Integral cryptanalysis

Type of cryptanalytic attack

In cryptography, integral cryptanalysis is a cryptanalytic attack that is particularly applicable to block ciphers based on substitution–permutation networks. It was originally designed by Lars Knudsen as a dedicated attack against Square, so it is commonly known as the Square attack. It was also extended to a few other ciphers related to Square: CRYPTON, Rijndael, and SHARK. Stefan Lucks generalized the attack to what he called a saturation attack and used it to attack Twofish, which is not at all similar to Square, having a radically different Feistel network structure. Forms of integral cryptanalysis have since been applied to a variety of ciphers, including Hierocrypt, IDEA, Camellia, Skipjack, MISTY1, MISTY2, SAFER++, KHAZAD, and FOX (now called IDEA NXT).

Unlike differential cryptanalysis, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses sets or even multisets of chosen plaintexts of which part is held constant, and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about the cipher's operation. This contrast between the differences of pairs of texts and the sums of larger sets of texts inspired the name "integral cryptanalysis", borrowing the terminology of calculus.

References

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Joan Daemen, Lars Knudsen, Vincent Rijmen (January 1997). The Block Cipher Square (PDF). 4th International Workshop on Fast Software Encryption (FSE '97), Volume 1267 of Lecture Notes in Computer Science. Haifa: Springer-Verlag. pp. 149–165. Retrieved 2007年02月15日.{{cite conference}}: CS1 maint: multiple names: authors list (link)
Carl D'Halluin, Gert Bijnens, Vincent Rijmen, Bart Preneel (March 1999). Attack on Six Rounds of Crypton (PDF/PostScript). 6th International Workshop on Fast Software Encryption (FSE '99). Rome: Springer-Verlag. pp. 46–59. Retrieved 2007年03月03日.{{cite conference}}: CS1 maint: multiple names: authors list (link)
N. Ferguson, J. Kelsey, S. Lucks, B. Schneier, M. Stay, D. Wagner, D. Whiting (April 2000). Improved Cryptanalysis of Rijndael (PDF/PostScript). 7th International Workshop on Fast Software Encryption (FSE 2000). New York City: Springer-Verlag. pp. 213–230. Retrieved 2007年03月06日.{{cite conference}}: CS1 maint: multiple names: authors list (link)
Stefan Lucks (September 14, 2000). The Saturation Attack - a Bait for Twofish (PDF/PostScript). 8th International Workshop on Fast Software Encryption (FSE '01). Yokohama: Springer-Verlag. pp. 1–15. Retrieved 2006年11月30日.
Paulo S. L. M. Barreto, Vincent Rijmen, Jorge Nakahara, Jr., Bart Preneel, Joos Vandewalle, Hae Yong Kim (April 2001). Improved SQUARE Attacks against Reduced-Round HIEROCRYPT (PDF). 8th International Workshop on Fast Software Encryption (FSE '01). Yokohama: Springer-Verlag. pp. 165–173. Retrieved 2007年03月03日.{{cite conference}}: CS1 maint: multiple names: authors list (link)
Jorge Nakahara, Jr.; Paulo S.L.M. Barreto; Bart Preneel; Joos Vandewalle; Hae Y. Kim (2001). "SQUARE Attacks on Reduced-Round PES and IDEA Block Ciphers" (PDF/PostScript). Retrieved 2007年03月03日. {{cite journal}}: Cite journal requires |journal= (help)
Yongjin Yeom; Sangwoo Park; Iljun Kim (February 2002). On the Security of CAMELLIA against the Square Attack (PDF). 9th International Workshop on Fast Software Encryption (FSE '02). Leuven: Springer-Verlag. pp. 89–99. Retrieved 2007年03月03日.^{[permanent dead link ]}
Kyungdeok Hwang; Wonil Lee; Sungjae Lee; Sangjin Lee; Jongin Lim (February 2002). Saturation Attacks on Reduced Round Skipjack. 9th International Workshop on Fast Software Encryption (FSE '02). Leuven: Springer-Verlag. pp. 100–111. Archived from the original (PDF) on 2007年05月25日. Retrieved 2007年03月03日.
Lars Knudsen; David Wagner (December 11, 2001). Integral cryptanalysis (PDF/PostScript). 9th International Workshop on Fast Software Encryption (FSE '02). Leuven: Springer-Verlag. pp. 112–127. Retrieved 2006年11月30日.
Gilles Piret, Jean-Jacques Quisquater (February 16, 2003). "Integral Cryptanalysis on reduced-round Safer++" (PDF/PostScript). Retrieved 2007年03月03日. {{cite journal}}: Cite journal requires |journal= (help)
Frédéric Muller (December 2003). A New Attack against Khazad. Advances in Cryptology – ASIACRYPT 2003. Taipei: Springer-Verlag. pp. 347–358. Archived from the original (PDF) on 2007年07月23日. Retrieved 2007年03月03日.
Wu Wenling; Zhang Wentao; Feng Dengguo (August 25, 2005). "Improved Integral Cryptanalysis of FOX Block Cipher" (PDF). Retrieved 2007年03月03日. {{cite journal}}: Cite journal requires |journal= (help)

v t e Block ciphers (security summary)
Common algorithms	AES Blowfish DES (internal mechanics, Triple DES) Serpent SM4 Twofish
Less common algorithms	ARIA Camellia CAST-128 GOST IDEA LEA RC5 RC6 SEED Skipjack TEA XTEA
Other algorithms	3-Way Adiantum Akelarre Anubis Ascon 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 Grand Cru Hasty Pudding cipher Hierocrypt ICE IDEA NXT Intel Cascade Cipher Iraqi Kalyna KASUMI KeeLoq KHAZAD Khufu and Khafre KN-Cipher Kuznyechik Ladder-DES 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 QARMA RC2 REDOC Red Pike S-1 SAFER SAVILLE SC2000 SHACAL SHARK Simon Speck Spectr-H64 Square SXAL/MBAL Threefish Treyfer UES xmx XXTEA Zodiac
Design	Feistel network Key schedule Lai–Massey scheme Product cipher S-box P-box SPN Confusion and diffusion Round 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 Side-channel Timing Power-monitoring Electromagnetic Acoustic Differential-fault XSL Interpolation Partitioning Rubber-hose Black-bag Davies Rebound Weak key Tau Chi-square Time/memory/data tradeoff
Standardization	AES process CRYPTREC NESSIE NSA Suite B CNSA
Utilization	Initialization vector Mode of operation Padding

v t e Cryptography
General	History of cryptography Outline of cryptography Classical cipher Cryptographic protocol Authentication protocol Cryptographic primitive Cryptanalysis Cryptocurrency Cryptosystem Cryptographic nonce Cryptovirology Hash function Cryptographic hash function Key derivation function Secure Hash Algorithms Digital signature Kleptography Key (cryptography) Key exchange Key generator Key schedule Key stretching Keygen Machines Ransomware Random number generation Cryptographically secure pseudorandom number generator (CSPRNG) Pseudorandom noise (PRN) Secure channel Insecure channel Subliminal channel Encryption Decryption End-to-end encryption Harvest now, decrypt later Information-theoretic security Plaintext Codetext Ciphertext Shared secret Trapdoor function Trusted timestamping Key-based routing Onion routing Garlic routing Kademlia Mix network
Mathematics	Cryptographic hash function Block cipher Stream cipher Symmetric-key algorithm Authenticated encryption Public-key cryptography Quantum key distribution Quantum cryptography Post-quantum cryptography Message authentication code Random numbers Steganography
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