ICE (cipher)

ICE
General
The ICE Feistel function
Designers	Matthew Kwan
First published	1997
Derived from	DES
Cipher detail
Key sizes	64 bits (ICE), 64×n bits (ICE-n)
Block sizes	64 bits
Structure	Feistel network
Rounds	16 (ICE), 8 (Thin-ICE), 16×n (ICE-n)
Best public cryptanalysis
Differential cryptanalysis can break 15 out of 16 rounds of ICE with complexity 2⁵⁶. Thin-ICE can be broken using 2²⁷ chosen plaintexts with a success probability of 95%.

In cryptography, ICE (Information Concealment Engine) is a symmetric-key block cipher published by Kwan in 1997. The algorithm is similar in structure to DES, but with the addition of a key-dependent bit permutation in the round function. The key-dependent bit permutation is implemented efficiently in software. The ICE algorithm is not subject to patents, and the source code has been placed into the public domain.

ICE is a Feistel network with a block size of 64 bits. The standard ICE algorithm takes a 64-bit key and has 16 rounds. A fast variant, Thin-ICE, uses only 8 rounds. An open-ended variant, ICE-n, uses 16n rounds with 64n bit key.

Van Rompay et al. (1998) attempted to apply differential cryptanalysis to ICE. They described an attack on Thin-ICE which recovers the secret key using 2²³ chosen plaintexts with a 25% success probability. If 2²⁷ chosen plaintexts are used, the probability can be improved to 95%. For the standard version of ICE, an attack on 15 out of 16 rounds was found, requiring 2⁵⁶ work and at most 2⁵⁶ chosen plaintexts.

Structure

ICE is a 16-round Feistel network. Each round uses a 32→32 bit F function, which uses 60 bits of key material.

The structure of the F function is somewhat similar to DES: The input is expanded by taking overlapping fields, the expanded input is XORed with a key, and the result is fed to a number of reducing S-boxes which undo the expansion.

First, ICE divides the input into 4 overlapping 10-bit values. They are bits 0–9, 8–17, 16–25, and 24–33 of the input, where bits 32 and 33 are copies of bits 0 and 1.

Second is a keyed permutation, which is unique to ICE. Using a 20-bit permutation subkey, bits are swapped between halves of the 40-bit expanded input. (If subkey bit i is 1, then bits i and i+20 are swapped.)

Third, the 40-bit value is exclusive-ORed with 40 more subkey bits.

Fourth, the value is fed through 4 10-bit S-boxes, each of which produces 8 bits of output. (These are much larger than DES's 8 6→4 bit S-boxes.)

Fifth, the S-box output bits are permuted so that each S-box's outputs are routed to each 4-bit field of 32-bit word, including 2 of the 8 "overlap" bits duplicated during the next round's expansion.

Like DES, a software implementation would typically store the S-boxes pre-permuted, in 4 1024×32 bit lookup tables.

References

Matthew Kwan, The Design of the ICE Encryption Algorithm, Fast Software Encryption 1997, pp. 69–82 .
Bart van Rompay, Lars R. Knudsen and Vincent Rijmen, Differential Cryptanalysis of the ICE Encryption Algorithm, Fast Software Encryption 1998, pp270–283 (PDF) (link dead 2013-Jun-23).

External links

Block ciphers (security summary)

Common algorithms	AES Blowfish DES (Internal Mechanics, Triple DES) Serpent Twofish

Less common algorithms	Camellia CAST-128 IDEA RC2 RC5 RC6 SEED ARIA Skipjack TEA XTEA

Other algorithms	3-Way Akelarre Anubis BaseKing BassOmatic BATON BEAR and LION CAST-256 Chiasmus CIKS-1 CIPHERUNICORN-A CIPHERUNICORN-E CLEFIA CMEA Cobra COCONUT98 Crab Cryptomeria/C2 CRYPTON CS-Cipher DEAL DES-X DFC E2 FEAL FEA-M FROG G-DES GOST Grand Cru Hasty Pudding cipher Hierocrypt ICE IDEA NXT Intel Cascade Cipher Iraqi KASUMI KeeLoq KHAZAD Khufu and Khafre KN-Cipher Kuznyechik Ladder-DES Libelle LOKI (97, 89/91) Lucifer M6 M8 MacGuffin Madryga MAGENTA MARS Mercy MESH MISTY1 MMB MULTI2 MultiSwap New Data Seal NewDES Nimbus NOEKEON NUSH PRESENT Prince Q RC6 REDOC Red Pike S-1 SAFER SAVILLE SC2000 SHACAL SHARK Simon SM4 Speck Spectr-H64 Square SXAL/MBAL Threefish Treyfer UES Xenon xmx XXTEA Zodiac

Design	Feistel network Key schedule Lai-Massey scheme Product cipher S-box P-box SPN Avalanche effect Block size Key size Key whitening (Whitening transformation)

Attack (cryptanalysis)	Brute-force (EFF DES cracker) MITM (Biclique attack, 3-subset MITM attack) Linear (Piling-up lemma) Differential (Impossible Truncated Higher-order) Differential-linear Distinguishing (Known-key) Integral/Square Boomerang Mod n Related-key Slide Rotational Timing XSL Interpolation Partitioning Davies' Rebound Weak key Tau Chi-square Time/memory/data tradeoff

Standardization	AES process CRYPTREC NESSIE

Utilization	Initialization vector Mode of operation Padding

Cryptography

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Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography

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