FPGA IMPLEMENTATION OF HIGH SPEED CRYPTOGHRAPIC PROCESSOR

Project Title

FPGA IMPLEMENTATION OF HIGH SPEED CRYPTOGHRAPIC PROCESSOR

Project Area of Specialization Electrical/Electronic EngineeringProject Summary FPGA Implementation of High Speed Cryptographic Processor      

The advancement and evolution of technology has allowed people to transmit information over great distances. This information is transmitted over different mediums such as internet. Due to the improvement in technology the volume of sensitive and important information being exchanged over the insecure medium has increased dramatically. Due to this fact the need of cryptographic sustem has also increased and looking ahead to the future even more so. Elliptic curve cryptography (ECC) has become widely accepted as an efficient mechanism to secure private data using public-key protocols. The main operation in ECC based crypto systems is scalar point multiplication. But unfortunately scalar point multiplication is computationally expensive. Point multiplication is based on point addition and point doubling. Point multiplication can be achieved by iterative execution of point addition and point doubling groups operations which in turn are based on finite field arithmetic operations such as addition, subtraction, multiplication and division. These finite field arithmetic operations, especially the finite field multiplication and division are the pivotal operation of any ECC based crypto-system. To reduce the computational cost of point multiplication operation, the optimization of these finite field arithmetic operations is very important.

            Developing a high-speed elliptic curve cryptographic (ECC) processor which performs fast point multiplication with low hardware utilization is something that the fields of cryptography and network security demands. This paper presents ECC high-speed cryptographic processor over a prime field, implemented on field-programmable gate array (FPGA), which has low-area and is secure from side-channel attacks (SCAs). Field Programmable gate arrays (FPGA) due to its reconfigurable nature and having less development time, is a very popular choice for hardware implementation of cryptographic algorithms.

Project Objectives

Data security has become a crucial issue in the present world of internet. In recent years the field of wireless communication has really expanded, beyond any one’s imaginations in the past decade. The amount of data that is transferring from one part of the world to another is staggering. The amount of data that is being transferred in the present day was unimaginable in the past. But here we are, the advancement of wireless communication and technology has achieved something that was thought to be impossible. But with such large amount of data transfer on online platforms has raised a question about its security and privacy. To make this data secure, which is shared on various different platforms such as large servers or phones, the demands for efficient and secure cryptographic system has increased. Our aim is to secure these data transmissions over ensecure platforms using eliptic curve cryptography (ECC).

Project Implementation Method

Elliptic curve crypto-systems are based on scalar point multiplication. Point multiplication is further based on point addition and point doubling. These point addition and point doubling are in turn based on multiplication, division, addition and subtraction over finite field. Point multiplication is carried out by combination of point doubling and point multiplication. Finite field operations are at the bottom layer of the hierarchy. Multiplication and division operations over finite field, plays a crucial role in the efficiency of any ECC crypto system. The performance of elliptic curve cryptography based systems depend upon these finite field operations. So optimizing these field operations will significantly enhance the performance of the system. In affine coordinate system the division operation affects the performance of ECC. The reason for that is, in affine coordinate system the division require point addition and point doubling in each iteration. There are ways to avoid this issue. To address those issue some alternate coordinate systems were introduced such as projective coordinates.

“Point multiplication is the multiplication of a scalar with a point on the elliptic curve.” It can be expressed as L=m×Q,

Where, m is the scalar value (integer),

Q is the point on the elliptic curve,

And L is the result of point multiplication.

The result L of the point multiplication will also lie on the elliptic curve. Points ‘Q’ and ‘L’ are public, means everyone can easily access them, but on the other hand ‘m’ which is the scalar value is kept secret hence it will be private. The security level and strength of the ECC systems will depend upon the computational hardness in calculating the value of ‘m’ from given public values. It is the basis of all ECC based cryptographic systems and it is known as Elliptic Curve Discrete Logarithm Problem (ECDLP).

“Point doubling is the addition of a point on elliptic curve with itself”. Point Doubling can be performed in both affine coordinate system and also in projective (Jacobian) coordinate system.

“Point addition is the addition of a point on elliptic curve with another point on the same elliptic curve”. Just like point doubling, point addition can also be performed in both affine coordinate system and in projective (Jacobian) coordinate system.

Point multiplication will be applied on the elliptic curve, it will have a starting point, then a key will be selected which will decide how many times the point is multiplied. It will yield a result which cannot be traced back or alteast be very difficult to find the starting point unless the private key is availiable. So only the one who has the private key can decode the result.

Benefits of the Project

Elliptic Curve Cryptography (ECC) has existed since the mid-1980s, but it is still looked on as the newcomer in the world of SSL, and has only begun to gain adoption in the past few years. ECC is a fundamentally different mathematical approach to encryption than the venerable RSA algorithm. An elliptic curve is an algebraic function (y2 = x3 + ax + b) which looks like a symmetrical curve parallel to the x axis when plotted. As with other forms of public key cryptography, ECC is based on a one-way property in which it is easy to perform a calculation but infeasible to reverse or invert the results of the calculation to find the original numbers.

The foremost benefit of ECC is that it’s simply stronger than RSA for key sizes in use today. The typical ECC key size of 256 bits is equivalent to a 3072-bit RSA key and 10,000 times stronger than a 2048-bit RSA key! To stay ahead of an attacker’s computing power, RSA keys must get longer. The CA/Browser Forum and leading browser vendors officially ended support for 1024-bit RSA keys after 2013, so all new SSL certificates must use keys that are twice as long. Moreover, future RSA key sizes quickly expand while ECC key lengths increase linearly with strength.Another security benefit of ECC is simply that it provides an alternative to RSA and DSA. If a major weakness in RSA is discovered, ECC is likely to be the best alternative, especially if the RSA weakness suddenly requires a sharp increase in key size to compensate.

ECC is also faster for a number of reasons. First off, smaller keys means less data that must be transmitted from the server to the client during an SSL handshake. In addition, ECC requires less processing power (CPU) and memory, resulting in significantly faster response times and throughput on Web servers when it is in use.

A third critical benefit of using ECC is Perfect Forward Secrecy (PFS). While PFS is not a property of ECC, the cipher suites supported by modern Web servers and browsers that implement PFS also implement ECC. Web servers that prefer Ephemeral ECDH (ECDHE) using cipher suites such as “TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA” gain the benefits of both ECC and PFS.

Technical Details of Final Deliverable

The above menthioned methods and their archetecture will be simulated in verilog language using Modelsim 6.3f and for synthesis Xilinx 14.1 design suite is used. Then it will be implemented on FPGA. Our aim is to reduce the critical path delay of point multiplication. This is acheived by using projective coordinates instead of affine coordinates which uses division in every cycle. In our implementation we are using regular algorithms instead of irregular algorithms to perform point multiplication, and the reason for that if that irregular algorithms are venruble to side channel attacks. Our main priority is to make the elliptic curve cryptographic processor fast and secure.

Final Deliverable of the Project Hardware SystemCore Industry SecurityOther Industries IT , Telecommunication Core Technology BlockchainOther Technologies OthersSustainable Development Goals Industry, Innovation and InfrastructureRequired Resources

Item Name	Type	No. of Units	Per Unit Cost (in Rs)	Total (in Rs)
			Total in (Rs)	65000
Nexys 3 Spartan-6 FPGA Trainer Board	Equipment	1	65000	65000