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This paper focus on incremental cryptographic schemes that solve the privacy problem introduced by Bellare, Goldreich and Goldwasser. To our knowledge, none of the schemes designed so far provide simultaneously strong privacy guarantees and byte-wise incremental operations. We propose a new method that extends a block-wise incremental cryptographic scheme into a fully byte-wise incremental one while keeping good performances. This one insures the property of perfect privacy with the same average overhead for both the size of the cryptographic form and the number of operations to perform when applying the conjugate algorithm.