n = 31752220290850128181513412164141482602298589253012293644796723695601 ( 225 bit ) I will show that n is a Blum number. ---------- Alice : a = 25719308640489063716765945502887550616749933882734709790295552473391 Bob : e = -1 Alice : x = 10175640475394333628933987520533833598233922757089098760656036591994 Bob : x^2 mod n = 25719308640489063716765945502887550616749933882734709790295552473391 jacobi(x,n) = -1 ---------- Alice : a = 1170163090078159998396003524177287442938976882293682826871245416227 Bob : e = 1 Alice : x = 11728261499193488366726080110378344588526493145779959438170540884544 Bob : x^2 mod n = 1170163090078159998396003524177287442938976882293682826871245416227 jacobi(x,n) = 1 ---------- Alice : a = 28505725881874334255091804331463407613322239903942189075334319550806 Bob : e = -1 Alice : x = 30904006634532716500810178347049649587914889442645057631020714545931 Bob : x^2 mod n = 28505725881874334255091804331463407613322239903942189075334319550806 jacobi(x,n) = -1 ---------- Alice : a = 6784348593822264970846132216282568683864219925925024940540210202363 Bob : e = -1 Alice : x = 21337643165898977781811863318068290248918011488479448247377075498839 Bob : x^2 mod n = 6784348593822264970846132216282568683864219925925024940540210202363 jacobi(x,n) = -1 ---------- Alice : a = 1379270343532345550709829393489630584082311130179412327412169109235 Bob : e = 1 Alice : x = 8513603833827460573596328205385375709484166884992025756342968481834 Bob : x^2 mod n = 1379270343532345550709829393489630584082311130179412327412169109235 jacobi(x,n) = 1 ---------- Alice : a = 5462781859298536158728672349522396998968949298801041592304098640108 Bob : e = -1 Alice : x = 27471215978339913488024085995435253674551268929308325280237847786011 Bob : x^2 mod n = 5462781859298536158728672349522396998968949298801041592304098640108 jacobi(x,n) = -1 ---------- Alice : a = 16280619659770043156821269514492766710256159088980965430680487185291 Bob : e = 1 Alice : x = 23241488705116633852020575406071865013447450135942406655431659240404 Bob : x^2 mod n = 16280619659770043156821269514492766710256159088980965430680487185291 jacobi(x,n) = 1