“Rijndael key schedule”的意思、由来-开放百科全书

词条

Rijndael key schedule

释义

Round constants
The key schedule
Notes
References
External links

AES (Rijndael) uses a key schedule to expand a short key into a number of separate round keys. This is known as the Rijndael key schedule. The three AES variants have a different number of rounds. Each variant requires a separate 128-bit round key for each round plus one more. The key schedule produces the needed round keys from the initial key.

Round constants

rc_i}} in hexadecimal
i	1	2	3	4	5	6	7	8	9	10
rc_i	01	02	04	08	10	20	40	80	1B	36

The round constant {{mvar|rcon_i}} for round {{mvar|i}} of the key expansion is the 32-bit word:

where {{mvar|rc_i}} is an eight-bit value defined as:

where is the bitwise XOR operator and constants such as {{math|00₁₆}} and {{math|11B₁₆}} are given in hexadecimal. Equivalently:

where the bits of {{mvar|rc_i}} are treated as the coefficients of an element of the finite field , so that e.g. represents the polynomial .

AES uses up to {{math|rcon₁₀}} for AES-128 (as 11 round keys are needed), up to {{math|rcon₈}} for AES-192, and up to {{math|rcon₇}} for AES-256.^[1]

The key schedule

Define:

{{mvar|N}} as the length of the key in 32-bit words: 4 words for AES-128, 6 words for AES-192, and 8 words for AES-256
{{math|K₀}}, {{math|K₁}}, ... {{math|K_N-1}} as the 32-bit words of the original key
{{mvar|R}} as the number of round keys needed: 11 round keys for AES-128, 13 keys for AES-192, and 15 keys for AES-256^[2]
{{math|W₀}}, {{math|W₁}}, ... {{math|W_4R-1}} as the 32-bit words of the expanded key^[3]

Also define {{Math|RotWord}} as a one-byte left circular shift:

and {{Math|SubWord}} as an application of the AES S-box to each of the four bytes of the word:

Then for :

Notes

1. ^The Rijndael variants with larger block sizes use more of these constants, up to {{math|rcon₂₉}} for Rijndael with 128-bit keys and 256 bit blocks (needs 15 round keys of each 256 bit, which means 30 full rounds of key expansion, which means 29 calls to the key schedule core using the round constants). The remaining constants for {{math|i ≥ 11}} are: 6C, D8, AB, 4D, 9A, 2F, 5E, BC, 63, C6, 97, 35, 6A, D4, B3, 7D, FA, EF and C5
2. ^Other Rijndael variants require {{math|max(N, B) + 7}} round keys, where {{mvar|B}} is the block size in words
3. ^Other Rijndael variants require {{math|BR}} words of expanded key

References

FIPS PUB 197: the official AES standard (PDF file)

External links

Description of Rijndael's key schedule
schematic view of the key schedule for 128 and 256 bit keys for 160-bit keys on Cryptography Stack Exchange

2 : Advanced Encryption Standard|Key management

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。