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Pramod Kumar Meher - One of the best experts on this subject based on the ideXlab platform.

  • Low-Complexity Systolic Multiplier for GF(2m) using Toeplitz Matrix-Vector Product Method
    2019 IEEE International Symposium on Circuits and Systems (ISCAS), 2019
    Co-Authors: Pramod Kumar Meher
    Abstract:

    Low-complexity systolic multipliers for GF(2m) are required in several high-performance cryptographic systems. In this paper, we propose a novel design strategy to derive efficient systolic multiplier for GF(2m) based on Toeplitz Matrix-Vector Product (TMVP) approach. The proposed work is carried out through two coherent interdependent stages. (i) A novel multiplication algorithm based on TMVP method to obtain subquadratic space complexity is proposed first. (ii) The proposed algorithm is then mapped unto to a novel and efficient architecture which is optimized further to derive a low-complexity systolic structure. The complexity analysis and comparison show that the proposed design outperforms the existing work. The proposed design can thus be used in many practical cryptosystems.

  • ISCAS - Low-Complexity Systolic Multiplier for GF(2 m ) using Toeplitz Matrix-Vector Product Method
    2019 IEEE International Symposium on Circuits and Systems (ISCAS), 2019
    Co-Authors: Jiafeng Xie, Chiou-yng Lee, Pramod Kumar Meher
    Abstract:

    Low-complexity systolic multipliers for GF(2m) are required in several high-performance cryptographic systems. In this paper, we propose a novel design strategy to derive efficient systolic multiplier for GF(2m) based on Toeplitz Matrix-Vector Product (TMVP) approach. The proposed work is carried out through two coherent interdependent stages. (i) A novel multiplication algorithm based on TMVP method to obtain subquadratic space complexity is proposed first. (ii) The proposed algorithm is then mapped unto to a novel and efficient architecture which is optimized further to derive a low-complexity systolic structure. The complexity analysis and comparison show that the proposed design outperforms the existing work. The proposed design can thus be used in many practical cryptosystems.

  • Low-Complexity Digit-Serial Multiplier Over $GF(2^{m})$ Based on Efficient Toeplitz Block Toeplitz Matrix–Vector Product Decomposition
    IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2017
    Co-Authors: Pramod Kumar Meher, Shyanming Yuan
    Abstract:

    In this paper, we have shown that a regular Toeplitz Matrix-Vector Product (TMVP) can be transformed into a Toeplitz block TMVP (TBTMVP) using a suitable permutation Matrix. Based on the TBTMVP representation, we have proposed a new (a,b)-way TBTMVP decomposition algorithm for implementing a digit-serial multiplication. Moreover, it is shown that, based on iterative block recombination, we can improve the space complexity of the proposed TBTMVP decomposition. From the synthesis results, we have shown that the proposed TBTMVP-based multiplier involves less area, less area-delay Product, and higher throughput compared with the existing digit-serial multipliers.

  • Efficient Subquadratic Space Complexity Architectures for Parallel MPB Single- and Double-Multiplications for All Trinomials Using Toeplitz Matrix-Vector Product Decomposition
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2015
    Co-Authors: Pramod Kumar Meher
    Abstract:

    Subquadratic multiplication algorithm has received significant attention of cryptographic hardware researchers for efficient implementation public-key cryptosystems. In this paper, we derive a new shifted MPB (SMPB) representation based on modified polynomial basis (MPB). We have shown that by using MPB and SMPB, the proposed double basis multiplication can be transformed into Toeplitz Matrix-Vector Product (TMVP) structure. Furthermore, by employing this formulation of double basis multiplication, we show that three-operand multiplication over GF(2m) for all trinomials can be realized efficiently by the recursive TMVP (RTMVP) formulation. To perform the three-operand multiplication with the RTMVP formulation, we have derived a new RTMVP decomposition scheme. The proposed single- and double-multiplications can, respectively, use TMVP and RTMVP decompositions to achieve subquadratic space complexity architectures. By theoretical analysis, it is shown that the proposed subquadratic multipliers involve significantly less space complexity and less computation time compared to the existing subquadratic multipliers using TMVP and Karatsuba algorithms. Moreover, our proposed double-multiplication design can be used in several applications involving successive multiplications, such as exponentiation, inversion, and elliptic curve point multiplication.

  • Speeding up Subquadratic Finite Field Multiplier over GF(2m) Generated by Trinomials Using Toeplitz Matrix-Vector with Inner Product Formula
    2011 Fifth International Conference on Genetic and Evolutionary Computing, 2011
    Co-Authors: Pramod Kumar Meher
    Abstract:

    A new four way split method of bit-level Toeplitz Matrix-Vector Product for computing trinomial-based multiplier over GF(2m) is presented. The proposed scheme is based on two way splitting method to use Toeplitz Matrix-Vector Product using inner Product (TMVPIP) formula. Applying the proposed TMVPIP architecture, it is shown that the computation time of proposed sub quadratic multiplier can be reduced from O(log2m) of the existing sub quadratic multipliers to O(log2log2m). Our proposed sub quadratic multiplier with TMVPIP formula is suitable for efficient implementation of the point multiplication in Koblitz curves.

Changho Seo - One of the best experts on this subject based on the ideXlab platform.

  • efficient multiplier based on hybrid approach for toeplitz Matrix Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Efficient multiplier based on hybrid approach for Toeplitz Matrix–Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

Ku-young Chang - One of the best experts on this subject based on the ideXlab platform.

