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This paper presents extremely fast algorithms for code-based public-key cryptography, including full protection against timing attacks. For example, at a 2128 security level, this paper achieves a reciprocal decryption throughput of just 60493 cycles (plus cipher cost etc.) on a single Ivy Bridge core. These algorithms rely on an additive FFT for fast root computation, a transposed additive FFT for fast syndrome computation, and a sorting network to avoid cache-timing attacks.