Definitions

# International Data Encryption Algorithm

In cryptography, the International Data Encryption Algorithm (IDEA) is a block cipher designed by Xuejia Lai and James Massey of ETH Zurich and was first described in 1991. The algorithm was intended as a replacement for the Data Encryption Standard. IDEA is a minor revision of an earlier cipher, PES (Proposed Encryption Standard); IDEA was originally called IPES (Improved PES).

The cipher was designed under a research contract with the Hasler Foundation, which became part of Ascom-Tech AG. The cipher is patented in a number of countries but is freely available for non-commercial use. The name "IDEA" is also a trademark. The patents will expire in 2010–2011. Today, IDEA is licensed worldwide by MediaCrypt.

IDEA was used in Pretty Good Privacy (PGP) v2.0, and was incorporated after the original cipher used in v1.0, BassOmatic, was found to be insecure. IDEA is an optional algorithm in the OpenPGP standard.

## Operation

IDEA operates on 64-bit blocks using a 128-bit key, and consists of a series of eight identical transformations (a round, see the illustration) and an output transformation (the half-round). The processes for encryption and decryption are similar. IDEA derives much of its security by interleaving operations from different groupsmodular addition and multiplication, and bitwise eXclusive OR (XOR) — which are algebraically "incompatible" in some sense. In more detail, these operators, which all deal with 16-bit quantities, are:

• Bitwise eXclusive OR (denoted with a blue ⊕).
• Addition modulo 216 (denoted with a green ).
• Multiplication modulo 216+1, where the all-zero word (0x0000) is interpreted as 216 (denoted by a red ).

After the eight rounds comes a final "half round", the output transformation illustrated below:

### Key schedule

Each round uses six sub-keys, while the half-round uses four. Each sub-key is a sixteen-bit value. The first eight sub-keys are extracted directly from the key, with K1 from the first round being the lower sixteen bits; further groups of eight keys are created by rotating the main key left 25 bits between each group of eight. This means that it is rotated less than once per round, on average, for a total of six rotations.

## Security

The designers analysed IDEA to measure its strength against differential cryptanalysis and concluded that it is immune under certain assumptions. No successful linear or algebraic weaknesses have been reported. Some classes of weak keys have been found — E.g. (Daemen et al, 1994) — but these are of little concern in practice, being so rare as to be unnecessary to avoid explicitly. As of 2007, the best attack which applies to all keys can break IDEA reduced to 6 rounds (the full IDEA cipher uses 8.5 rounds).

Bruce Schneier thought highly of IDEA in 1996, writing, "In my opinion, it is the best and most secure block algorithm available to the public at this time." (Applied Cryptography, 2nd ed.) However, by 1999 he was no longer recommending IDEA due to the availability of faster algorithms, some progress in its cryptanalysis, and the issue of patents

IDEA is patented in Austria, France, Germany, Italy, Netherlands, Spain, Sweden, Switzerland, United Kingdom, (European patent EP-B-0482154), the United States (US patent #5,214,703, issued May 25, 1993) and Japan (JP 3225440).

MediaCrypt is now also offering a successor to IDEA and focuses on its new cipher (official release on May 2005) IDEA NXT, which was previously called FOX.

## References

• J. Daemen, R. Govaerts, and J. Vandewalle, Weak keys for IDEA, CRYPTO '93. pp224–231.
• Hüseyin Demirci, Erkan Türe, Ali Aydin Selçuk, A New Meet in the Middle Attack on The IDEA Block Cipher, 10th Annual Workshop on Selected Areas in Cryptography, 2004.
• Xuejia Lai and James L. Massey, A Proposal for a New Block Encryption Standard, EUROCRYPT 1990, pp389–404
• Xuejia Lai and James L. Massey and S. Murphy, Markov ciphers and differential cryptanalysis, Advances in Cryptology — Eurocrypt '91, Springer-Verlag (1992), pp17–38.
• Eli Biham, Orr Dunkelman, Nathan Keller, A New Attack on 6-round IDEA, Fast Software Encryption Workshop, 2007.