1.3     STATEMENT OF THE PROBLEM

           The computer security problem includes lots of buggy and insecure applications.  Attackers can infect your system with malware and steal credentials like credit card details, passwords etc. Example of this is a malware called SilentBanker. It appends itself to your computer and stays silent. Now anytime your computer makes a web request to port 80 or 443 it monitors the request. Though port 443 is encrypted using SSL it doesn’t bother the malware. The malware injects malicious javascript to the target page to change it so whenever you type your password for authentication the password would get sent to the attacker. This malware was used to steal a lot of passwords from UK banks.

 An attacker can steal your IP address and use it to send spam messages. An attacker does this to protect himself and shift the blame to the person whose computer he uses to send the spam messages. There are organizations that provide Denial of Service as a service. That is they can attack a web page or web server for a fee you pay. They do this by bombarding either a web server or web page with a lot of requests than it can process.

Nowadays, we see the spread of war from physical space to the cyber space. An example of this is the Stuxnet virus (2008) which the NSA and Israeli Intelligence agencies used in shutting down Iran’s nuclear power plant. What the attackers did was that they use four zero day windows exploit to infect the computer of the administrator that maintains the nuclear facility. This exploits just sits on your windows computer and only functions if you have the Siemens PCS 7 SCADA control software on your windows computer. It will wait for your to connect the Siemens controller to the network then it will affect the network. This malware in the target computers serves as logic bombs. They used this to attack the nuclear plant thereby shutting down a billion dollar project with just a malware.

           Snowden (2013), an NSA whistleblower released a top secret espionage carried out by US and British Intelligence agencies in which they intercept over 80% of web traffics from sites like Facebook, Google, Twitter etc. and store this information to be used for various activities. This revelations together with the ones from whistleblowing site WikiLeaks made aware of the insecurity of the web which we depend so greatly for our daily activities.

          More recently, we were made aware that some Nigerian governors use the exploits of the malware firm Hacking Team. Hacking Team is a legal malware company that creates exploit used to attack varieties of devices ranging from web servers, computers and anything you can think of. This exposes the fact that in Nigeria today there are people who poses this weaponized- cyber tools that can be used to access virtually almost all devices and steal information, plant information for the purpose of implicating the target.

          Noting this problems we face in this modern era, we turn to cryptography. Cryptography is used to encrypt data so it can only be read by the person who has the secret key. So, even though an attacker breaks into our system he cannot decode our information.

1.4     AIM AND OBJECTIVES OF STUDY

          Despite the use of public key cryptography in simplifying encryption processes, we are still stuck with security bottlenecks. Now we see advanced viruses, worms, Trojans etc. Most applications are not implemented correctly. The goal of this project includes

1. To analyze some versions of RSA implemented in HTTPS.
2.  To show the strengths and weaknesses of RSA. Some common attacks on it.
3. To show how RSA cryptosystem can be used correctly to build intrusion tolerant application that can function correctly even when attacked.
4. To design a version of RSA cryptosystem which is tamper-resistant and can be used for encryption, session setup etc.
5. To develop a software based on this design.

1.5     SIGNIFICANCE OF THE STUDY

          RSA is the most widely used public key cryptosystem. It is used for encryption, session startups, implementing digital signatures and many others. It is implemented in our smart cards, the operating system we use and the browsers we use for surfing the internet etc. However over the years versions of RSA implemented in WEP, HTTP etc has been broken. This project analysis the security of RSA in WEB, HTTP etc and also covers attacks on RSA, and at the end designing and implement a version of RSA that is intrusion tolerant.    

1.6     SCOPE OF THE STUDY

          This project covers ITTC (Boneh et al, 1999), an intrusion tolerant application that uses RSA for encryption. ITTC is a projects that protects the private keys of web servers and certificate authorities by splitting server into smaller share servers so that even if the attacker penetrates a few of the servers he cannot compromise the whole system. Also, I discussed about SITAR (Sargor et al, 2001) a DARPA-funded research project that investigates the intrusion tolerance in distributed system to provide reliable services. I showed some attacks on RSA like the binding attack, common modulus attack etc. and I also analyzed security problems of some versions of RSA like the PKCS1 etc. I also showed how to design and implemented RSA correctly.

1.7     LIMITATIONS OF THE STUDY

The main limitation is that I could not access specialized hardware suitable for RSA. Most specialized RSA implementation are implemented in both hardware and software. Also I did not cover properly its use in environments like smart cards because of limited tools to analysis security in these environments.

1.8     DEFINITION OF TERMS

          This are the meaning of keywords used in the project:

1. ITTC: Intrusion Tolerant via Threshold Cryptography
2. MAFTIA: Malicious and Accidental Fault Tolerance for Internet Applications
3. COTS: Commercial Off the Shelf
4. SITAR: Scalable Intrusion Tolerant Architecture
5. DPASA: Designing Protections and Adaptation into a Survivability    Architecture
6. PKI: Public Key Infrastructure
7. SCIT: Self Cleansing Intrusion Tolerance
8. ACT: Adaptive Cluster Transformation
9. MAC: Message Authentication Code

10. RSA:Rivest Shamir Adleman

11. CA: Certificate Authority

12. MD5: Message Digest 5

13. RFITS: Randomized Failover Intrusion Tolerant System.

This are the definition of some of the terms used in this project.

1. PUBLIC KEY CRYPTOGRAPHY: This is a cryptography in which a pair of keys is used to encrypt and decrypt a message. The public key is used to encrypt the message, while the private key is used to decrypt the cipher-text.
2. CRYPTOSYSTEM: This refers to a suite of cryptographic algorithms needed to implement a particular security service. Typically it consists of three algorithms, one for key generation, one for encryption, and one for decryption.
3. THRESHOLD CYPTOSYSTEM: A cryptosystem is threshold if in order to decrypt an encrypted message, several parties must cooperate in the decryption protocol.
4. CRYPTOGRAPHY: This is the practice and study of techniques for secure communication in the presence of third parties.
5. CRYPTANALYSIS: This is the study of techniques used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown.
6. SYMMETRIC-KEY ALGORITHMS: These are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of cipher-text