Serpent (cipher)

Serpent
General
Serpent's linear mixing stage
Designers	Ross Anderson, Eli Biham, Lars Knudsen
First published	1998-08-21
Derived from	Square
Certification	AES finalist
Cipher detail
Key sizes	128, 192 or 256 bits
Block sizes	128 bits
Structure	Substitution-permutation network
Rounds	32
Best public cryptanalysis
All publicly known attacks are computationally infeasible, and none of them affect the full 32-round Serpent. A 2011 attack breaks 11 round Serpent (all key sizes) with 2¹¹⁶ known plaintexts, 2^107.5 time and 2¹⁰⁴ memory (as described in ^[1]). The same paper also describes two attacks which break 12 rounds of Serpent-256. The first requires 2¹¹⁸ known plaintexts, 2^228.8 time and 2²²⁸ memory. The other attack requires 2¹¹⁶ known plaintexts and 2¹²¹ memory but also requires 2^237.5 time.

Serpent is a symmetric key block cipher that was a finalist in the Advanced Encryption Standard (AES) contest, where it was ranked second to Rijndael. Serpent was designed by Ross Anderson, Eli Biham, and Lars Knudsen.

Like other AES submissions, Serpent has a block size of 128 bits and supports a key size of 128, 192 or 256 bits.^[2] The cipher is a 32-round substitution-permutation network operating on a block of four 32-bit words. Each round applies one of eight 4-bit to 4-bit S-boxes 32 times in parallel. Serpent was designed so that all operations can be executed in parallel, using 32 bit slices. This maximizes parallelism, but also allows use of the extensive cryptanalysis work performed on DES.

Serpent took a conservative approach to security, opting for a large security margin: the designers deemed 16 rounds to be sufficient against known types of attack, but specified 32 rounds as insurance against future discoveries in cryptanalysis. The official NIST report on AES competition classified Serpent as having a high security margin along with MARS and Twofish, in contrast to the adequate security margin of RC6 and Rijndael (currently AES).^[3] In final voting, Serpent had the least number of negative votes among the finalists, but scored second place overall because Rijndael had substantially more positive votes, the deciding factor being that Rijndael allowed for a far more efficient software implementation.

The Serpent cipher algorithm is in the public domain and has not been patented.^[4] The reference code is public domain software and the optimized code is under GPL.^[5] There are no restrictions or encumbrances whatsoever regarding its use. As a result, anyone is free to incorporate Serpent in their software (or hardware implementations) without paying license fees.

Rijndael vs. Serpent

Rijndael is a substitution-linear transformation network with ten, twelve, or fourteen rounds, depending on the key size, and with block sizes of 128 bits, 192 bits, or 256 bits, independently specified. Serpent is a substitution-permutation network which has thirty-two rounds, plus an initial and a final permutation to simplify an optimized implementation. The round function in Rijndael consists of three parts: a nonlinear layer, a linear mixing layer, and a key-mixing XOR layer. The round function in Serpent consists of key-mixing XOR, thirty-two parallel applications of the same 4×4 S-box, and a linear transformation, except in the last round, wherein another key-mixing XOR replaces the linear transformation. The nonlinear layer in Rijndael uses an 8×8 S-box whereas Serpent uses eight different 4×4 S-boxes. The 32 rounds means that Serpent has a higher security margin than Rijndael; however, Rijndael with 10 rounds is faster and easier to implement for small blocks.^[6] Hence, Rijndael was selected as the winner in the AES competition.

Serpent-0 vs. Serpent-1

The original Serpent, Serpent-0, was presented at the 5th workshop on Fast Software Encryption, but a somewhat tweaked version, Serpent-1, was submitted to the AES competition. The AES submission paper discuss the changes, which include key scheduling differences.

Security

The XSL attack, if effective, would weaken Serpent (though not as much as it would weaken Rijndael, which became AES). However, many cryptanalysts believe that once implementation considerations are taken into account the XSL attack would be more expensive than a brute force attack.

In 2000, a paper by Kohno et al. presents a meet-in-the-middle attack against 6 of 32 rounds of Serpent and an amplified boomerang attack against 9 of 32 rounds in Serpent.^[7]

A 2001 attack by Eli Biham, Orr Dunkelman and Nathan Keller presents a linear cryptanalysis attack that breaks 10 of 32 rounds of Serpent-128 with 2¹¹⁸ known plaintexts and 2⁸⁹ time, and 11 rounds of Serpent-192/256 with 2¹¹⁸ known plaintexts and 2¹⁸⁷ time.^[8]

A 2009 paper has noticed that the nonlinear order of Serpent s-boxes were not 3 as was claimed by the designers. ^[9]

A 2011 attack by Hongjun Wu, Huaxiong Wang and Phuong Ha Nguyen, also using linear cryptanalysis, breaks 11 rounds of Serpent-128 with 2¹¹⁶ known plaintexts, 2^107.5 time and 2¹⁰⁴ memory.^[1]

The same paper also describes two attacks which break 12 rounds of Serpent-256. The first requires 2¹¹⁸ known plaintexts, 2^228.8 time and 2²²⁸ memory. The other attack requires 2¹¹⁶ known plaintexts and 2¹²¹ memory but also requires 2^237.5 time.

Footnotes

1 2 Huaxiong Wang, Hongjun Wu & Phuong Ha Nguyen (2011). "Improving the Algorithm 2 in Multidimensional Linear Cryptanalysis" (PDF). ACISP 2011. doi:10.1007/978-3-642-22497-3_5.
↑ Ross J. Anderson (2006-10-23). "Serpent: A Candidate Block Cipher for the Advanced Encryption Standard". University of Cambridge Computer Laboratory. Retrieved 2013-01-14.
↑ NIST (2000), Report on the Development of the Advanced Encryption Standard (AES) (PDF), NIST
↑ Serpent Holds the Key to Internet Security - Finalists in world-wide encryption competition announced (1999)
↑ SERPENT - A Candidate Block Cipher for the Advanced Encryption Standard "Serpent is now completely in the public domain, and we impose no restrictions on its use. This was announced on the 21st August at the First AES Candidate Conference. The optimised implementations in the submission package are now under the General Public License (GPL), although some comments in the code still say otherwise. You are welcome to use Serpent for any application. If you do use it, we would appreciate it if you would let us know!" (1999)
↑ Bruce Schneier; John Kelsey; Doug Whiting; David Wagner; Chris Hall. Niels Fergusonk; Tadayoshi Kohno; Mike Stay (2000). "The Twofish Team's Final Comments on AES Selection" (PDF).
↑ Tadayoshi Kohno; John Kelsey & Bruce Schneier (2000). "Preliminary Cryptanalysis of Reduced-Round Serpent".
↑ Eli Biham, Orr Dunkelman & Nathan Keller (2001). "Linear Cryptanalysis of Reduced Round Serpent". FSE 2001.
↑ Bhupendra Singh; Lexy Alexander; Sanjay Burman (2009). "On Algebraic Relations of Serpent S-Boxes" (PDF).

External links

256bit Ciphers - SERPENT Reference implementation and derived code

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

History of cryptography Cryptanalysis Outline of cryptography

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

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