Hey! I'm David, cofounder of zkSecurity and the author of the Real-World Cryptography book. I was previously a crypto architect at O(1) Labs (working on the Mina cryptocurrency), before that I was the security lead for Diem (formerly Libra) at Novi (Facebook), and a security consultant for the Cryptography Services of NCC Group. This is my blog about cryptography and security and other related topics that I find interesting.

# Nothing up my sleeve numbers posted February 2015

Why does the round constants in sha1 have those specific values?

Kt is the round constant of round t;

from SH1-1 - Wikipedia:

The constant values used are chosen to be nothing up my sleeve numbers: the four round constants k are 230 times the square roots of 2, 3, 5 and 10. The first four starting values for h0 through h3 are the same with the MD5 algorithm, and the fifth (for h4) is similar.

In cryptography, nothing up my sleeve numbers are any numbers which, by their construction, are above suspicion of hidden properties. They are used in creating cryptographic functions such as hashes and ciphers. These algorithms often need randomized constants for mixing or initialization purposes. The cryptographer may wish to pick these values in a way that demonstrates the constants were not selected for a nefarious purpose, for example, to create a backdoor to the algorithm. These fears can be allayed by using numbers created in a way that leaves little room for adjustment. An example would be the use of initial digits from the number π as the constants. Using digits of π millions of places into its definition would not be considered as trustworthy because the algorithm designer might have selected that starting point because it created a secret weakness the designer could later exploit.

#### Maxime

It's not always sufficient to pick a nothing up my sleeve numbers.
Those constants never raised serious concern for the symmetric crypto primitives because in this cas, introducing a trap seems extremely hard ... but it's not anymore the case for asymmetric crypto ... think of the infamous Dual-EC-DRBG.
https://eprint.iacr.org/2014/571.pdf

#### david

Maxime: in the case of Dual EC, the two values P and Q are not NUMP values

#### Maxime

David : You are perfectly right ! But what I mean is, you have to be very careful with the use of NUMP in asymmetric crypto.