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In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, creating diffusion while transposing.^[1]

In block ciphers based on substitution-permutation network, the P-boxes, together with the "substitution" S-boxes are used to make the relation between the plaintext and the ciphertext difficult to understand (see Shannon's Confusion and diffusion). P-boxes are typically classified as compression, expansion, and straight, depending on whether the number of output bits is less than, greater than, or equal to the number of input bits, respectively. Only straight P-boxes are invertible.

References

^ Nayaka & Biradar 2013, p. 3.

Sources

Nayaka, Raja Jitendra; Biradar, R. C. (2013). 2013 Annual International Conference on Emerging Research Areas and 2013 International Conference on Microelectronics, Communications and Renewable Energy. IEEE. doi:10.1109/aicera-icmicr.2013.6575944.

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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