Partitioning cryptanalysis

In cryptography, partitioning cryptanalysis is a form of cryptanalysis for block ciphers. Developed by Carlo Harpes in 1995, the attack is a generalization of linear cryptanalysis. Harpes originally replaced the bit sums (affine transformations) of linear cryptanalysis with more general balanced Boolean functions. He demonstrated a toy cipher that exhibits resistance against ordinary linear cryptanalysis but is susceptible to this sort of partitioning cryptanalysis. In its full generality, partitioning cryptanalysis works by dividing the sets of possible plaintexts and ciphertexts into efficiently computable partitions such that the distribution of ciphertexts is significantly non-uniform when the plaintexts are chosen uniformly from a given block of the partition. Partitioning cryptanalysis has been shown to be more effective than linear cryptanalysis against variants of DES and CRYPTON. A specific partitioning attack called mod n cryptanalysis uses the congruence classes modulo some integer for partitions.

References

Carlo Harpes, Gerard G. Kramer, James L. Massey (May 1995). A Generalization of Linear Cryptanalysis and the Applicability of Matsui's Piling-up Lemma (PDF/PostScript). Advances in Cryptology — Eurocrypt '95. Saint-Malo: Springer-Verlag. pp. 24–38. Retrieved 9 September 2007.{{cite conference}}: CS1 maint: miscellaneous url (link) CS1 maint: multiple names: authors list (link)
Thomas Jakobsen (1995). "Security Against Generalized Linear Cryptanalysis and Partitioning Cryptanalysis" (PDF/PostScript). Retrieved 9 September 2007. {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: miscellaneous url (link)
T. Jakobsen; C. Harpes (1996). Bounds On Non-Uniformity Measures For Generalized Linear Cryptanalysis And Partitioning Cryptanalysis (PDF/PostScript). Pragocrypt '96. Prague: Czech Technical University Publishing House. pp. 467–479. Retrieved 9 September 2007.{{cite conference}}: CS1 maint: miscellaneous url (link)
C. Harpes; J. Massey (January 1997). Partitioning Cryptanalysis (PDF/PostScript). 4th International Workshop in Fast Software Encryption (FSE '97). Haifa: Springer-Verlag. pp. 13–27. Retrieved 9 September 2007.{{cite conference}}: CS1 maint: miscellaneous url (link)
Marine Minier, Henri Gilbert (April 2000). Stochastic Cryptanalysis of Crypton (PDF). 7th International Workshop in Fast Software Encryption (FSE 2000). New York City: Springer-Verlag. pp. 121–133. Retrieved 10 September 2007.^{[permanent dead link]}
Thomas Baignères, Pascal Junod, Serge Vaudenay (December 2004). How Far Can We Go Beyond Linear Cryptanalysis? (PDF). Advances in Cryptology — ASIACRYPT 2004. Jeju Island: Springer-Verlag. pp. 432–450. Retrieved 9 September 2007.{{cite conference}}: CS1 maint: multiple names: authors list (link)
Gaëtan Leurent (October 2015). Differential and Linear Cryptanalysis of ARX with Partitioning (PDF). Cryptology ePrint Archive. Retrieved 10 October 2015.

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 Algebraic Cube attack Gröbner 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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