Question

State the value of the padding field and the value of the length field in SHA-512 if the length of the message is:
(Show your calculations/Justify your answer)

2049 bits

562 bits

Answer 1

In the first step of SHA-512 algorithm, we append the bits which are 128 less than the multiple of 1024.

1).

Here, for 2049, it is 1 more than multiple of 1024 which is 2048.
So, the next multiple of 1024 is : 3072.

3072 - 2049 = 1023

1023 - 128 = 895

So, we need to append 895 bits as 1 followed by 894 0s.

Then the total size will be 2049 + 895 = 2944
and then 2944 + 128 = 3072 which is multiple of 1024.

The value of length field is always 128-bit unsinged int big endian and it says the message length without padding. So, for this, it is 2049 represented as 128-bits.

So, for 2049 bits message,

padding field value = 1 followed by 894 0s and length field value = 0x00000000000000000000000000000801

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2).

562 bits is message size. So, next 1024 multiple is 1024 itself.

1024 - 562 = 462

462 - 128 = 334.

So, 334 is padding field length. So, 1 followed by 333 0s is the value of padding field.

length field will represent 562 in 128-bits.

So, for 562 bits message,

padding field value = 1 followed by 333 0s.
length field value = 0x00000000000000000000000000000232.

Note: I wrote next multiple of 1024, you may have studied mod 1024 concept. Both are the same, this may become simpler so I wrote like that.

I tried to make it as simple and specific as i could. But do comment if there is any query. Thank you. :)