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Tuesday, May 31, 2011
آموزشگاه موسیقی
Monday, May 30, 2011
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Sunday, May 22, 2011
Game-theoretic approach to mitigate packet dropping in wireless Ad-hoc networks
Game-theoretic approach to mitigate packet dropping in wireless Ad-hoc networks
Tootaghaj, Diman Zad ; Farhat, Farshid ; Pakravan, Mohammad-Reza ; Aref, Mohammad-Reza ;
Information Systems and Security Lab (ISSL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran
This paper appears in: Consumer Communications and Networking Conference (CCNC), 2011 IEEE
Issue Date : 9-12 Jan. 2011
On page(s): 163
Print ISBN: 978-1-4244-8789-9
Digital Object Identifier : 10.1109/CCNC.2011.5766444
Date of Current Version : 12 May 2011
ABSTRACT
Performance of routing is severely degraded when misbehaving nodes drop packets instead of properly forwarding them. In this paper, we propose a Game-Theoretic Adaptive Multipath Routing (GTAMR) protocol to detect and punish selfish or malicious nodes which try to drop information packets in routing phase and defend against collaborative attacks in which nodes try to disrupt communication or save their power. Our proposed algorithm outranks previous schemes because it is resilient against attacks in which more than one node coordinate their misbehavior and can be used in networks which wireless nodes use directional antennas. We then propose a game theoretic strategy, ERTFT, for nodes to promote cooperation. In comparison with other proposed TFT-like strategies, ours is resilient to systematic errors in detection of selfish nodes and does not lead to unending death spirals.
Risk of attack coefficient effect on availability of Ad-hoc networks
Risk of attack coefficient effect on availability of Ad-hoc networks
Tootaghaj, Diman Zad ; Farhat, Farshid ; Pakravan, Mohammad-Reza ; Aref, Mohammad-Reza ;
Information Systems and Security Lab (ISSL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran
This paper appears in: Consumer Communications and Networking Conference (CCNC), 2011 IEEE
Issue Date : 9-12 Jan. 2011
On page(s): 166
Print ISBN: 978-1-4244-8789-9
Digital Object Identifier : 10.1109/CCNC.2011.5766445
Date of Current Version : 12 May 2011
ABSTRACT
Security techniques have been designed to obtain certain objectives. One of the most important objectives all security mechanisms try to achieve is the availability, which insures that network services are available to various entities in the network when required. But there has not been any certain parameter to measure this objective in network. In this paper we consider availability as a security parameter in ad-hoc networks. However this parameter can be used in other networks as well. We also present the connectivity coefficient of nodes in a network which shows how important is a node in a network and how much damage is caused if a certain node is compromised.
Wednesday, May 18, 2011
Game-Theoretic Approach in Network Security, Availability and Privacy
Game-Theoretic Network Simulator
This is GTNS: game theoretic network simulator help document. In order to download GTNS click it. To download samples click it!
Introduction:
GTNS is a discrete-event network simulator targeted primarily for research and educational use.
GTNS is written in Visual C++ programming language and supports different network topologies. This simulator was first produced to implement locally multipath adaptive routing (LMAR) protocol, classified as a new reactive distance vector routing protocol for MANETs. LMAR can find an ad-hoc path without selfish nodes and wormholes using an exhaustive search algorithm in polynomial time. Also when the primary path fails, it discovers an alternative safe path if network graph remains connected after eliminating selfish/malicious nodes. The key feature of LMAR to seek safe route free of selfish and malicious nodes in polynomial time is its searching algorithm and flooding stage that its generated traffic is equi-loaded compared to single-path routing protocols but its security efficiency to bypass the attacks is much better than the other multi-path routing protocols. LMAR concept is introduced to provide the security feature known as availability and a simulator has been developed to analyze its behavior in complex network environments [1]. Then we have added detection mechanism to the simulator, which can detect selfish nodes in network. The proposed algorithm is resilient against collision and can be used in networks which wireless nodes use directional antennas and it also defend against an attack that malicious nodes try to break communications by relaying the packets in a specific direction. Some game theoretic strategies to enforce cooperation in network have been implemented in GTNS, for example Forwarding-Ratio Strategy, TFT-Strategy and ERTFT. This tutorial helps new users to get familiar with GTNS and run different network scenarios.
