Argon2

Kriptanaliz

Argon2d'ye uygulanabilecek genel bir kripto analizi olmamasına rağmen, Argon2i fonksiyonuna karşı yayınlanan iki saldırı vardır. İlk saldırı sadece Argon2i'nin eski sürümüne uygulanabilirken, ikincisi en son sürüme kadar uzatılmıştır (1.3)
İlk saldırı, zaman cezası olmadan, istenen alanın çeyreği ile beşte biri arasında kullanılması ile, tek geçişli Argon2i fonksiyonunu hesaplamanın ve yine zaman cezası olmadan, sadece N/e < N/2.71 alanı kullanarak birçok geçişli Argon2i hesaplamanın mümkün olduğunu göstermektedir. Argon2 yazarlarına göre, bu saldırı vektörü 1.3 sürümünde düzeltilmiştir.
İkinci saldırı, Argon2i'nin, seçilen tüm parametreler için, örneğin; σ(alan maliyeti), τ(zaman maliyeti), ve n=σ∗τ olan izlek sayısı, karmaşıklığı O(n7/4 log(n)) olan bir algoritma ile hesaplanabildiğini göstermektedir.
Argon2 yazarları, Argon2i üç veya daha fazla geçişle kullanılırsa bu saldırının etkili olmadığını iddia eder. Bununla birlikte, Joël Alwen ve Jeremiah Blocki saldırıyı iyileştirmiş ve saldırının başarısız olması için Argon2i 1.3'ün bellek üzerinde 10'dan fazla geçişe ihtiyaç duyduğunu göstermiştir.

Algoritma

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 [./https://en.wikipedia.org/wiki/Kibibyte 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 [./https://en.wikipedia.org/wiki/Kibibyte 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] = G(Bᵢ[columnCount-1], Bi′[j′])
           else
             Bᵢ[j] = 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)

Değişken uzunluklu özet fonksiyonu

Argon2, 2³² byte uzunluğuna kadar özet üretebilen özet fonksiyonunu kullanır. Bu özet fonksiyonu dahili olarak Blake2 üzerine kuruludur. 
Function Hash(message, digestSize)
   Inputs:
      message:         Bytes (0..2³²-1)     Message to be hashed
      digestSize:      Integer (1..2³²)     Desired number of bytes to be returned
   Output:
      digest:          Bytes (digestSize)   The resulting generated bytes, digestSize bytes long

   Hash is a variable-length hash function, built using Blake2b, capable of generating
   digests up to 2³² bytes.

   If the requested digestSize is 64-bytes or lower, then we use Blake2b directly
   if (digestSize <= 64) then
      return Blake2b(digestSize ∥ message, digestSize) //concatenate 32-bit little endian digestSize with the message bytes

   For desired hashes over 64-bytes (e.g. 1024 bytes for Argon2 blocks),
   we use Blake2b to generate twice the number of needed 64-byte blocks,
   and then only use 32-bytes from each block

   Calculate the number of whole blocks (knowing we're only going to use 32-bytes from each)
   r ← Ceil(digestSize/32)-1;

   Generate r whole blocks.
   Initial block is generated from message
   V₁ ← Blake2b(digestSize ∥ message, 64);
   Subsequent blocks are generated from previous blocks
   for i ← 2 to r do
      Vᵢ ← Blake2b(Vᵢ₋₁, 64)
   Generate the final (possibly partial) block
   partialBytesNeeded ← digestSize – 32*r;
   Vᵣ₊₁ ← Blake2b(Vᵣ, partialBytesNeeded)

   Concatenate the first 32-bytes of each block Vᵢ
   (except the possibly partial last block, which we take the whole thing)
   Let Aᵢ represent the lower 32-bytes of block Vᵢ
   return A₁ ∥ A₂ ∥ ... ∥ Aᵣ ∥ Vᵣ₊₁