Abstract. Several ideal-lattice-based cryptosystems have been broken by recent attacks that exploit special structures of the rings used in those cryptosystems. The same structures are also used in the leading proposals for post-quantum lattice-based cryptography, including the classic NTRU cryptosystem and typical Ring-LWE-based cryptosystems. This paper (1) proposes NTRU Prime, which tweaks NTRU to use rings without these structures; (2) proposes Streamlined NTRU Prime, a public-key cryptosystem optimized from an implementation perspective, subject to the standard design goal of IND-CCA2 security; (3) finds high-security post-quantum parameters for Streamlined NTRU Prime; and (4) optimizes a constant-time implementation of those parameters. The resulting sizes and speeds show that reducing the attack surface has very low cost.

Abstract. This paper introduces high-security constant-time variable-base-point Diffie-Hellman software using just 274593 Cortex-A8 cycles, 91460 Sandy Bridge cycles, 90896 Ivy Bridge cycles, or 72220 Haswell cycles. The only higher speed appearing in the literature for any of these platforms is a claim of 60000 Haswell cycles for unpublished software performing arithmetic on a binary elliptic curve.The new speeds rely on a synergy between (1) state-of-the-art formulas for genus-2 hyperelliptic curves and (2) a modern trend towards vectorization in CPUs. The paper introduces several new techniques for efficient vectorization of Kummer-surface computations.

This paper analyzes the cost of breaking ECC under the following assumptions: (1) ECC is using a standardized elliptic curve that was actually chosen by an attacker; (2) the attacker is aware of a vulnerability in some curves that are not publicly known to be vulnerable. This cost includes the cost of exploiting the vulnerability, but also the initial cost of computing a curve suitable for sabotaging the standard. This initial cost depends heavily upon the acceptability criteria used by the public to decide whether to allow a curve as a standard, and (in most cases) also upon the chance of a curve being vulnerable.This paper shows the importance of accurately modeling the actual acceptability criteria: i.e., figuring out what the public can be fooled into accepting. For example, this paper shows that plausible models of the "Brainpool acceptability criteria" allow the attacker to target a one-in-a-million vulnerability and that plausible models of the "Microsoft NUMS criteria" allow the attacker to target a one-in-a-hundred-thousand vulnerability.

This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77M per bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.