Robert Gallant

Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms

The fundamental operation in elliptic curve cryptographic schemes is the multiplication of an elliptic curve point by an integer. This paper describes a new method for accelerating this operation on classes of elliptic curves that have efficiently-computable endomorphisms. One advantage of the new method is that it is applicable to a larger class of curves than previous such methods. For this special class of curves, a speedup of up to 50% can be expected over the best general methods for point multiplication.

Improving the parallelized Pollard lambda search on anomalous binary curves

The best algorithm known for finding logarithms on an elliptic curve (E) is the (parallelized) Pollard lambda collision search. We show how to apply a Pollard lambda search on a set of equivalence classes derived from E, which requires fewer iterations than the standard approach. In the case of anomalous binary curves over F 2 m, the new approach speeds up the standard algorithm by a factor of √2m.

Provably Secure Implicit Certificate Schemes

Optimal mail certificates, introduced in [12], are efficient types of implicit certificates which offer many advantages over traditional (explicit) certificates. For example, an optimal mail certificate is small enough to fit on a two-dimensional digital postal mark together with a digital signature. This paper defines a general notion of security for implicit certificates, and proves that optimal mail certificates are secure under this definition.

Accelerated verification of ECDSA signatures

Verification of ECDSA signatures is considerably slower than generation of ECDSA signatures. This paper describes a method that can be used to accelerate verification of ECDSA signatures by more than 40% with virtually no added implementation complexity. The method can also be used to accelerate verification for other ElGamal-like signature algorithms, including DSA.