Abstract. This paper introduces a high-security post-quantum stateless hash-based signature scheme that signs hundreds of messages per second on a modern 4-core 3.5GHz Intel CPU. Signatures are 41 KB, public keys are 1 KB, and private keys are 1 KB. The signature scheme is designed to provide long-term 2 128 security even against attackers equipped with quantum computers. Unlike most hash-based designs, this signature scheme is stateless, allowing it to be a drop-in replacement for current signature schemes.

Abstract. This paper presents new software speed records for the computation of cryptographic pairings. More specifically, we present a software which computes the optimal ate pairing on a 257-bit Barreto-Naehrig curve in only 4,470,408 cycles on one core of an Intel Core 2 Quad Q6600 processor. This speed is achieved by combining 1.) state-of-the-art high-level optimization techniques, 2.) a new representation of elements in the underlying finite fields which makes use of the special modulus arising from the Barreto-Naehrig curve construction, and 3.) implementing arithmetic in this representation using the double-precision floating-point SIMD instructions of the amd64 architecture.

We analyze how fast we can solve general systems of multivariate equations of various low degrees over F2; this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive search technique, our improved approach is more efficient both asymptotically and practically. We implemented several optimized versions of our techniques on CPUs and GPUs. Our technique runs more than 10 times faster on modern graphic cards than on the most powerful CPU available. Today, we can solve 48+ quadratic equations in 48 binary variables on a 500-dollar NVIDIA GTX 295 graphics card in 21 minutes. With this level of performance, solving systems of equations supposed to ensure a security level of 64 bits turns out to be feasible in practice with a modest budget. This is a clear demonstration of the computational power of GPUs in solving many types of combinatorial and cryptanalytic problems.