World Library  
Flag as Inappropriate
Email this Article

Xxtea

Article Id: WHEBN0010919454
Reproduction Date:

Title: Xxtea  
Author: World Heritage Encyclopedia
Language: English
Subject: Cobra ciphers, Xor-encrypt-xor, Lai-Massey scheme, BEAR and LION ciphers, Chiasmus (cipher)
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Xxtea

Corrected Block TEA (XXTEA)
One round of XXTEA
General
Designers David Wheeler, Roger Needham
First published October 1998
Derived from Block TEA
Cipher detail
Key sizes 128 bits
Block sizes arbitrary, at least two words (64 bits)
Structure Unbalanced Feistel Network
Rounds depends on the block size; ~52+6*words (6-32 full cycles)
Best public cryptanalysis
XXTEA is vulnerable to a chosen-plaintext attack requiring 259 queries and negligible work.[1]

In cryptography, Corrected Block TEA (often referred to as XXTEA) is a block cipher designed to correct weaknesses in the original Block TEA.[2][3]

XXTEA is vulnerable to a chosen-plaintext attack requiring 259 queries and negligible work. See cryptanalysis below.

The cipher's designers were Roger Needham and David Wheeler of the Cambridge Computer Laboratory, and the algorithm was presented in an unpublished technical report in October 1998 (Wheeler and Needham, 1998). It is not subject to any patents.

Formally speaking, XXTEA is a consistent incomplete source-heavy heterogeneous UFN (unbalanced Feistel network) block cipher. XXTEA operates on variable-length blocks that are some arbitrary multiple of 32 bits in size (minimum 64 bits). The number of full cycles depends on the block size, but there are at least six (rising to 32 for small block sizes). The original Block TEA applies the XTEA round function to each word in the block and combines it additively with its leftmost neighbour. Slow diffusion rate of the decryption process was immediately exploited to break the cipher. Corrected Block TEA uses a more involved round function which makes use of both immediate neighbours in processing each word in the block.

XXTEA is likely to be more efficient than XTEA for longer messages.

Needham & Wheeler make the following comments on the use of Block TEA:

For ease of use and general security the large block version is to be preferred when applicable for the following reasons.
  • A single bit change will change about one half of the bits of the entire block, leaving no place where the changes start.
  • There is no choice of mode involved.
  • Even if the correct usage of always changing the data sent (possibly by a message number) is employed, only identical messages give the same result and the information leakage is minimal.
  • The message number should always be checked as this redundancy is the check against a random message being accepted.
  • Cut and join attacks do not appear to be possible.
  • If it is not acceptable to have very long messages, they can be broken into chunks say of 60 words and chained analogously to the methods used for DES.

However, due to the incomplete nature of the round function, two large ciphertexts of 53 or more 32-bit words identical in all but 12 words can be found by a simple brute-force collision search requiring 296−N memory, 2N time and 2N+296−N chosen plaintexts, in other words with a total time*memory complexity of 296, which is actually 2wordsize*fullcycles/2 for any such cipher. It is currently unknown if such partial collisions pose any threat to the security of the cipher. Eight full cycles would raise the bar for such collision search above complexity of parallel brute-force attacks.

The unusually small size of the XXTEA algorithm would make it a viable option in situations where there are extreme constraints e.g. legacy hardware systems (perhaps embedded) where the amount of available RAM is minimal.

Cryptanalysis

An attack published in 2010 by E. Yarrkov presents a chosen-plaintext attack against full-round XXTEA, requiring 259 queries and negligible work. It is based on differential cryptanalysis.[1]

Reference code

The original formulation of the Corrected Block TEA algorithm, published by David Wheeler and Roger Needham, is as follows:[4]

  #define MX (z>>5^y<<2) + (y>>3^z<<4)^(sum^y) + (k[p&3^e]^z);
  
  long btea(long* v, long n, long* k) {
    unsigned long z=v[n-1], y=v[0], sum=0, e, DELTA=0x9e3779b9;
    long p, q ;
    if (n > 1) {          /* Coding Part */
      q = 6 + 52/n;
      while (q-- > 0) {
        sum += DELTA;
        e = (sum >> 2) & 3;
        for (p=0; p> 2) & 3;
        for (p=n-1; p>0; p--) z = v[p-1], y = v[p] -= MX;
        z = v[n-1];
        y = v[0] -= MX;
        sum -= DELTA;
      }
      return 0;
    }
    return 1;
  }

According to Needham and Wheeler:

BTEA will encode or decode n words as a single block where n > 1
  • v is the n word data vector
  • k is the 4 word key
  • n is negative for decoding
  • if n is zero result is 1 and no coding or decoding takes place, otherwise the result is zero
  • assumes 32 bit 'long' and same endian coding and decoding

Note that the initialization of z will cause a segmentation fault in some languages – it would be better placed inside the 'Coding Part' block. Also, in the definition of MX some programmers would prefer to use bracketing to clarify operator precedence.

A clarified version including those improvements is as follows:

  #include 
  #define DELTA 0x9e3779b9
  #define MX (((z>>5^y<<2) + (y>>3^z<<4)) ^ ((sum^y) + (key[(p&3)^e] ^ z)))
  
  void btea(uint32_t *v, int n, uint32_t const key[4]) {
    uint32_t y, z, sum;
    unsigned p, rounds, e;
    if (n > 1) {          /* Coding Part */
      rounds = 6 + 52/n;
      sum = 0;
      z = v[n-1];
      do {
        sum += DELTA;
        e = (sum >> 2) & 3;
        for (p=0; p> 2) & 3;
        for (p=n-1; p>0; p--) {
          z = v[p-1];
          y = v[p] -= MX;
        }
        z = v[n-1];
        y = v[0] -= MX;
        sum -= DELTA;
      } while (--rounds);
    }
  }

See also

  • RC4: A stream cipher that, just like XXTEA, is designed to be very simple to implement.
  • XTEA: Block TEA's precursor.
  • TEA: XTEA's precursor.

References

  1. ^ a b Elias Yarrkov (2010-05-04). "Cryptanalysis of XXTEA". 
  2. ^ Matthew D. Russell (2004-02-27). "Tinyness: An Overview of TEA and Related Ciphers". Archived from the original on 2007-08-12. 
  3. ^ Roger M. Needham and David J. Wheeler (October 1997). "Tea extensions". Computer Laboratory, Cambridge University, England. Retrieved 2008-07-04. 
  4. ^ David J. Wheeler and Roger M. Needham (October 1998). "Correction to XTEA". Computer Laboratory, Cambridge University, England. Retrieved 2008-07-04. 

External links

  • a JavaScript implementation
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.