SHA-1

The SHA-1 compression function

One step of the SHA-1 state update transformation

1 General Description

SHA-1 is an iterated hash function. It can be used to compute a 160-bit hash value for messages having a length of less than 2⁶⁴ bits, cf. FIPS 180-2 Secure Hash Standard. As most iterated hash functions, SHA-1 applies MD strengthening.

1.1 Compression Function

The compression function processes input message blocks of 512 bits and produces a 160-bit chaining value. The compression function of SHA-1 basically consists of two parts: the message expansion and the state update transformation. The chaining variable (iv in the first iteration) is added to the output of the state update transformation (feed forward).

1.1.1 Message Expansion

In SHA-1, the message expansion is defined as follows. A single 512-bit input message block block is represented by 16 32-bit words, denoted by , with . The message input is linearly expanded into 80 32-bit words defined as follows:

1.1.2 State Update Transformation

The state update transformation starts from a fixed initial value iv for 5 32-bit registers (also referred to as state variables) and updates these registers in 80 steps () by using the word and the step constant in step . One step of the state update transformation is defined as

The function depends on the step number: steps use the IF-function referred to as and steps use the MAJ-function referred to as . The remaining steps, use a 3-input XOR referred to as . The Boolean functions are defined as follows:

1.3 Constants and Initial Value

1.3.1 Constants

1.3.2 Initial Value

3 Security Anaylsis

• Best know attack: 2⁶³ by Wang et.al.
• Best known collision example: 64-step collision by De Canniere and Rechberger

something like: best know attack to date: kind of attack, which variant has been looked at (e.g. round-reduced), complexity, and reference to paper and abstract.

may be make here a new page with the other cryptanalysis results.

• [Detailed overview of cryptanalysis results for SHA-1]