{'fraction_non_alphanumeric': 0.04837430610626487, 'fraction_numerical': 0.004758128469468675, 'mean_word_length': 3.9296875, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Batch point compression in the context of advanced pairing-based protocols

. This paper continues previous ones about compression of points on elliptic curves E b : y 2 = x 3 + b (with j -invariant 0) over a finite field F q of characteristic > 3. More precisely, we show in detail how any two (resp. three) points from E b ( F q ) can be quickly compressed to two (resp. three) elements of F q (apart from a few auxiliary bits) in such a way that the corresponding decompression stage requires to extract only one cubic (resp. sextic) root in F q (with several multiplications and without inversions). As a result, for many q occurring in practice the new compression-decompression methods are more efficient than the classical one with the two (resp. three) x or y coordinates of the points, which extracts two (resp. three) roots in F q . We explain why the new methods are useful in the context of modern real-world pairing-based protocols. As a by-product, when q ≡ 2 (mod 3) (in particular, E b is supersingular), we obtain a two-dimensional analogue of Boneh–Franklin’s encoding, that is a way to sample two “independent” F q -points on E b at the cost of one cubic root in F q . Finally, we comment on the case of four and more points from E b ( F q ).