  • efficient multiplier based on hybrid approach for toeplitz Matrix Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Efficient multiplier based on hybrid approach for Toeplitz Matrix–Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Subquadratic Space Complexity Multiplier Using Even Type GNB Based on Efficient Toeplitz Matrix-Vector Product
    IEEE Transactions on Computers, 2018
    Co-Authors: Sun Mi Park, Ku-young Chang, Dowon Hong
    Abstract:

    Multiplication schemes based on Toeplitz Matrix-Vector Product (TMVP) have been proposed by many researchers. TMVP can be computed using the recursive two-way and three-way split methods, which are composed of four blocks. Among them, we improve the space complexity of the component Matrix formation (CMF) block. This result derives the improvements of multiplication schemes based on TMVP. Also, we present a subquadratic space complexity $GF(2^m)$ multiplier with even type Gaussian normal basis (GNB). In order to design the multiplier, we formulate field multiplication as a sum of two TMVPs and efficiently compute the sum. As a result, for type 2 and 4 GNBs, the proposed multipliers outperform other similar schemes. The proposed type 6 GNB is the first subquadrtic space complexity multiplier with its explicit complexity formula.

  • Comments on “Multiway Splitting Method for Toeplitz Matrix Vector Product”
    IEEE Transactions on Computers, 2016
    Co-Authors: Sun Mi Park, Ku-young Chang, Dowon Hong
    Abstract:

    We propose block decompositions for the Toeplitz Matrix-Vector Product (TMVP) using the k-way splitting method presented in the above paper. As a result, we show that the space complexity for TMVP can be improved.

Dowon Hong - One of the best experts on this subject based on the ideXlab platform.

  • efficient multiplier based on hybrid approach for toeplitz Matrix Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Efficient multiplier based on hybrid approach for Toeplitz Matrix–Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Subquadratic Space Complexity Multiplier Using Even Type GNB Based on Efficient Toeplitz Matrix-Vector Product
    IEEE Transactions on Computers, 2018
    Co-Authors: Sun Mi Park, Ku-young Chang, Dowon Hong
    Abstract:

    Multiplication schemes based on Toeplitz Matrix-Vector Product (TMVP) have been proposed by many researchers. TMVP can be computed using the recursive two-way and three-way split methods, which are composed of four blocks. Among them, we improve the space complexity of the component Matrix formation (CMF) block. This result derives the improvements of multiplication schemes based on TMVP. Also, we present a subquadratic space complexity $GF(2^m)$ multiplier with even type Gaussian normal basis (GNB). In order to design the multiplier, we formulate field multiplication as a sum of two TMVPs and efficiently compute the sum. As a result, for type 2 and 4 GNBs, the proposed multipliers outperform other similar schemes. The proposed type 6 GNB is the first subquadrtic space complexity multiplier with its explicit complexity formula.

  • Comments on “Multiway Splitting Method for Toeplitz Matrix Vector Product”
    IEEE Transactions on Computers, 2016
    Co-Authors: Sun Mi Park, Ku-young Chang, Dowon Hong
    Abstract:

    We propose block decompositions for the Toeplitz Matrix-Vector Product (TMVP) using the k-way splitting method presented in the above paper. As a result, we show that the space complexity for TMVP can be improved.

Sun Mi Park - One of the best experts on this subject based on the ideXlab platform.

  • efficient multiplier based on hybrid approach for toeplitz Matrix Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Efficient multiplier based on hybrid approach for Toeplitz Matrix–Vector Product
    Information Processing Letters, 2018
    Co-Authors: Ku-young Chang, Sun Mi Park, Dowon Hong, Changho Seo
    Abstract:

    Abstract We propose a hybrid approach for a Toeplitz Matrix–Vector Product (TMVP) of size k ⋅ 2 i 3 j , where k ≥ 1 and i , j ≥ 0 . It is possible to make trade-offs between time and space complexities for a TMVP by choosing values k, i, and j properly. We show that the multiplier based on the proposed hybrid TMVP approach has lower space as well as time complexities than other subquadratic space complexity multipliers for five fields recommended by NIST. Moreover, for those five fields, the space complexities of the proposed multiplier are reduced by a minimum 59 % and a maximum 77 % compared with quadratic space complexity multiplier.

  • Subquadratic Space Complexity Multiplier Using Even Type GNB Based on Efficient Toeplitz Matrix-Vector Product
    IEEE Transactions on Computers, 2018
    Co-Authors: Sun Mi Park, Ku-young Chang, Dowon Hong
    Abstract:

    Multiplication schemes based on Toeplitz Matrix-Vector Product (TMVP) have been proposed by many researchers. TMVP can be computed using the recursive two-way and three-way split methods, which are composed of four blocks. Among them, we improve the space complexity of the component Matrix formation (CMF) block. This result derives the improvements of multiplication schemes based on TMVP. Also, we present a subquadratic space complexity $GF(2^m)$ multiplier with even type Gaussian normal basis (GNB). In order to design the multiplier, we formulate field multiplication as a sum of two TMVPs and efficiently compute the sum. As a result, for type 2 and 4 GNBs, the proposed multipliers outperform other similar schemes. The proposed type 6 GNB is the first subquadrtic space complexity multiplier with its explicit complexity formula.

  • Comments on “Multiway Splitting Method for Toeplitz Matrix Vector Product”
    IEEE Transactions on Computers, 2016
    Co-Authors: Sun Mi Park, Ku-young Chang, Dowon Hong
    Abstract:

    We propose block decompositions for the Toeplitz Matrix-Vector Product (TMVP) using the k-way splitting method presented in the above paper. As a result, we show that the space complexity for TMVP can be improved.