SHA-2

SHA-2 is a family of cryptographic hash functions including SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224 and SHA-512/256. NIST specifies these algorithms in FIPS 180-4. Their digest lengths are respectively 224, 256, 384, 512, 224 and 256 bits; the algorithm name therefore matters as well as the output size.^[ref]

The SHA-224/SHA-256 branch uses 32-bit words and 512-bit message blocks. The SHA-384/SHA-512 branch and its specified truncation variants use 64-bit words and 1024-bit message blocks. Different initial values are part of the definitions. In particular, SHA-512/256 is not simply the first 256 bits of an ordinary SHA-512 digest.^[ref]

For a computed example, hashing the three ASCII bytes 61 62 63 with SHA-512/256 produces

53048e2681941ef99b2e29b76b4c7dabe4c2d0c634fc6d46e0e2f13107e7af23.

Taking the first 256 bits of the SHA-512 digest of those same bytes instead gives

ddaf35a193617abacc417349ae20413112e6fa4e89a97ea20a9eeee64b55d39a.

Both outputs occupy 32 bytes and require 64 hexadecimal digits, yet they differ. An interface identifying its hash only as a 256-bit digest leaves the selected algorithm ambiguous.

A digest is deterministic and does not conceal low-entropy inputs by itself. Nor does an unkeyed digest establish who supplied a message: a sender-authentication mechanism such as HMAC uses a cryptographic key and an appropriate security definition. Preimage resistance, second-preimage resistance and collision resistance are distinct properties; their meanings should not be replaced by the mere observation that two displayed examples have different outputs.

SHA-512/t is the family of $t$-bit cryptographic hash functions built using the SHA-512 computation with a $t$-specific hash initialization vector and final truncation. The FIPS 180-4 construction takes a positive integer $t<512$, excluding $t=384$; SHA-384 has its separately specified initialization. The 2015 standard explicitly specifies SHA-512/224 and SHA-512/256 as the approved members, rather than treating every permissible parameter as a standardized choice.^[ref]

The initialization procedure first XORs each ordinary SHA-512 initial word with hexadecimal a5a5a5a5a5a5a5a5. It then hashes the ASCII label SHA-512/t, replacing t with its decimal value without leading zeros, using that modified initial state. The resulting full 512-bit value becomes the selected member's fixed initial state.^[ref]

For a concrete word calculation,where $\oplus$ denotes bitwise exclusive or. All eight words are modified, not just this first one. At $t=256$, the label is the eleven ASCII bytes 53 48 41 2d 35 31 32 2f 32 35 36. At $t=224$, its final three bytes are instead 32 32 34. The slash is an actual label byte, not a division operation or a parser instruction.

The generated initial state's first word is 22312194fc2bf72c for SHA-512/256 and 8c3d37c819544da2 for SHA-512/224. These fixed values separate the algorithms before the user's message is processed. Hashing the label with ordinary SHA-512 initialization would follow a different procedure.^[ref]

After processing the message with its member-specific initialization, retain the first $t$ bits of the final state. For an abstract $t=13$ serialization exercise, a state beginning with bytes ab cd would yield bits 1010101111001; the lower three bits of the second byte are excluded. This illustrates bit truncation, not a recommendation to use a 13-bit digest. Output length, initialization and protocol selection all remain part of the algorithm's identity.

SHA-512/256 is a SHA-2 cryptographic hash function with a 256-bit digest. It uses the 1024-bit blocks and 64-bit word operations of SHA-512, a variant-specific hash initialization vector, and the first 256 bits of the final state. It is one member of SHA-512/t.^[ref]

Its initialization illustrates cryptographic domain separation. Let $v$ be the eight-word ordinary SHA-512 initial state. First form $\tilde{v}$ by applying bitwise exclusive or to each word with the hexadecimal word a5a5a5a5a5a5a5a5. Run the SHA-512 computation on the ASCII label SHA-512/256, using $\tilde{v}$ as its initial state. The full 512-bit result is the variant's fixed initial state $v^{(256)}$. This label computation is part of defining the function, not an extra message prefix chosen by its user.^[ref]

If ${SHA512}^{v^{(256)}}(m)$ denotes the full final state obtained by hashing $m$ with that initialization, thenThe output comprises four 64-bit words: 32 bytes or 64 hexadecimal digits. The initial state is public and fixed; it is not a cryptographic salt or a secret key.

