{"publication_status":"published","month":"05","title":"Lossy functions do not amplify well","date_published":"2012-05-04T00:00:00Z","abstract":[{"lang":"eng","text":"We consider the problem of amplifying the &quot;lossiness&quot; of functions. We say that an oracle circuit C*: {0,1} m → {0,1}* amplifies relative lossiness from ℓ/n to L/m if for every function f:{0,1} n → {0,1} n it holds that 1 If f is injective then so is C f. 2 If f has image size of at most 2 n-ℓ, then C f has image size at most 2 m-L. The question is whether such C* exists for L/m ≫ ℓ/n. This problem arises naturally in the context of cryptographic &quot;lossy functions,&quot; where the relative lossiness is the key parameter. We show that for every circuit C* that makes at most t queries to f, the relative lossiness of C f is at most L/m ≤ ℓ/n + O(log t)/n. In particular, no black-box method making a polynomial t = poly(n) number of queries can amplify relative lossiness by more than an O(logn)/n additive term. We show that this is tight by giving a simple construction (cascading with some randomization) that achieves such amplification."}],"page":"458 - 475","intvolume":"      7194","alternative_title":["LNCS"],"doi":"10.1007/978-3-642-28914-9_26","acknowledgement":"We would like to thank Oded Goldreich and Omer Rein- gold for discussions at an early stage of this project, and Scott Aaronson for clarifications regarding the collision problem.\r\n","date_updated":"2021-01-12T07:42:22Z","quality_controlled":"1","publisher":"Springer","day":"04","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"None","volume":7194,"year":"2012","conference":{"start_date":"2012-03-19","name":"TCC: Theory of Cryptography Conference","location":"Taormina, Sicily, Italy","end_date":"2012-03-21"},"citation":{"ista":"Pietrzak KZ, Rosen A, Segev G. 2012. Lossy functions do not amplify well. TCC: Theory of Cryptography Conference, LNCS, vol. 7194, 458–475.","chicago":"Pietrzak, Krzysztof Z, Alon Rosen, and Gil Segev. “Lossy Functions Do Not Amplify Well,” 7194:458–75. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-28914-9_26\">https://doi.org/10.1007/978-3-642-28914-9_26</a>.","short":"K.Z. Pietrzak, A. Rosen, G. Segev, in:, Springer, 2012, pp. 458–475.","apa":"Pietrzak, K. Z., Rosen, A., &#38; Segev, G. (2012). Lossy functions do not amplify well (Vol. 7194, pp. 458–475). Presented at the TCC: Theory of Cryptography Conference, Taormina, Sicily, Italy: Springer. <a href=\"https://doi.org/10.1007/978-3-642-28914-9_26\">https://doi.org/10.1007/978-3-642-28914-9_26</a>","ama":"Pietrzak KZ, Rosen A, Segev G. Lossy functions do not amplify well. In: Vol 7194. Springer; 2012:458-475. doi:<a href=\"https://doi.org/10.1007/978-3-642-28914-9_26\">10.1007/978-3-642-28914-9_26</a>","ieee":"K. Z. Pietrzak, A. Rosen, and G. Segev, “Lossy functions do not amplify well,” presented at the TCC: Theory of Cryptography Conference, Taormina, Sicily, Italy, 2012, vol. 7194, pp. 458–475.","mla":"Pietrzak, Krzysztof Z., et al. <i>Lossy Functions Do Not Amplify Well</i>. Vol. 7194, Springer, 2012, pp. 458–75, doi:<a href=\"https://doi.org/10.1007/978-3-642-28914-9_26\">10.1007/978-3-642-28914-9_26</a>."},"type":"conference","_id":"3281","publist_id":"3365","date_created":"2018-12-11T12:02:26Z","department":[{"_id":"KrPi"}],"status":"public","author":[{"full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654","last_name":"Pietrzak","first_name":"Krzysztof Z"},{"last_name":"Rosen","full_name":"Rosen, Alon","first_name":"Alon"},{"last_name":"Segev","full_name":"Segev, Gil","first_name":"Gil"}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"http://www.iacr.org/archive/tcc2012/tcc2012-index.html"}]}