Getting Started with GTNS:
After debugging GTNS simulator you can see the following window:
Figure 1- GTNS simulator environment
Network-Router:
To implement your own network you can click on Network-Router as you can see in figure 2 and 3 you can add one node by clicking on add button, or you can add different number of nodes, randomly placed over screen by clicking the Self-Generate button. In figure 4 you can see a sample network topology created by adding 5 nodes to the network. You can change the default preferences of node by clicking on Default Preferences button, or you can change different parameters of any node in the network by clicking on that node in the screen. Any node in the network can be deleted or you can change its parameters during simulation or you can force it as a selfish node. Figure 5 shows different parameters of nodes that can be changed. You can change the router's caption, its coverage range, delay, X_axis and Y_axis of the router in the screen, the length and width of router image and battery power of any router can be changed in the network.
Figure 2- Network-Router button
Figure 3- Network-Router-Self-Generate button
Figure 4- A sample of network topology created by adding 5 nodes in GTNS environment
Figure 5- Editing node parameters by clicking on any node on the screen
Creating Links between nodes in GTNS:
As it is seen in figure 6 you can add links between nodes by clicking on Network-Link-Self-Generate button. All nodes which are in the coverage range of each other will be connected with a full-duplex link.
You can also add links between any two nodes in network by clicking on Network-Link-Add. Figure 7 shows different parameters that can be changed by clicking this button. You can select two routers that you want to make a link between them and frequency and duplicity of the link. You can add wormhole links between any two nodes by creating links between nodes which are not in the coverage range of each other. During simulation you can add or delete a specific link between any two nodes in network.
Figure 8 shows a sample topology created by using Link-Self-Generate button.
Figure 6- Adding links between nodes in GTNS simulator
Figure 7- Different parameters that can be changed by clicking Link-Add button
Figure 8- A sample network created by adding self-generate links between 10 nodes in GTNS
Adding Traffic to network:
As you see from figure 9, you can add traffic between any two nodes in network by clicking Network-Traffic-Add. Figure 10 shows different parameters that you can change when you want to add traffic between any two source and destination node in network. You can select routing protocol and start time of traffic sparks.
Figure 9- Adding traffic to the network
In GTNS you can add random traffic to network. Figure 11 shows the window when you click on Network-Traffic-Self-Generate-Ad-hoc. You can select the starting and stopping time of random traffic generated, and number of connections during this interval. Data traffic rate and different protocols can be selected in this window.
Figure 10- different parameters that can be changed during adding traffic between any two nodes
Figure 11- Different parameters that can be selected by adding random traffic in network
Simulation in GTNS:
To simulate the network created in GTNS, you should click on Simulation-Profile button as you can see in figure 12. Then the Simulation window will be opened where you can see the clock and view events. Figure 13 shows Simulation window. You can also change the speed of simulation by moving Master and slave speed buttons.
By clicking on Resume button you can run the simulation and see different packet exchange in network.
For example we have created one connection between node 1 and 64. After clicking Resume button node 1 will broadcast RReq packets. Figure 14 shows broadcasting of RReq packets, when RReq passes a link, it will become blue. When the first RReq packet reaches to destination, node 64 will broadcast RRep packets. Figure 15 shows broadcasting of RRep packets. Links become yellow when RRep packets pass them.
Figure 12- A sample grid network topology and simulation button in GTNS
Figure 13- Simulation-Profile window
Figure 14- A sample grid network topology and broadcasting of RReq packets
Figure 15- A sample grid network topology and broadcasting of RRep packets
Afterwards node 1 sends the traffic towards node 64 by choosing the shortest path in its routing table. The intermediate nodes send the traffic towards their first index entry, the best path. The purple line in Figure 16 shows the forwarding path from the source to the destination (this line is overwritten by the return path of ACK packet). The ACK packet traverses the reverse path (the green line) back to the source, as the intermediate nodes set the reverse hop back to the source in their routing tables. So the green line of reverse path over-color the purple line of forwarding path.
Figure 16: Established connection with the shortest path
Getting results:
You can see different statistic results of the simulation by clicking on Simulation-Statistic button as shown in figure 17. Figure 18 shows the Statistics window opened when you click on this button. You can see different parameters of network. For example you can see number of data packets that have been forwarded by intermediate nodes in Data Trans. No, you can see number of forwarded RReq and RRep packets in the fields RReq Trans. No and RRep Trans. No respectively. Also number of data packets and number of Ack packets generated during simulation are shown in Gen. Data No. CN and Gen. Ack No. CN. Number of established connections and total power of network after simulation and number of ad-hoc nodes and selfish nodes of type 1 and 2 and clock of the system is shown in this window.