For a computed example, the three ASCII bytes 61 62 63 give

53048e2681941ef99b2e29b76b4c7dabe4c2d0c634fc6d46e0e2f13107e7af23.

Ordinary SHA-512 of those bytes begins ddaf35a193617aba, while SHA-256 begins ba7816bf8f01cfea. Neither output implements SHA-512/256. In particular, the slash and output width do not mean “hash with ordinary SHA-512 and keep 256 bits”.

The padding also follows the SHA-512 family: a 128-bit length field and 1024-bit blocks. An input of 56 bytes therefore fits into one padded block here, while SHA-256 needs two of its smaller blocks. The identical 32-byte digest sizes say nothing about those different computations.

SHA-512/224 is a SHA-2 cryptographic hash function returning 224 bits. It uses the SHA-512 computation with its own hash initialization vector and outputs the first 224 bits of the final state. The SHA-512/t initialization procedure uses the ASCII label SHA-512/224, so its initial state differs from that of SHA-512/256 as well as ordinary SHA-512.^[ref]

Output serialization needs care because $224=3\times 64+32$. If the final eight 64-bit words are $H_0,\dots ,H_7$, the digest containswhere $\Vert$ denotes concatenation in the standard's most-significant-bit-first order. It has 28 bytes, or 56 hexadecimal digits. For a simple serialization example, if $H_3$ were 89abcdef01234567, its contribution would be the four bytes 89 ab cd ef. Taking the four bytes 01 23 45 67 would keep the wrong half. An implementation's machine endianness does not change the specified digest bytes.

For a computed example, hashing ASCII bytes 61 62 63 gives

4634270f707b6a54daae7530460842e20e37ed265ceee9a43e8924aa.

SHA-224 of the same bytes begins 23097d223405d822, despite having the same 224-bit output size. The two functions use different compression structures, initial states and message-padding conventions. Taking a prefix of the ordinary SHA-512 digest also gives a different result.

The distinction matters in a cryptographic test vector: a 28-byte expected digest cannot identify the intended algorithm by its size alone. The vector must name SHA-512/224 and specify the exact input bytes. The different label used during initialization is fixed by the algorithm; applications do not choose it separately for each hash.

SHA-512 is a SHA-2 cryptographic hash function with a 512-bit digest. It processes 1024-bit message blocks through eighty rounds using eight 64-bit state words and additions modulo $2^{64}$. Its message-length field is 128 bits.^[ref]

For bit length $\ell <2^{128}$, padding appends one bit and $k$ zero bits so thatthen appends the 128-bit original length. The hash initialization vector is fixed by the algorithm; it is not a fresh secret for each message. The padded blocks update the state in order, and the final eight words form the digest.

For a computed example, hash the three ASCII bytes 61 62 63. Here $\ell =24$, so $k=871$ and $24+1+871+128=1024$. One padded 128-byte block is processed. Its digest, in hexadecimal, is

ddaf35a193617abacc417349ae20413112e6fa4e89a97ea20a9eeee64b55d39a2192992a274fc1a836ba3c23a3feebbd454d4423643ce80e2a9ac94fa54ca49f.

The 128 hexadecimal digits represent 64 bytes. They do not represent the 128-byte padded input. For another padding-count example, 111 input bytes fit into one padded block, while 112 input bytes require two; the digest remains 64 bytes in either case.

SHA-384, SHA-512/224 and SHA-512/256 reuse the SHA-512 compression structure but have specified different initial states and output rules. Taking a prefix of an ordinary SHA-512 digest therefore does not implement those algorithms. A cryptographic test vector must identify the exact hash, input encoding and expected output rather than only a digest length.

