Argon2

Argon2는 2015년 7월 암호 해싱 대회에서 우승작으로 선정된 키 유도 함수이다. 설계자는 룩셈부르크 대학교의 Alex Biryukov, Daniel Dinu, Dmitry Khovratovich이다. Argon2의 참조 구현체는 크리에이티브 커먼즈 CC0(퍼블릭 도메인) 또는 아파치 라이선스 2.0으로 배포되며 이와 관련된 3개의 버전을 제공한다:

 Argon2d: GPU 크래킹 공격의 저항성을 극대화한다.
 Argon2i: 사이드 채널 공격 저항에 최적화되어 있다. 암호와 독립된 순서로 메모리 배열에 접근한다.
 Argon2id: 하이브리드 버전. 메모리 처음 절반을 Argon2i이 접근하고 이후 패스는 Argon2d가 접근한다.

이 모드 3개는 모두 3개의 통제 변수를 사용한다:
 실행 시간
 필요한 메모리
 병렬 수준

알고리즘 

 Function Argon2
    Inputs:
       password (P):       Bytes (0..232-1)    Password (or message) to be hashed
       salt (S):           Bytes (8..232-1)    Salt (16 bytes recommended for password hashing)
       parallelism (p):    Number (1..224-1)   Degree of parallelism (i.e. number of threads)
       tagLength (T):      Number (4..232-1)   Desired number of returned bytes
       memorySizeKB (m):   Number (8p..232-1)  Amount of memory (in kibibytes) to use
       iterations (t):     Number (1..232-1)   Number of iterations to perform
       version (v):        Number (0x13)       The current version is 0x13 (19 decimal)
       key (K):            Bytes (0..232-1)    Optional key (Errata: PDF says 0..32 bytes, RFC says 0..232 bytes)
       associatedData (X): Bytes (0..232-1)    Optional arbitrary extra data
       hashType (y):       Number (0=Argon2d, 1=Argon2i, 2=Argon2id)
    Output:
       tag:                Bytes (tagLength)   The resulting generated bytes, tagLength bytes long

    Generate initial 64-byte block H0.
     All the input parameters are concatenated and input as a source of additional entropy.
     Errata: RFC says H0 is 64-bits; PDF says H0 is 64-bytes.
     Errata: RFC says the Hash is H^, the PDF says it's ℋ (but doesn't document what ℋ is). It's actually Blake2b.
     Variable length items are prepended with their length as 32-bit little-endian integers.
    buffer ← parallelism ∥ tagLength ∥ memorySizeKB ∥ iterations ∥ version ∥ hashType
          ∥ Length(password)       ∥ Password
          ∥ Length(salt)           ∥ salt
          ∥ Length(key)            ∥ key
          ∥ Length(associatedData) ∥ associatedData
    H0 ← Blake2b(buffer, 64) //default hash size of Blake2b is 64-bytes

    Calculate number of 1 KB blocks by rounding down memorySizeKB to the nearest multiple of 4*parallelism kibibytes
    blockCount ← Floor(memorySizeKB, 4*parallelism)

    Allocate two-dimensional array of 1 KiB blocks (parallelism rows x columnCount columns)
    columnCount ← blockCount / parallelism;   //In the RFC, columnCount is referred to as q

    Compute the first and second block (i.e. column zero and one ) of each lane (i.e. row)
    for i ← 0 to parallelism-1 do for each row
       Bi[0] ← Hash(H0 ∥ 0 ∥ i, 1024) //Generate a 1024-byte digest
       Bi[1] ← Hash(H0 ∥ 1 ∥ i, 1024) //Generate a 1024-byte digest

    Compute remaining columns of each lane
    for i ← 0 to parallelism-1 do //for each row
       for j ← 2 to columnCount-1 do //for each subsequent column
          //i' and j' indexes depend if it's Argon2i, Argon2d, or Argon2id (See section 3.4)
          i′, j′ ← GetBlockIndexes(i, j)  //the GetBlockIndexes function is not defined
          Bi[j] = G(Bi[j-1], Bi′[j′]) //the G hash function is not defined

    Further passes when iterations > 1
    for nIteration ← 2 to iterations do
       for i ← 0 to parallelism-1 do for each row
         for j ← 0 to columnCount-1 do //for each subsequent column
            //i' and j' indexes depend if it's Argon2i, Argon2d, or Argon2id (See section 3.4)
            i′, j′ ← GetBlockIndexes(i, j)
            if j == 0 then
              Bi[0] = Bi[0] xor G(Bi[columnCount-1], Bi′[j′])
            else
              Bi[j] = Bi[j] xor G(Bi[j-1], Bi′[j′])

    Compute final block C as the XOR of the last column of each row
    C ← B0[columnCount-1]
    for i ← 1 to parallelism-1 do
       C ← C xor Bi[columnCount-1]

    Compute output tag
    return Hash(C, tagLength)

각주

외부 링크 
 Argon2 source code repository on Github
 Argon2 specification
 Password Hashing Competition
 Uni.Lu Argon2 Page
 Balloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks

키 유도 함수
2015년 컴퓨팅