possibles that have both characteristics. Hence, instead of searching for plaintext by counting coincidences, we are searching the decrypts for solutions that have zero redundancy and a relative entropy value close to one. How many solutions will have both these qualities? I don't know. But if the compression method is known, brute force will be tried, and only having to try to decompress (read) data that has the resultant characteristics of compressed information will speed things up by quite a bit. Others may disagree with my thought-experiment and my approach, but I think this is quite possible ... even to persons with limited computing resources. Brian Durham bdurham@metronet.com
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Brian Durham -
paul＠fatmans.demon.co.uk