Serpent (cipher)

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.

Serpent

Serpent's linear mixing stage
General
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 2^116 known plaintexts, 2^107.5 time and 2^104 memory (as described in[1]). The same paper also describes two attacks which break 12 rounds of Serpent-256. The first requires 2^118 known plaintexts, 2^228.8 time and 2^228 memory. The other attack requires 2^116 known plaintexts and 2^121 memory but also requires 2^237.5 time.

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 fewest 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.

See also

• Tiger – hash function by the same authors

Footnotes

1. Huaxiong Wang, Hongjun Wu & Phuong Ha Nguyen (2011). "Improving the Algorithm 2 in Multidimensional Linear Cryptanalysis" (PDF). Information Security and Privacy. Lecture Notes in Computer Science. 6812. ACISP 2011. pp. 61–74. doi:10.1007/978-3-642-22497-3_5. ISBN 978-3-642-22496-6.
2. Ross J. Anderson (23 October 2006). "Serpent: A Candidate Block Cipher for the Advanced Encryption Standard". University of Cambridge Computer Laboratory. Retrieved 14 January 2013.
3. NIST (2000), Report on the Development of the Advanced Encryption Standard (AES) (PDF), NIST
4. Serpent Holds the Key to Internet Security – Finalists in world-wide encryption competition announced (1999)
5. 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)
6. 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). Cite journal requires |journal= (help)
7. Tadayoshi Kohno; John Kelsey & Bruce Schneier (2000). "Preliminary Cryptanalysis of Reduced-Round Serpent". Cite journal requires |journal= (help)
8. Eli Biham, Orr Dunkelman & Nathan Keller (2001). "Linear Cryptanalysis of Reduced Round Serpent". FSE 2001. CiteSeerX 10.1.1.78.6148. Cite journal requires |journal= (help)
9. Bhupendra Singh; Lexy Alexander; Sanjay Burman (2009). "On Algebraic Relations of Serpent S-Boxes" (PDF). Cite journal requires |journal= (help)

Further reading

• Anderson, Ross; Biham, Eli; Knudsen, Lars (1998). "Cryptography – 256 bit ciphers: Reference (AES submission) implementation".
• Biham, Eli. "Serpent – A New Block Cipher Proposal for AES".
• Halbfinger, David M (5 May 2008). "In Pellicano Case, Lessons in Wiretapping Skills". The New York Times.
• Stajano, Frank (10 February 2006). "Serpent reference implementation". University of Cambridge Computer Laboratory.

External links

• Official website
• 256 bit ciphers – SERPENT Reference implementation and derived code