FPGARelated.com

Polynomial Inverse

Mike November 23, 20152 comments

One of the important steps of computing point addition over elliptic curves is a division of two polynomials.


One Clock Cycle Polynomial Math

Mike November 20, 20157 comments

Error correction codes and cryptographic computations are most easily performed working with GF(2^n)


Elliptic Curve Cryptography

Mike November 16, 20156 comments

Secure online communications require encryption. One standard is AES (Advanced Encryption Standard) from NIST. But for this to work, both sides need the same key for encryption and decryption. This is called Private Key encryption.


Polynomial Math

Mike November 3, 20152 comments

Elliptic Curve Cryptography is used as a public key infrastructure to secure credit cards, phones and communications links. All these devices use either FPGA's or embedded microprocessors to compute the algorithms that make the mathematics work. While the math is not hard, it can be confusing the first time you see it.  This blog is an introduction to the operations of squaring and computing an inverse over a finite field which are used in computing Elliptic Curve arithmetic. ...


Elliptic Curve Cryptography - Key Exchange and Signatures

Mike October 21, 2023

Elliptic curve mathematics over finite fields helps solve the problem of exchanging secret keys for encrypted messages as well as proving a specific person signed a particular document. This article goes over simple algorithms for key exchange and digital signature using elliptic curve mathematics. These methods are the essence of elliptic curve cryptography (ECC) used in applications such as SSH, TLS and HTTPS.


Polynomial Math

Mike November 3, 20152 comments

Elliptic Curve Cryptography is used as a public key infrastructure to secure credit cards, phones and communications links. All these devices use either FPGA's or embedded microprocessors to compute the algorithms that make the mathematics work. While the math is not hard, it can be confusing the first time you see it.  This blog is an introduction to the operations of squaring and computing an inverse over a finite field which are used in computing Elliptic Curve arithmetic. ...


Elliptic Curve Cryptography - Security Considerations

Mike October 16, 2023

The security of elliptic curve cryptography is determined by the elliptic curve discrete log problem. This article explains what that means. A comparison with real number logarithm and modular arithmetic gives context for why it is called a log problem.


New book on Elliptic Curve Cryptography

Mike August 30, 20234 comments

New book on Elliptic Curve Cryptography now online. Deep discount for early purchase. Will really appreciate comments on how to improve the book because physical printing won't happen for a few more months. Check it out here: http://mng.bz/D9NA