Also after clicking on Simulation-Statistics button, the results of simulation will be saved in my_file.txt file. An example of this file and simulation results of some simulations are shown in figure 19.
Figure 17- Simulation-Statistics button in GTNS
Figure 18- The Statistics window which shows the simulation results created in GTNS
Figure 19- Simulation results written in my_file.txt in GTNS
REFERENCES:
[1] F. Farhat, M. R. Pakravan, M. Salmasizadeh, M. R. Aref, "Locally Multipath Adaptive Routing Protocol Resilient to Selfishness and Wormholes", ISPEC 2010: 187-200.
[2] http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5766445
[3] http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5766444
- Location and data privacy
- Privacy and security mechanisms with selfish players
We study security/privacy mechanisms in the presence of selfish stakeholders, notably by means of game theory. For more information,
click here. We are applying this approach notably to:
. Securing online advertisement
. Recommendation systems
. Revocation
. Location privacy
- Secure neighbor discovery
Other aspects of wireless networks (these projects have been phased out)
- Secure vehicular communications
- Non-cooperative behavior in wireless networks
- Key management in decentralized wireless networks
- DOMINO (protecting WiFi hotspots against greedy behavior)
- CommonSense (Water management in rural areas by means of wireless sensors)
- Wireless Sensor Networks with Mobile Elements
- Group Communication in ad hoc networks
Saturday, May 14, 2011
Workshop on Information Hiding Systems
Workshop on Information Hiding Systems
کارگاه علمی سیستم های پنهان سازی اطلاعات
شاخه دانشجويي انجمن رمز ايران در دانشگاه صنعتي شريف کارگاه علمی تحت عنوان سيستم هاي پنهان سازی اطلاعات (Information Hiding Systems) را در روزهاي 29 و 30 آبان ماه سال جاري در سالن کهرباي دانشکده مهندسي برق دانشگاه صنعتي شريف برگزارکرد. هدف از برگزاري اين کارگاه علمی آموزشي آشناکردن پژوهشگران شاغل در دانشگاه و صنعت با مفاهيم نهان نگاری، نشان گذاری و تحليل نهان نگاري ميباشد که در ادامه موضوعات مورد بحث در کارگاه به تفصيل بيان شده است.
برنامه روز چهارشنبه 29 آبان 1387 (مباحث مقدماتی):
9:00 تلاوت آیاتی از قرآن مجید
9:05 سخنرانی فرشید فرحت، رئیس شاخه دانشجویی انجمن رمز ایران در دانشگاه صنعتی شریف
9:15 سمینار نهان نگاری، اهداف و کاربردهای آن (محمد علي اخايي، دانشجوی دکتری شریف)
9:55 سمینار نیازمنديهاي يک سيستم پنهان نگار (1) (نيما خادمي کلانتری، دانشجوی کارشناسی ارشد امیرکبیر)
• مدلهاي بينايي و شنوايي انسان و نقش آن در نامحسوس بودن نهان نگاره
• متريکهاي نهان نگاري (SNR,PSNR, PEAQ, Qindex, Watson Distance, etc)
10:30 تنفس و پذیرایی
10:45 سمینار نيازمنديهاي يک سيستم پنهان نگار (2) (حسين کورکچي، کارشناسی ارشد شریف)
• نقش تبديلها در نهان نگاري (فرکانس, ويولت, ريجلت, کانتورلت و ...)
