Judul: Breast development and age at menarche of girls in Semarang
Abstrak: Pubertas adalah fase transisi dari anak-anak sampai dewasa yang merupakan reaktivasi dari sistem saraf pusat untuk perkembangan seksual ditandai dengan peningkatan hormon seks. Tanda umum digunakan untuk menentukan waktu pubertas perempuan perkembangan payudara dan menarke. Tujuan dari penelitian ini adalah untuk menentukan waktu pubertas perempuan di Semarang berdasarkan pada usia menarke dan perkembangan payudara. Penelitian ini menggunakan total 998 subyek berusia 8-19 tahun. Waktu pubertas perempuan di Semarang berusia 11,94 tahun lebih cepat bila dibandingkan dengan hasil penelitian sebelumnya antara kota Bogor, daerah pedesaan Pekalongan, dan kota Purwokerto. Hal ini terjadi karena perbedaan status sosial ekonomi dan pengeluaran keluarga untuk makan. Perkembangan payudara dapat diklasifikasikan ke dalam lima tahap. Hasil analisis menunjukkan rata-rata usia tahap dua di tua 8,2 tahun. Rata-rata dari tiga tahap dan tahap empat diamati pada 10,46 dan 12,01 tahun, masing-masing. Rata-rata usia tahap lima diamati pada usia 13,42 tahun. Berdasarkan hasil ini, menarche telah berkorelasi dengan perkembangan payudara tahap empat.
Keyword: Age at menarche, Breast development, Nutrition status, Puberty, Socioeconomic status, Sex hoemones, Puberty, Central nervous system, Sexual developemnt, Women puberty

Judul: Menarcheal Age and Breast Development in Purwokerto
Abstrak: Puberty is a transition from childhood into adulthood. It occurs as a result of the hypothalamic pituitary gonadal axis activity which stimulates the central inhibitory feedback and lifts the Gonadotropin Releasing Hormone (GnRH). The activation of GnRH increasingly stimulates the secretion of Follicle Stimulating Hormone (FSH) and Lutenizing Hormone (LH) from the pituitary gland. Both of these hormones stimulate the production of estrogen, which allows for menarche and the development of secondary sexual characteristics. The aim of this research is determine the menarcheal age and breast development in Purwokerto. I used 99 individual subject aged 8-14 years old which contained 28 menarche subjects. The result showed that the menarcheal age average in Purwokerto was 12.4 years old. In this study, the breast measurement showed three stages of breast development. The youngest and the average age of Tanner stage two were 9 and 10 years old. The youngest and average age of Tanner stage three were 10.8 and 12.5 years old. Based on the result, menarche has correlated with the breast development stage three. The present study had similar result between Bogor, Jakarta, but differ with Pekalongan. This maybe because the samples from Purwokerto, Bogor, and Jakarta came from urban areas whereas samples from Pekalongan came from rural area
Keyword: socioeconomic status, puberty, nutrition status, menarche, breast development

Judul: Algorithm Construction of HLI Hash Function
Abstrak: Cryptography is a study of mathematical techniques related to aspects of information security regarding on confidentiality, data integrity, entity authentication, and data origin authentication. Data integrity is a service, which is associated with the conversion of data carried out by unauthorized parties. To maintain data integrity, one can use hash functions. An hash function is a computationally efficient function to map an arbitrary length bitstring to a fixed length bitstring called as hash value. The use of hash function in maintaining the information integrity and authentication is in digital signatures, virus protection, and software distribution. Illustration of the hash function in the integrity and authentication of information that is emailed as follow. The sender sends the information and hash value to the recipient. If the hash value of the information is equal to the hash value that is sent by the sender, then information has not been changed. Otherwise the information has been changed. An hash function has two properties, one way and collision resistance. An hash function is called one way if it is computationally infeasible to find any input such that when given any hash value . Meanwhile an hash function is called collision resistant if it is computationally infeasible to find any two inputs where such that . The purpose of this study is to construct a HLI hash function algorithm, to analyze the speed and security of the hash functions as a results of construction. Furthermore, it is to compare it with SWIFFT. Hash function is constructed based on the result of algebraic operations on modular polynomial ringwith . Modular polynomial ring noted as is a set of all polynomials of degree at most with coefficients in . can be represented as a set of integer vector of modulo in dimension . So, it is simple to implement in a computer. In vector operations, is lattice . Furthermore, alattice that is defined from certain polynomial ring is called ideal lattice. HLI hash function is consists of addition and multiplication algorithm in the ring. Addition algorithm consists of sumation operations of modulo and multiplication consists of multiplication operations of modulo . Generally, algorithm of HLI hash function consists of multiplication operations of modulo and addition operations of modulo . However, if the input is binary number then multiplication algorithm only consists of multiplication operation of modulo , so algorithm of HLI hash function consists of multiplication operations of modulo and addtion operations of modulo . An hash function is secured if it has two properties, i.e., one way and collision resistance. HLI hash function hash is one way, it is following the proof of Micciancio. It is has collision resistant because of polynomial is irreducible over and monic. Moreover, it is proved that for every unit vector , the vector is small vector. If the input of hash function is a binary number then HLI hash function only involves addition operations of modulo . So the time that used almost same with SWIFFT. The excellence of HLI hash function is the key size smaller than SWIFFT. This effect on
Keyword: hash function, modular polynomial ring, lattice