2 года назад
Useful and efficient algorithms for secp256k1 elliptic curve
CRYPTO DEEP TECH In this article, we will consider several useful and efficient algorithms for an elliptic curve  E  over a field  GF(p)  given by the short Weierstrass equation у^2 = х^3 + Ах + В Modular operations (integers) on a finite field (or Galois field) Elliptic Curve Point Operation The point  P(x  0  , y  0  )  on the elliptic curve  E  means: its coordinates  x  0  and  y  0  are elements of the field, and the coordinates  x  0  and  y  0  satisfy the equation. Divider Divisor  (Divisor)  D...
2 года назад
One weak transaction in ECDSA on the Bitcoin blockchain and with the help of Lattice Attack we received a Private Key to BTC coins
CRYPTO DEEP TECH What do we know about the lattice attack? To begin with, the elliptic curve digital signature algorithm (ECDSA) is a common digital signature scheme that we see in many of our code reviews. It has some desirable properties, but can also be very fragile to recover the private key with a side-channel attack that reveals less than one bit of the secret nonce. ECDSA is a special form of the digital signature algorithm (DSA). DSA is a fairly common digital signature scheme, which is defined by three algorithms: key generation, signature, and verification...