EC NIST P-256 FIPS-186-4 B.5.1 Per-Message Secret Number Generation Using Extra Random Bits operation

Renard

7/23/23, 8:43 AM

I need to implement following operation:

w = (z mod (n-1)) + 1

where

z: 40-byte array

n: the order n of base point defined for NIST P-256.

I assume that resulted 'w' could be a point on the curve.

Any opinions are more than welcome

0 + 0

elliptic-curves

Daniel S

7/23/23, 8:58 AM

$w$ is not a point on the curve but rather a secret value corresponding to $k$ in section 4.5 of the DSS document. It should be used to compute a point $wG$ on the curve where $G$ is the base point. This is analogous to the calculation of $g^k$ in section 4.6 of the DSS document.

fgrieu

7/23/23, 9:25 AM

You need to interpret the byte array $z$ as an integer per the appropriate, system-dependent convention (in the context that would be big-endian binary if the data is in the form it has externally), reduce it modulo $(n-1)$ (where $n$ is the integer given in [D.1.2.3](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#page=100)), then add $1$, yielding (pseudorandom) integer $z$ in the interval $[1,n-1]$. That's not a point. but $w\,G$ would be a pseudorandom point. Except for side-channel considerations, the rest is a programming problem, thus off-topic.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: EC NIST P-256 FIPS-186-4 B.5.1 Per-Message Secret Number Generation Using Extra Random Bits operation

TH: EC NIST P-256 FIPS-186-4 B.5.1 การสร้างหมายเลขลับต่อข้อความโดยใช้การดำเนินการบิตสุ่มพิเศษ

RO: EC NIST P-256 FIPS-186-4 B.5.1 Generarea numerelor secrete per mesaj utilizând operarea cu biți extra aleatori

RU: EC NIST P-256 FIPS-186-4 B.5.1 Генерация секретного номера для каждого сообщения с использованием операции Extra Random Bits

VI: EC NIST P-256 FIPS-186-4 B.5.1 Tạo số bí mật cho mỗi thông báo bằng thao tác Bit ngẫu nhiên bổ sung

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