• معرفي حملات و مشخصه ويژه هر حمله بر روي سيگنال نهان نگاري شده
11:35 سمینار نهان نگاري از ديدگاه تئوري اطلاعات (هانیه خليليان، کارشناسی ارشد شریف)
• مدلسازي کانال, سيستم و مفاهيم ظرفيتي
12:00 وقت نماز و ناهار
13:15 سمینار روشهاي نخستين پنهان نگاري (1) (سعيد سررشته داري، کارشناسی ارشد شریف)
• LSB, Patchwork, Echo, etc
14:00 سمینار روشهاي نخستين پنهان نگاري (2) (بهاره اخباری، دانشجوی دکتری شریف)
• QIM, SS, Phase Mod, etc
14:45 تنفس و پذیرایی
15:00 سمینار نهان نگاري زبان (یلدا محسن زاده، کارشناسی ارشد شریف)
15:35 سمینار الگوريتم هاي يادگيري ماشين و نقش آن در تحليل نهان نگاره (سوده بخشنده، کارشناسی ارشد)
برنامه روز پنجشنبه 30 آبان 1387 (مباحث پیشرفته):
8:25 تلاوت آیاتی از قرآن مجید
8:30 سمینار روشهاي پنهان نگاري وفقي (مجتبی سيد حسيني، کارشناسی ارشد)
9:10 سمینار روشهاي تحليل نهان نگاره (سعيدرضا خسروي راد، کارشناسی ارشد)
• متغيرهاي آناليز و آماره هاي درجه بالا
10:00 تنفس و پذیرایی
10:20 سمینار روشهاي نوين مبتني بر کوانتيزاسيون (نيما خادمي کلانتری، کارشناسی ارشد)
• Vector Quant, Projection quant, lattice based
11:10 سمینار روشهاي پيشرفته طيف گسترده (محمد علي اخايي، دانشجوی دکتری شریف)
• جمعي و ضربي و کار پيشنهادي
12:00 مراسم اتقدیر از برگزارکنندگان با حضور دکتر امیر دانشگر
12:20 وقت نماز و ناهار
13:30 سمینار نهان سازي و ارتباط آن با مسايل Forensics (یلدا محسن زاده، کارشناسی ارشد)
14:10 مسائل مهم و بروز پنهان نگاري (سعیدرضا خسروي راد و مجتبی سيد حسيني، کارشناسی ارشد)
• سمینار مقاومت در برابر حملات geometric
• سمینار مقاومت در برابر حمله Gain
Workshop on A5/1 Algorithm Cryptanalysis
شاخه دانشجویی انجمن رمز ایران در دانشگاه صنعتی شریف، کارگاه آموزشی تحلیل-رمز الگوریتم A5/1 را در تاریخ 1387/7/14 در پنجمین کنفرانس رمز ایران (دانشگاه صنعتی مالک اشتر) برگزار نمود. برنامه های ارائه شده در کارگاه آموزشی در قالب سمینار هایی به شرح زیر است:
Tuesday, May 10, 2011
Workshop on Design and Cryptanalysis of eVoting Protocols
Design and Cryptanalysis of e-Voting Protocols Workshop, the 6th
Kahroba Hall, Electrical Engineering Department, Sharif University of Technology, 26 May 2011
Register Now
کارگاه علمی طراحی و تحلیل پروتکل های رای گیری الکترونیکی
سالن کهربای دانشکده مهندسی برق دانشگاه صنعتی شریف، 5 خرداد 1390
Kahroba Hall, Electrical Engineering Department, Sharif University of Technology, 26 May 2011
Register Now
کارگاه علمی طراحی و تحلیل پروتکل های رای گیری الکترونیکی
سالن کهربای دانشکده مهندسی برق دانشگاه صنعتی شریف، 5 خرداد 1390
Workshop on Design and Cryptanalysis of eVoting Protocols
Design and Cryptanalysis of e-Voting Protocols Workshop, the 6th
Kahroba Hall, Electrical Engineering Department, Sharif University of Technology, 26 May 2011
Register Now
کارگاه علمی طراحی و تحلیل پروتکل های رای گیری الکترونیکی
سالن کهربای دانشکده مهندسی برق دانشگاه صنعتی شریف، 5 خرداد 1390
Kahroba Hall, Electrical Engineering Department, Sharif University of Technology, 26 May 2011
Register Now
کارگاه علمی طراحی و تحلیل پروتکل های رای گیری الکترونیکی
سالن کهربای دانشکده مهندسی برق دانشگاه صنعتی شریف، 5 خرداد 1390
Friday, May 6, 2011
Workshop on Cryptography and Information Theoretic Security
Cryptography and Information Theoretic Security Workshop
Department of Electrical Engineering, Sharif University of Technology.
Date & Location
Wednesday, 4th of May, 2011 (Ordibehesht 14, 1390)
Kahroba Hall, EE Dep, Sharif Uni of Tech.
