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# Tiny Encryption Algorithm

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### Tiny Encryption Algorithm

 General Two Feistel rounds (one cycle) of TEA[1] Roger Needham, David Wheeler 1994 XTEA 128 bits 64 bits Feistel network variable; recommended 64 Feistel rounds (32 cycles) TEA suffers from equivalent keys (Kelsey et al., 1996) and can be broken using a related-key attack requiring 223 chosen plaintexts and a time complexity of 232.[2] The best structural cryptanalysis of TEA in the standard single secret key setting is the zero-correlation cryptanalysis breaking 21 rounds in 2121.5 time with less than the full code book [3]

In cryptography, the Tiny Encryption Algorithm (TEA) is a block cipher notable for its simplicity of description and implementation, typically a few lines of code. It was designed by David Wheeler and Roger Needham of the Cambridge Computer Laboratory; it was first presented at the Fast Software Encryption workshop in Leuven in 1994, and first published in the proceedings of that workshop.[4]

The cipher is not subject to any patents.

## Contents

• Properties 1
• Versions 2
• Reference code 3
• Notes 5
• References 6

## Properties

TEA operates on two 32-bit unsigned integers (could be derived from a 64-bit data block) and uses a 128-bit key. It has a Feistel structure with a suggested 64 rounds, typically implemented in pairs termed cycles. It has an extremely simple key schedule, mixing all of the key material in exactly the same way for each cycle. Different multiples of a magic constant are used to prevent simple attacks based on the symmetry of the rounds. The magic constant, 2654435769 or 9E3779B916 is chosen to be ⌊232/ϕ⌋, where ϕ is the golden ratio.[4]

TEA has a few weaknesses. Most notably, it suffers from equivalent keys—each key is equivalent to three others, which means that the effective key size is only 126 bits.[5] As a result, TEA is especially bad as a cryptographic hash function. This weakness led to a method for hacking Microsoft's Xbox game console, where the cipher was used as a hash function.[6] TEA is also susceptible to a related-key attack which requires 223 chosen plaintexts under a related-key pair, with 232 time complexity.[2] Because of these weaknesses, the XTEA cipher was designed.

## Versions

The first published version of TEA was supplemented by a second version that incorporated extensions to make it more secure. Block TEA (sometimes referred to as XTEA) operates on arbitrary-size blocks in place of the 64-bit blocks of the original.

A third version (XXTEA), published in 1998, described further improvements for enhancing the security of the Block TEA algorithm.

## Reference code

Following is an adaptation of the reference encryption and decryption routines in C, released into the public domain by David Wheeler and Roger Needham:[4]

#include

void encrypt (uint32_t* v, uint32_t* k) {
uint32_t v0=v[0], v1=v[1], sum=0, i;           /* set up */
uint32_t delta=0x9e3779b9;                     /* a key schedule constant */
uint32_t k0=k[0], k1=k[1], k2=k[2], k3=k[3];   /* cache key */
for (i=0; i < 32; i++) {                       /* basic cycle start */
sum += delta;
v0 += ((v1<<4) + k0) ^ (v1 + sum) ^ ((v1>>5) + k1);
v1 += ((v0<<4) + k2) ^ (v0 + sum) ^ ((v0>>5) + k3);
}                                              /* end cycle */
v[0]=v0; v[1]=v1;
}

void decrypt (uint32_t* v, uint32_t* k) {
uint32_t v0=v[0], v1=v[1], sum=0xC6EF3720, i;  /* set up */
uint32_t delta=0x9e3779b9;                     /* a key schedule constant */
uint32_t k0=k[0], k1=k[1], k2=k[2], k3=k[3];   /* cache key */
for (i=0; i<32; i++) {                         /* basic cycle start */
v1 -= ((v0<<4) + k2) ^ (v0 + sum) ^ ((v0>>5) + k3);
v0 -= ((v1<<4) + k0) ^ (v1 + sum) ^ ((v1>>5) + k1);
sum -= delta;
}                                              /* end cycle */
v[0]=v0; v[1]=v1;
}

Note that the reference implementation acts on multi-byte numeric values. The original paper does not specify how to derive the numbers it acts on from binary or other content.

• RC4 - A stream cipher that, just like TEA, is designed to be very simple to implement.
• XTEA - First version of Block TEA's successor.
• XXTEA - Corrected Block TEA's successor.
• Treyfer - A simple and compact encryption algorithm with 64 bit key size and block size.

## Notes

1. ^ Matthew D. Russell (27 Feb 2004). "Tinyness: An Overview of TEA and Related Ciphers". Archived from the original on 12 August 2007.
2. ^ a b Kelsey, John; Schneier, Bruce; Wagner, David (1997). "Related-key cryptanalysis of 3-WAY, Biham-DES, CAST, DES-X NewDES, RC2, and TEA". Lecture Notes in Computer Science 1334: 233–246.
3. ^ Bogdanov, Andrey; Wang, Meiqin (2012). "Zero-Correlation Linear Cryptanalysis with Reduced Data Complexity" (PDF). Lecture Notes in Computer Science (Fast Software Encryption 2012) 7549: 29–48.
4. ^ a b c Wheeler, David J.; Needham, Roger M. (1994-12-16). "TEA, a tiny encryption algorithm". Lecture Notes in Computer Science (Leuven, Belgium: Fast Software Encryption: Second International Workshop) 1008: 363–366.
5. ^ Kelsey, John; Schneier, Bruce; Wagner, David (1996). "Key-schedule cryptanalysis of IDEA, G-DES, GOST, SAFER, and Triple-DES" (PDF). Lecture Notes in Computer Science 1109: 237–251.
6. ^ Michael Steil. "17 Mistakes Microsoft Made in the Xbox Security System". Archived from the original on 16 April 2009.

## References

• Andem, Vikram Reddy (2003). "A Cryptanalysis of the Tiny Encryption Algorithm, Masters thesis" (PDF). Tuscaloosa: The University of Alabama.
• Hernández, Julio César; Isasi, Pedro; Ribagorda, Arturo (2002). "An application of genetic algorithms to the cryptoanalysis of one round TEA". Proceedings of the 2002 Symposium on Artificial Intelligence and its Application.
• Hernández, Julio César; Sierra, José María; Isasi, Pedro; Ribargorda. Arturo (2003). "Finding efficient distinguishers for cryptographic mappings, with an application to the block cipher TEA". Proceedings of the 2003 Congress on Evolutionary Computation 3: 2189.
• Hernández, Julio César; Sierra, José María; Ribagorda, Arturo; Ramos, Benjamín; Mex-Perera, J. C. (2001). "Distinguishing TEA from a random permutation: Reduced round versions of TEA do not have the SAC or do not generate random numbers" (PDF). Proceedings of the IMA Int. Conf. on Cryptography and Coding 2001: 374–377.
• Moon, Dukjae; Hwang, Kyungdeok; Lee, Wonil; Lee, Sangjin; Lim, Jongin (2002). "Impossible differential cryptanalysis of reduced round XTEA and TEA" (PDF).
• Hong, Seokhie; Hong, Deukjo; Ko, Youngdai; Chang, Donghoon; Lee, Wonil; Lee, Sangjin (2003). "Differential cryptanalysis of TEA and XTEA". In Proceedings of ICISC 2003.