SHA-384 is a SHA-2 cryptographic hash function producing 384 bits. It uses the 64-bit word operations, 1024-bit blocks and eighty-round computation of SHA-512, with its own hash initialization vector. Its result is the first 384 bits of that differently initialized computation.^[ref]

Write its final eight-word state as $H_0,\dots ,H_7$, with each word containing 64 bits. The output iswhere $\Vert$ denotes concatenation. Six words give $6\times 64=384$ bits, or 48 bytes and 96 hexadecimal digits. The computation still maintains eight state words while processing the message; the shorter output does not reduce every intermediate state to six words.

For a computed example using ASCII bytes 61 62 63, SHA-384 gives

cb00753f45a35e8bb5a03d699ac65007272c32ab0eded1631a8b605a43ff5bed8086072ba1e7cc2358baeca134c825a7.

The ordinary SHA-512 digest begins ddaf35a193617aba, so truncating that digest to 48 bytes already disagrees at the beginning. Different initialization, rather than merely a shorter printed result, distinguishes the algorithms.

A streaming implementation can process message blocks using the SHA-512 family machinery while retaining the selected variant's initial state and final serialization. Treating those choices as part of the function is essential when a digital signature or HMAC specification names SHA-384. Changing to another 384-bit output transformation changes the algorithm, even if the receiving buffer still has the expected size.

SHA-224 is a SHA-2 cryptographic hash function producing a 224-bit digest. It follows the SHA-256 computation with a different hash initialization vector and a final output shortened to its first seven 32-bit state words.^[ref]

If the final state words are $H_0,\dots ,H_7$, the digest isThis is $7\times 32=224$ bits, or 28 bytes and 56 hexadecimal digits. The input is still padded into 512-bit blocks, and each block still undergoes the SHA-256 family's 64-round computation. Output width and internal processing width are different quantities.

For a computed example, the ASCII bytes 61 62 63 give

23097d223405d8228642a477bda255b32aadbce4bda0b3f7e36c9da7.

A SHA-256 digest of the same bytes begins ba7816bf8f01cfea. Keeping only its first 28 bytes therefore does not give SHA-224. The algorithm's different initial values are applied before processing any message block.

The same output length also does not make SHA-224 identical to SHA-512/224. The latter uses the 64-bit SHA-512 family structure, a different initial state and a different padding/length-field convention. For instance, a 56-byte input takes two padded blocks in SHA-224 but only one in the SHA-512-based variant. Both results have 28 bytes, so a digest field's size cannot identify which function produced it.

The intended cryptographic protocol must select the hash explicitly. A cryptographic test vector for SHA-224 checks that defined function, whereas an HMAC vector also specifies its key and keyed construction.

SHA-256 is a SHA-2 cryptographic hash function producing a 256-bit digest. It processes a padded message in 512-bit blocks, with eight 32-bit state words and 64 processing rounds per block. The specified additions use modular arithmetic modulo $2^{32}$.^[ref]

Padding is part of the function. For input bit length $\ell <2^{64}$, append a one bit, then the smallest nonnegative number $k$ of zero bits satisfyingthen append the 64-bit representation of $\ell$. This makes the complete length a multiple of 512 bits.^[ref]

For an original byte-count example, the three ASCII bytes 61 62 63 have length 24 bits. Here $k=423$, andThe padded block consists of the original three bytes, byte 80, 52 zero bytes and an eight-byte length field representing 24. The padded input occupies 64 bytes; the final digest occupies 32 bytes. Computing SHA-256 gives

ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad.

Adding a newline changes the byte sequence and the digest. Displayed text, its character encoding and its line terminator must therefore be specified when comparing hash values.

The padding boundary is also visible without computing a digest. A 55-byte input fits its padding into one 64-byte block, whereas a 56-byte input requires two blocks because the length field no longer fits. Both still produce a 256-bit output. Digest length is not the padded-message length or a reversible compressed representation of the input.

Finite output size necessarily allows collisions over a larger input set; collision resistance concerns the difficulty of finding them. SHA-256 also supplies the hash operation used inside common HMAC and HKDF instantiations, whose keyed constructions and security properties differ from an ordinary unkeyed digest.