Presentations Schedule
| 8 - 9 | Registration, Welcome and Opening |
| 9 - 9:30 | Mrs. Somayeh Salimi (PhD Student): Secret key sharing from the information theoretic point of view |
| 9:30 - 10 | Ms. Parisa Babaheydarian (MSc Student): A new secret key agreement scheme in a four-terminal networks |
| 10 - 10:30 | Mr. Amir Sonee (MSc Graduate): Cooperation for secrecy in relay networks |
| 10:30 - 11 | Coffee Break |
| 11 - 11:30 | Ms. Maryam Rajabzadeh Assar (PhD Student): Design and Analysis of Electronic Voting Protocols |
| 11:30 - 12 | Mr. Mahdi Alaghband (PhD Student): Key management infrastructures in heterogeneous wireless sensor networks |
| 12 - 12:30 | Ms. Diman ZadTootaghaj (MSc Graduate): Game-theoretic approach to mitigate packet dropping in wireless ad hoc networks |
| 12:30 - 14 | Lunch and Pray |
| 14 - 14:30 | Mr. Mohammad Ehdaie (PhD Student): Key Pre-Distribution Schemes for Wireless Sensor Networks |
| 14:30 - 15 | Ms. Zahra Ahmadian (PhD Student): Distinguishing Attack on Shannon cipher |
| 15 - 15:30 | Mr. Farshid Farhat (PhD Student): Security Improvement of Routing Protocols in Ad hoc Networks |
| 15:30 - 16 | Closing Ceremony |
"Mr. Hadi Soleymani (MSc Graduate): On the security o AES" Will not be presented!
Sponsors
Center of Excellence in Cryptology
Cryptology Chair of Iranian National Science Foundation
Student Branch of Iranian Society of Cryptology
At
Department of Electrical Engineering
Sharif University of Technology
Workshop on Integer Factorization
Workshop on Integer Factorization
شاخه دانشجويي انجمن رمز ايران در دانشگاه صنعتي شريف کارگاه علمی تحت عنوان تجزیه اعداد صحیح (Integer Factorization) را با همکاری اعضای خود در دانشکده ریاضی به سرپرستی آقای بهزاد خزایی در روز 6 خرداد ماه سال جاري در سالن کهرباي دانشکده مهندسي برق دانشگاه صنعتي شريف برگزار کرد. هدف از برگزاري اين کارگاه علمی آموزشي آشناکردن پژوهشگران شاغل در دانشگاه و صنعت با مفاهيم تجزیه اعداد بود که در ادامه موضوعات مورد بحث در کارگاه به تفصيل بيان شده است.
مسابقه تجزیه اعداد
به 3 نفر از برگزیدگانی که عدد 103 رقمی زیر را تجزیه کنند، جوایزی از طرف انجمن رمز ایران اهدا خواهد شد.
248961597133671436654819868443345749095434319307711171205566690 4025046627241207850771410070555734313594220859
لطفا پاسخ های خود را به همراه توضیحی مختصر از نحوه تجزیه، حداکثر تا تاریخ 1388/3/31 به آدرس sharif at isc.org.ir ارسال نمایید.
برنامه زمان بندی کارگاه علمی
9-9:10 تلاوت آیاتی چند از کلام الله مجید
9:10-9:15 پخش سرود ملی جمهوری اسلامی ایران
9:15-9:35 سخنرانی افتتاحیه
9:35-9:45 سخنرانی فرشید فرحت رئیس شاخه دانشجویی (دانشجوی دکتری شریف)
9:45-11 سمینار مساله تجزیه اعداد و گواهی دیجیتال (آقای بهزاد خزایی، کارشناسی ارشد شریف)
11-11:15 زمان تنفس و استراحت
11:15-12 سمینار مبانی ریاضی و روشهای کلاسیک در تجزیه اعداد (خانم نادرخانی، کارشناسی)
12-13:30 وقت نماز و ناهار
13:30-14:30سمینار GNFS (آقای پویان فرزاد، کارشناسی ارشد شریف)
14:30-15:30سمینار SNFS (آقای طالبی زاده، کارشناسی شریف)
15:30-16 طرح ستار (آقای بهزاد خزایی، کارشناسی ارشد شریف)
16-16:20 سخنرانی اختتامیه
همانطور كه مي دانيم بسياري از روش هاي رمزنگاري متداول، خصوصا در سيستم هاي رمز با كليد رمزگذاري عمومي (RSA و ... )، امنيت وابسته به پيچيدگي مساله تجزيه اعداد صحيح به عوامل اول است. براي اين مساله با پيشينه تاريخي بيش از 2500 ساله، الگوريتم هاي مختلفي از جمله CFRAC، SQUFOF، QS، MPQS، SNFS، GNFS، روش هاي كوانتومي، خم هاي بيضوي و .... پيشنهاد شده است. اگر چه بعضي از اين روش ها در حالات خاص كارايي خوبي دارند اما در حالت كلي، مساله تجزيه اعداد صحيح كماكان تنها در زمان نمايي نسبت به عدد، ممكن است. بنابراين حفظ سلامت تبادلات اطلاعات كشور، در گرو توان آن براي تجزيه اعداد چند صد رقمي است؛ كه علاوه بر توسعه امكانات سخت افزاري لازم، نيازمند تحقيقاتي جدي در زمينه الگوريتم هاي تجزيه اعداد است.
بر اين اساس پیشنهاد می شود که برگزاری یک كارگاه يك روزه در تجزيه اعداد در شاخه دانشجویی انجمن رمز ايران در دانشگاه صنعتی شریف، با محتوای زیر لحاظ شود:
1. معرفی کلاس های پیچیدگی محاسبه P، NP و بیان اهمیت مسائل NP-complete در رمزنگاری و جایگاه مساله تجزیه اعداد در این رده بندی. مرور بعضي روش هاي رمزنگاري كه امنيت در آنها بر پيچيدگي تجزيه اعداد به عوامل اول، استوار است. دراین بخش با مروری اجمالی بر سیستم رمز با کلید عمومی به معرفی سیستم RSA و ... به تاریخچه تجزیه اعداد RSA-129 و RSA- 130 و ... خواهیم پرداخت.
2. مباني رياضي از نظريه اعداد شامل قضیه کوچک فرما، قضیه باقیمانده درجه 2 به هنگ عدد اول p، اعداد شبه اول، میدان های متناهی، لگاریتم لگاریتم گسسسته، خم هاي بيضوي و ... كه در تجزيه اعداد مورد كاربرد قرار مي گيرند. بر اساس فصل 1-4 مرجع [1]
3. روش های کلاسیک در تجزيه اعداد از جمله غربال درجه 2 (QS)، خم های بیضوی، M-B، و مقایسه پیچیدگی آنها. بر اساس فصل 4و5 مرجع [1] و مرجع [2]
4. معرفی غربال مبتنی بر میدان اعداد (GNFS و SNFS) و تعیین پیچیدگی محاسبه آنها. بر اساس مرجع [3]
5. معرفي محك هاي جديد چند جمله اي در تعيين اول يا مركب بودن اعداد كه مساله اي به مراتب ساده تر از تجزيه به عوامل اول است. بر اساس مرجع [4]
6. مسائل پیاده سازی الگوریتم های تجزیه در حالت offline و online و استفاده از کامپیوتر های کوانتومی برای تجزیه اعداد
7. بررسی مرز های توانمندی در تجزیه اعداد در سطح جهانی و برنامه های لازم در بالا بردن امکانات کشور در تجزیه اعداد برای تامین سلامت فضای تبادل اطلاعات در کشور
اين كارگاه براي دانشجويان سال هاي آخر كارشناسي و كارشناسي ارشد كه با مفاهيم بنيادين رمزشناسي آشنا هستند، طراحي شده و سعي مي شود مقدمات اساسي بحث در كارگاه يادآوري شود. همچنين فایل ارائه ها و مقالات مهم در زمينه تجزيه اعداد در اختیار شركت كندگان در كارگاه قرار خواهد گرفت.
[1] Koblitz N. , A Course in Number Theory and Cryptography, Springer-Verlag
[2] A. K. Lensra, Integer Factoring, Design, Codes and Cryptography, 19, 101-128 (2000)
[3] A. K. Lenstra, H. W. lenstra, Jr., The development of the Number Field Sieve, Lecture notes in Math., Springer-Verlag (1993)
[4] M. Agrawal, N. Kayal, N. Saxena, Primes is in P, Annals of Mathematics, 160 (2004), 781-793.
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